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<!-- Creation Date :2026-05-07T14:53:21.5379+00:00 -->
<!-- Copyright (c) 2026 Donnelley Financial Solutions, Inc. All Rights Reserved. -->
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel2Member_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value Inputs Level 2[Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Weighted Average Exercise Price [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted Average Exercise Price</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_LesseeOperatingLeaseMonthlyRentExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Monthly rent expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash and Cash Equivalents, Fair Value Disclosure</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash equivalents</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_TenantImprovementAllowance_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Tenant improvement allowance.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_TenantImprovementAllowance_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Tenant Improvement Allowance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_TenantImprovementAllowance_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Tenant improvement allowance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Event [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Subsequent Event [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeStockOptionMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Outstanding stock options</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentIncomeInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investment Income, Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentIncomeInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_SegmentGeographicalDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Geographical [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleTerm_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale, Term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleTerm_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Marketable securities, effective maturities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapitalCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Additional Paid in Capital, Common Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapitalCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Additional paid-in capital</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapitalCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Additional Paid in Capital, Common Stock, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapitalCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Additional Paid in Capital, Common Stock, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_BuildingTwoMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Building two.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_BuildingTwoMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Building Two [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_BuildingTwoMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">1250 Page Mill Road in Palo Alto</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_PaymentForSublease_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payment For Sublease</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_PaymentForSublease_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Payment For Sublease</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_PaymentForSublease_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Payment for sublease</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SignificantAccountingPoliciesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Significant Accounting Policies [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SignificantAccountingPoliciesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Significant Accounting Policies</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounts Payable and Accrued Liabilities, Current [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Grants in Period, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Granted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Stock options, granted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_LiabilityRelatedToSaleOfFutureRoyalties_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Liability related to sale of future royalties.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_LiabilityRelatedToSaleOfFutureRoyalties_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liability Related To Sale Of Future Royalties</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_LiabilityRelatedToSaleOfFutureRoyalties_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Liability related to sale of future royalties</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share, Basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Earnings Per Share, Basic, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net loss per share, basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Ending balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Beginning balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_CommitmentsAndContingenciesDisclosureLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Commitments and contingencies disclosure.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_CommitmentsAndContingenciesDisclosureLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Commitments And Contingencies Disclosure [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_CommitmentsAndContingenciesDisclosureLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Commitments And Contingencies Disclosure [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_ScheduleOfAccruedAndOtherCurrentLiabilitiesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Schedule of accrued and other current liabilities.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_ScheduleOfAccruedAndOtherCurrentLiabilitiesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule Of Accrued And Other Current Liabilities Table [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_ScheduleOfAccruedAndOtherCurrentLiabilitiesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Accrued and Other Current Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ImpairmentOfLeasehold_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Impairment of Leasehold</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ImpairmentOfLeasehold_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Non-cash lease impairment expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total current liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Adjustment to Reconcile Net Income to Cash Provided by (Used in) Operating Activity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Adjustments to reconcile net loss to net cash used in operating activities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity, Attributable to Parent [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stockholders&#8217; equity:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntitySmallBusiness_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Small Business</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntitySmallBusiness_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Small Business</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Retained Earnings (Accumulated Deficit)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accumulated deficit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Retained Earnings (Accumulated Deficit), Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Retained Earnings (Accumulated Deficit), Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Retained Earnings (Accumulated Deficit), Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_SalesForecasting_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Sales</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_SalesForecasting_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Sales Forecasting</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_SalesForecasting_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sales Forecasting</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockPricePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sale of Stock, Price Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockPricePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_ManufacturingAgreementTermThatCanBeExtended_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Manufacturing agreement, extended term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_ManufacturingAgreementTermThatCanBeExtended_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Manufacturing agreement term that can be extended.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_ManufacturingAgreementTermThatCanBeExtended_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Manufacturing Agreement Term That Can Be Extended</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_AutomaticRenewalInterval_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Automatic renewal interval.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_AutomaticRenewalInterval_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Automatic Renewal Interval</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_AutomaticRenewalInterval_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Automatic renewal interval</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock-Based Compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Organization, Consolidation and Presentation of Financial Statements [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeaseContractualTermAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lease Contractual Term [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_AmendmentFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Amendment Flag</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_AmendmentFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Amendment Flag</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesAndStockholdersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities and Equity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesAndStockholdersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Liabilities and stockholders&#8217; equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressPostalZipCode_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, Postal Zip Code</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressPostalZipCode_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Address, Postal Zip Code</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net cash used in operating activities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net cash used in operating activities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOperatingLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Operating Lease Liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOperatingLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingCodmProfitLossMeasureHowUsedDescription_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting, CODM, Profit (Loss) Measure, How Used, Description</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingCodmProfitLossMeasureHowUsedDescription_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">CODM Information, Description</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubordinatedBorrowingInterestRate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Subordinated borrowing, interest rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubordinatedBorrowingInterestRate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subordinated Borrowing, Interest Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangements by Share-Based Payment Award, Options, Grants in Period, Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Granted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressAddressLine1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Address, Address Line One</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressAddressLine1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, Address Line One</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MarketableSecuritiesTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Marketable Securities [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MarketableSecuritiesTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Marketable Securities [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueByFairValueHierarchyLevelAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Hierarchy and NAV [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueByFairValueHierarchyLevelAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Significant Observable Inputs (Level 2)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_ConsecutiveTradingDays_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Consecutive Trading Days</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_ConsecutiveTradingDays_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Consecutive Trading Days</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_ConsecutiveTradingDays_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Consecutive Trading days</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_PayrollAndPersonnelExpensesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payroll And Personnel Expenses [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_PayrollAndPersonnelExpensesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Payroll And Personnel Expenses [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_PayrollAndPersonnelExpensesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Payroll And Personnel Expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseRightOfUseAsset_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Right-of-Use Asset</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseRightOfUseAsset_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease right-of-use asset</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ForeignCurrencyFairValueHedgeDerivativeAtFairValueNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Foreign Currency Fair Value Hedge Derivative at Fair Value, Net, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ForeignCurrencyFairValueHedgeDerivativeAtFairValueNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Foreign Currency Fair Value Hedge Derivative at Fair Value, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ForeignCurrencyFairValueHedgeDerivativeAtFairValueNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Recognized fair value of foreign currency of derivative instruments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentType_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Type</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentType_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Document Type</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TypeOfArrangementAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Collaborative Arrangement and Arrangement Other than Collaborative [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ArrangementsAndNonarrangementTransactionsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Collaborative Arrangement and Arrangement Other than Collaborative [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCentralIndexKey_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Entity Central Index Key</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCentralIndexKey_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Central Index Key</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCentralIndexKey_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Central Index Key</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_JohnBorgesonMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">John Borgeson [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_JohnBorgesonMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">John Borgeson [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investments, Debt and Equity Securities [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseExcludingExchangeRateEffect_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Period Increase (Decrease), Excluding Exchange Rate Effect, Including Discontinued Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseExcludingExchangeRateEffect_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net decrease in cash, cash equivalents and restricted cash</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Event Type [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Subsequent Event Type</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Securities Excluded from Computation of Earnings Per Share, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Anti-dilutive securities excluded from the computation of diluted net loss per common share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="country_CH_lbl" xlink:role="http://www.xbrl.org/2003/role/label">SWITZERLAND</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="country_CH_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Switzerland</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Par or Stated Value Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock, par value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amortization of operating lease right-of-use asset</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Right-of-Use Asset, Periodic Reduction</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Weighted Average Remaining Contractual Term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted Average Remaining Contractual Term (in years)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Weighted Average Remaining Contractual Term (in years)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Marketable securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Debt Securities, Available-for-sale, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Exercises in Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Exercised</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Exercise of stock options, shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MarketableSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Marketable Securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MarketableSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Availability of Marketable Securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MarketableSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Marketable Securities, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accrued Liabilities, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued and other current liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total accrued and other current liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Expensed and Capitalized, Amount [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Employee Service Share Based Compensation Allocation Of Recognized Period Costs [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CurrentFiscalYearEndDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Current Fiscal Year End Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CurrentFiscalYearEndDate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current Fiscal Year End Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_CashCollateralizedLetterOfCredit_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Cash-collateralized letter of credit.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_CashCollateralizedLetterOfCredit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Collateralized Letter Of Credit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_CashCollateralizedLetterOfCredit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash-collateralized letter of credit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentQuarterlyReport_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Quarterly Report</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentQuarterlyReport_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Quarterly Report</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="stpr_CA_lbl" xlink:role="http://www.xbrl.org/2003/role/label">CALIFORNIA</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="stpr_CA_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">California</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressStateOrProvince_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, State or Province</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressStateOrProvince_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Address, State or Province</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Unvested, beginning balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Nonvested, Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Unvested, ending balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_TarcocimabProgramExpensesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Tarcocimab Program Expenses [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_TarcocimabProgramExpensesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Tarcocimab program expenses [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_TarcocimabProgramExpensesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Tarcocimab Program Expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Shares Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred Stock, shares outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Preferred Stock, Shares Outstanding, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Preferred Stock, Shares Outstanding, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockCapitalSharesReservedForFutureIssuance_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Capital Shares Reserved for Future Issuance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockCapitalSharesReservedForFutureIssuance_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Reserved for future award grants</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_StatementGeographicalAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Geographical [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_NumberOfOptionsToExtendLeaseTerm_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Number of options to extend lease term.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_NumberOfOptionsToExtendLeaseTerm_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Number Of Options To Extend Lease Term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_NumberOfOptionsToExtendLeaseTerm_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of options to extend lease term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Value, Stock Options Exercised</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Exercise of stock options</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableAccruedLiabilitiesAndOtherLiabilitiesDisclosureCurrentTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounts Payable, Accrued Liabilities, and Other Liabilities Disclosure, Current [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableAccruedLiabilitiesAndOtherLiabilitiesDisclosureCurrentTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued and Other Current Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PerformanceSharesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Performance Shares [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_DebtSecuritiesAvailableForSaleUnrealizedLossesNonCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Unrealized Losses, Non Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_DebtSecuritiesAvailableForSaleUnrealizedLossesNonCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities Available For Sale Unrealized Losses, Non Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_DebtSecuritiesAvailableForSaleUnrealizedLossesNonCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Debt Securities Available For Sale Unrealized Losses, Non Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Event [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Subsequent Event</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfAdditionalSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Number of Additional Shares Authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfAdditionalSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of common stock available for issuance increased</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAssetsNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Assets, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAssetsNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAssetsNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Other Assets, Noncurrent, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtSecuritiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtSecuritiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value, current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtSecuritiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Debt Securities, Available-for-sale, Current, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Securities [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Antidilutive Securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amortized Cost, Non Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale, Amortized Cost, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Award Vesting Rights, Percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Percentage of vested of award under performance based award</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfCompensationCostForShareBasedPaymentArrangementsAllocationOfShareBasedCompensationCostsByPlanTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Cost by Plan [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfCompensationCostForShareBasedPaymentArrangementsAllocationOfShareBasedCompensationCostsByPlanTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of stock-based compensation is classified in the consolidated statements of operations and comprehensive loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">AOCI Attributable to Parent [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accumulated Other Comprehensive Income (Loss)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finite-Lived Intangible Assets, Major Class Name [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Finite-Lived Intangible Assets, Major Class Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseOptionToExtend_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Option to Extend</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseOptionToExtend_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Lessee operating lease option to extend</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_DepositsOnPropertyAndEquipment_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Deposits on property and equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_DepositsOnPropertyAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deposits On Property And Equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_DepositsOnPropertyAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Deposits on property and equipment.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Value, Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Preferred Stock, Value, Issued, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Preferred Stock, Value, Issued, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Preferred Stock, Value, Issued, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Preferred stock, $0.0001 par value, 10,000,000 shares authorized: 0 shares issued and outstanding at March 31, 2024 and December 31, 2023, respectively</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred stock, $0.0001 par value - 10,000,000 shares authorized; none issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MinimumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Minimum [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MinimumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Minimum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Grants in Period, Weighted Average Grant Date Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Granted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancialInstrumentAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financial Instrument [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets, Current [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current assets:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnForeignCurrencyFairValueHedgeDerivatives_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Gain (Loss) on Foreign Currency Fair Value Hedge Derivatives</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnForeignCurrencyFairValueHedgeDerivatives_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Change in fair value recognized in other income (expense)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel3Member_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Inputs, Level 3 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel3Member_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value Inputs Level3 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Fair Value Hierarchy for Assets and Liabilities Measured at Fair Value on Recurring Basis</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Fair Value, Assets and Liabilities Measured on Recurring Basis [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueAssetsMeasuredOnRecurringBasisTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Assets Measured on Recurring Basis [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueAssetsMeasuredOnRecurringBasisTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Fair Value Hierarchy for Assets Measured at Fair Value on Recurring Basis</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities, Current [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current liabilities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_KSI-501ProgramExpensesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">KSI-501 Program Expenses [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_KSI-501ProgramExpensesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">KSI-501 Program Expenses [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_KSI-501ProgramExpensesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">KSI-501 Program Expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Shares, Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Ending balance, shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Beginning balance, shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubleaseIncome_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sublease Income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubleaseIncome_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Sublease Income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommitmentsAndContingencies_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Commitments and Contingencies</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommitmentsAndContingencies_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Commitments and contingencies (Note 5)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_CommitmentsAndContingenciesDisclosureTable_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Commitments and contingencies disclosure.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_CommitmentsAndContingenciesDisclosureTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Commitments And Contingencies Disclosure [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_CommitmentsAndContingenciesDisclosureTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Commitments And Contingencies Disclosure [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Nonvested, Weighted Average Grant Date Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Unvested, ending balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Unvested, beginning balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GeneralAndAdministrativeExpenseMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">General and Administrative Expense [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GeneralAndAdministrativeExpenseMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">General and Administrative</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Lease liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Operating Lease, Liability, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardEquityInstrumentsOtherThanOptionsAggregateIntrinsicValueAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Aggregate Intrinsic Value [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardEquityInstrumentsOtherThanOptionsAggregateIntrinsicValueAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Aggregate Intrinsic Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnDerivativeInstrumentsNetPretax_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Gain (Loss) on Derivative Instruments, Net, Pretax, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnDerivativeInstrumentsNetPretax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Gain (Loss) on Derivative Instruments, Net, Pretax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnDerivativeInstrumentsNetPretax_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Settlement of derivative contracts</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnDerivativeInstrumentsNetPretax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Settlement of derivative contracts</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeaseContractualTermDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lease Contractual Term [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Weighted Average Number of Shares Outstanding, Basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Weighted Average Number of Shares Outstanding, Basic, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted-average shares outstanding used, basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_AccruedResearchAndDevelopmentCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued manufacturing and research &amp; development costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_AccruedResearchAndDevelopmentCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Accrued research and development current.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_AccruedResearchAndDevelopmentCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accrued Research And Development Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_RiskAndUncertaintiesPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Risk and uncertainties.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_RiskAndUncertaintiesPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Risk And Uncertainties Policy [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_RiskAndUncertaintiesPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Risk and Uncertainties</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Share-Based Compensation Arrangements by Share-Based Payment Award [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule Of Share Based Compensation Arrangements By Share Based Payment Award [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Lived Tangible Asset [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Events [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Subsequent Events</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Cash_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Cash_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">APIC, Share-Based Payment Arrangement, Increase for Cost Recognition</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock-based compensation expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">APIC, Share-based Payment Arrangement, Increase for Cost Recognition, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_LesseeOperatingLeaseRentAbatement_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Lessee operating lease rent abatement.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_LesseeOperatingLeaseRentAbatement_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee Operating Lease Rent Abatement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_LesseeOperatingLeaseRentAbatement_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total rent abatement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity, Attributable to Parent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total stockholders&#8217; equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Par or Stated Value Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred stock, par value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementOfStockholdersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Stockholders' Equity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CorporateNoteSecuritiesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Corporate Note Securities [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CorporateNoteSecuritiesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Corporate Notes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_EquityIncentivePlan_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity Incentive Plan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_EquityIncentivePlan_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Equity Incentive Plan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_EquityIncentivePlan_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_EquityIncentivePlan_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Equity incentive plans</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_ManufacturingAgreementCapitalContributionsFixedAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Manufacturing agreement capital contributions fixed assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_ManufacturingAgreementCapitalContributionsFixedAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Manufacturing Agreement Capital Contributions Fixed Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_ManufacturingAgreementCapitalContributionsFixedAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Manufacturing agreement capital contributions fixed assets.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UseOfEstimates_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Use of Estimates, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UseOfEstimates_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Use of Estimates</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseImpairmentLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Non-cash lease impairment expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseImpairmentLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Impairment Loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueDisclosuresTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Disclosures [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueDisclosuresTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value Measurements</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisclosureOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disclosure of Share-Based Compensation Arrangements by Share-Based Payment Award [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisclosureOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of stock-based compensation expense by award type</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_LTProgramImplementationPlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">LT Program Implementation Plan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_LTProgramImplementationPlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">LT Program Implementation Plan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingRollForward_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of Options</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingRollForward_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding [Roll Forward]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative Instruments and Hedging Activities Disclosure [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_TermOfOfferingPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Term of offering period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_TermOfOfferingPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Term of offering period.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_TermOfOfferingPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Term Of Offering Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PlanNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Plan Name [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PlanNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Plan Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOtherOperatingAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Other Operating Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOtherOperatingAssets_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Other assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOtherOperatingAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Increase (Decrease) in Other Operating Assets, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_OfficeAndLaboratorySpaceMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Office and laboratory space.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_OfficeAndLaboratorySpaceMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Office And Laboratory Space [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_OfficeAndLaboratorySpaceMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Rottenstrasse 5 in Visp</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value Assets And Liabilities Measured On Recurring And Nonrecurring Basis [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_PerformanceBasedStockOptionsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Performance-based stock options.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_PerformanceBasedStockOptionsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Performance Based Stock Options [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_PerformanceBasedStockOptionsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Performance-based Stock Options</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant and Equipment, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Property and Equipment, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressCityOrTown_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, City or Town</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressCityOrTown_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Address, City or Town</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_BuildingOneMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Building one.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_BuildingOneMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Building One [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_BuildingOneMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">1200 Page Mill Road in Palo Alto</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_SecurityExchangeName_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Security Exchange Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_SecurityExchangeName_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Security Exchange Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_TwoThousandEighteenEmployeeSharePurchasePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Two thousand eighteen employee share purchase plan.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_TwoThousandEighteenEmployeeSharePurchasePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Two Thousand Eighteen Employee Share Purchase Plan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_TwoThousandEighteenEmployeeSharePurchasePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2018 Employee Share Purchase Plan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_AccruedLegalFeesAndProfessionalFees_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued legal fees and professional fees</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_AccruedLegalFeesAndProfessionalFees_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accrued legal fees and professional fees</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_AccruedLegalFeesAndProfessionalFees_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Accrued legal fees and professional fees</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_CounterpartyNameAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Counterparty Name [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_CounterpartyNameAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Counterparty Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Securities, Name [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Antidilutive Securities, Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_NumberOfLeasedBuildings_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Number of leased buildings.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_NumberOfLeasedBuildings_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Number Of Leased Buildings</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_NumberOfLeasedBuildings_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of buildings leased</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfEmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Expensed and Capitalized, Amount [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfEmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule Of Employee Service Share Based Compensation Allocation Of Recognized Period Costs [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RangeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statistical Measurement [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RangeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Statistical Measurement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total current assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AllocatedShareBasedCompensationExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AllocatedShareBasedCompensationExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock-based compensation expense recognized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AllocatedShareBasedCompensationExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Total stock-based compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NoncashOrPartNoncashAcquisitionFixedAssetsAcquired1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Noncash or Part Noncash Acquisition, Fixed Assets Acquired</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NoncashOrPartNoncashAcquisitionFixedAssetsAcquired1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Purchase of property and equipment under accounts payable and accruals</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentPeriodEndDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Period End Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentPeriodEndDate_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Document Period End Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementsFairValueHierarchyDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Hierarchy and NAV [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementsFairValueHierarchyDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value Hierarchy and NAV</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementOfFinancialPositionAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Financial Position [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestrictedStockUnitsRSUMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Restricted Stock Units (RSUs) [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_PerformanceBasedEquityAwardsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Performance based equity awards.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_PerformanceBasedEquityAwardsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Performance Based Equity Awards [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_PerformanceBasedEquityAwardsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Performance Based Equity Awards</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_ScheduleOfCommonStockAvailableForIssuanceUnderTheEquityIncentivePlans_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule Of Common Stock Available For Issuance Under The Equity Incentive Plans</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_ScheduleOfCommonStockAvailableForIssuanceUnderTheEquityIncentivePlans_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule Of Common Stock Available For Issuance Under The Equity Incentive Plans</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_ScheduleOfCommonStockAvailableForIssuanceUnderTheEquityIncentivePlans_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Schedule Of Common Stock Available For Issuance Under The Equity Incentive Plans</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Security, Excluded EPS Calculation [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule Of Antidilutive Securities Excluded From Computation Of Earnings Per Share [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Continuing Operation [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Reconciliation of cash, cash equivalents and restricted cash to consolidated balance sheets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale, Realized Gain (Loss)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Realized gains or losses recognized on sale or maturity of available-for-sale debt securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Debt Securities, Available-for-sale, Realized Gain (Loss), Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Liabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Liabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financial Instruments [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherThanTemporaryImpairmentLossDebtSecuritiesAvailableForSale_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other-than-temporary Impairment Loss, Debt Securities, Available-for-Sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherThanTemporaryImpairmentLossDebtSecuritiesAvailableForSale_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Impairment charges or recoveries related to marketable securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherThanTemporaryImpairmentLossDebtSecuritiesAvailableForSale_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Other-than-temporary Impairment Loss, Debt Securities, Available-for-sale, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_ManufacturingAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Manufacturing agreement.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_ManufacturingAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Manufacturing Agreement [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_ManufacturingAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Manufacturing Agreement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestrictedStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Unvested restricted shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestrictedStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Restricted Stock [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestrictedStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Restricted Shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Weighted Average Number of Shares Outstanding, Diluted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Weighted Average Number of Shares Outstanding, Diluted, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted-average shares outstanding used, diluted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityFileNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Securities Act File Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityFileNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Entity File Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_NonCashLeaseImpairmentExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Non Cash Lease Impairment Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_NonCashLeaseImpairmentExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Non Cash Lease Impairment Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_NonCashLeaseImpairmentExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Non Cash Lease Impairment Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CoverAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cover [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsPerformancePeriodExpiration_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Share based compensation arrangement by share based payment award options performance period expiration.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsPerformancePeriodExpiration_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share Based Compensation Arrangement By Share Based Payment Award Options Performance Period Expiration</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsPerformancePeriodExpiration_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Performance expiration date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidExpenseAndOtherAssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Prepaid Expense and Other Assets, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidExpenseAndOtherAssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Prepaid expenses and other current assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Forfeited in Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Canceled</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_LongTermDeposit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long Term Deposit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_LongTermDeposit_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Long Term Deposit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_LongTermDeposit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Long-term deposit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_USTreasurySecuritiesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">US Treasury Securities [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_USTreasurySecuritiesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">U.S. Treasury Securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Issuance of common stock pursuant to employee stock purchase plans</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Number of Shares Authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NumberOfOperatingSegments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Number of Operating Segments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NumberOfOperatingSegments_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of operating segments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Segment Information</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GeneralAndAdministrativeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">General and Administrative Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GeneralAndAdministrativeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">General and administrative</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GeneralAndAdministrativeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">General and Administrative Expense, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_OperatingLeaseRightOfUseAssetObtainedInExchangeForOperatingLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Operating lease right-of-use asset obtained in exchange for operating lease liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_OperatingLeaseRightOfUseAssetObtainedInExchangeForOperatingLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating lease right-of-use asset obtained in exchange for operating lease liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_OperatingLeaseRightOfUseAssetObtainedInExchangeForOperatingLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease right-of-use asset obtained in exchange for operating lease liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_OperatingLeaseRightOfUseAssetObtainedInExchangeForOperatingLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Operating lease right-of-use asset obtained in exchange for operating lease liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_AnnualRentYearOverYearIncreasePercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Annual rent year over year increase percentage.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_AnnualRentYearOverYearIncreasePercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Annual Rent Year Over Year Increase Percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_AnnualRentYearOverYearIncreasePercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Annual rent year-over-year increase percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedNumberOfShares_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock options, vested</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedNumberOfShares_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Vested, Number of Shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresAndExpirationsInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Forfeitures and Expirations in Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresAndExpirationsInPeriod_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Forfeited or canceled</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresAndExpirationsInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Share-based Compensation Arrangement by Share-based Payment Award, Options, Forfeitures and Expirations in Period, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Event [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Subsequent Event [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_VariableSubleaseIncome_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Variable Sublease Income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_VariableSubleaseIncome_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Variable Sublease Income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_VariableSubleaseIncome_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Variable sublease income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsAdditionalDisclosuresAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Additional Disclosures [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsAdditionalDisclosuresAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted Average Remaining Contractual Term (in years)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">New Accounting Pronouncements, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Recent Accounting Pronouncements</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Antidilutive Securities Excluded From Computation Of Earnings Per Share [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfSharebasedCompensationRestrictedStockAndRestrictedStockUnitsActivityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Restricted Stock and Restricted Stock Unit, Activity [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfSharebasedCompensationRestrictedStockAndRestrictedStockUnitsActivityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Restricted Shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnDispositionOfAssets1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Gain (Loss) on Disposition of Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnDispositionOfAssets1_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Gain (Loss) on Disposition of Assets, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnDispositionOfAssets1_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Loss on disposal of long-lived assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_TwoThousandEighteenEquityIncentivePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Two thousand eighteen equity incentive plan.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_TwoThousandEighteenEquityIncentivePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Two Thousand Eighteen Equity Incentive Plan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_TwoThousandEighteenEquityIncentivePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2018 Equity Incentive Plan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Depreciation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Depreciation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Depreciation_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Depreciation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Depreciation_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Depreciation, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseTermOfContract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Term of Contract</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseTermOfContract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Lessee, operating lease, term of contract</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Shares, Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock, shares outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Common Stock, Shares, Outstanding, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Common Stock, Shares, Outstanding, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Liability, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentTransitionReport_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Transition Report</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentTransitionReport_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Transition Report</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total operating expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResearchAndDevelopmentExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Research and Development Expense, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResearchAndDevelopmentExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Research and Development Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResearchAndDevelopmentExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Research and development</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Amortized Cost, current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amortized Cost, current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale, Amortized Cost, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementOfCashFlowsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Cash Flows [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted Average Grant Date Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Nonvested, Weighted Average Grant Date Fair Value [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Option, Activity [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Stock Options Activity under 2018 Plan and 2015 Equity Incentive Plan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Summary of stock options and performance-based stock options under 2021 LTPIP, 2018 Plan and 2015 Plan.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_TwoThousandEighteenAndTwoThousandFifteenEquityIncentivePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Two thousand eighteen and two thousand fifteen equity incentive plan.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_TwoThousandEighteenAndTwoThousandFifteenEquityIncentivePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Two Thousand Eighteen And Two Thousand Fifteen Equity Incentive Plan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_TwoThousandEighteenAndTwoThousandFifteenEquityIncentivePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2018 Plan and 2015 Equity Incentive Plan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net Loss per Common Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Net loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net loss and comprehensive loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Net loss</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Aggregate Intrinsic Value Beginning balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Intrinsic Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Aggregate Intrinsic Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseCost_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseCost_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Increase (Decrease) in Prepaid Expense and Other Assets, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Prepaid Expense and Other Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Prepaid expenses and other current assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentFiscalYearFocus_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Fiscal Year Focus</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentFiscalYearFocus_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Fiscal Year Focus</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash flows from investing activities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounts Payable, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accounts payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Accounts Payable, Current, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResearchAndDevelopmentExpenseMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Research and Development Expense [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResearchAndDevelopmentExpenseMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Research and Development</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investments in Debt and Marketable Equity Securities (and Certain Trading Assets) Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Marketable Securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_SahreBasedCompensationArrangementByShareBasedPaymentAwardAwardsOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sahre Based Compensation Arrangement By Share Based Payment Award Awards Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_SahreBasedCompensationArrangementByShareBasedPaymentAwardAwardsOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Sahre Based Compensation Arrangement By Share Based Payment Award Awards Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_SahreBasedCompensationArrangementByShareBasedPaymentAwardAwardsOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Outstanding stock awards</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_FacilitiesAndOtherResearchAndDevelopmentExpensesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Facilities And Other Research And Development Expenses [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_FacilitiesAndOtherResearchAndDevelopmentExpensesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Facilities And Other Research And Development Expenses [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_FacilitiesAndOtherResearchAndDevelopmentExpensesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Facilities And Other Research And Development Expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_PerformanceBasedRestrictedStockUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Performance Based Restricted Stock Units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_PerformanceBasedRestrictedStockUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Performance Based Restricted Stock Units [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_PerformanceBasedRestrictedStockUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Performance Based Restricted Stock Units [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromStockOptionsExercised_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from Stock Options Exercised</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromStockOptionsExercised_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Proceeds from stock options exercises</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromStockOptionsExercised_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Proceeds from stock option exercises</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueDisclosuresAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Disclosures [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommitmentsAndContingenciesDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Commitments and Contingencies Disclosure [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_ABCPlatformAndOtherProgramExpensesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">ABC Platform And Other Program Expenses [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_ABCPlatformAndOtherProgramExpensesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">ABC Platform And Other Program Expenses [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_ABCPlatformAndOtherProgramExpensesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">ABC Platform And Other Program Expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_PaymentOfPublicOfferingCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payment of Public Offering Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_PaymentOfPublicOfferingCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Payment of Public Offering Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_PaymentOfPublicOfferingCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Payment of public offering costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_PaymentOfPublicOfferingCosts_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Payment of public offering costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets, Fair Value Disclosure</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total cash equivalents</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net cash used in investing activities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_Security12bTitle_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Title of 12(b) Security</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_Security12bTitle_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Title of 12(b) Security</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Segment Reporting Information, by Segment [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Derivatives</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Forfeitures, Weighted Average Grant Date Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Canceled</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MoneyMarketFundsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Money Market Funds [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MoneyMarketFundsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Money Market Funds</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale, Allowance for Credit Loss</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Debt Securities, Available-for-sale, Allowance for Credit Loss, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Adjustment to Reconcile Net Income to Cash Provided by (Used in) Operating Activity, Increase (Decrease) in Operating Capital [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Changes in assets and liabilities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Beginning balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Ending balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Recurring and Nonrecurring [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value Assets And Liabilities Measured On Recurring And Nonrecurring Basis [Table]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Accrued Liabilities and Other Operating Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued and other current liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementFrequencyDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Measurement Frequency [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementFrequencyDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Measurement Frequency</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_ClinicalAndCommercialSupplyMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Clinical and commercial supply.</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_ClinicalAndCommercialSupplyMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Clinical and Commercial Supply of Drug Substance</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_TradingSymbol_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Trading Symbol</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_TradingSymbol_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Trading Symbol</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_ManufacturingAgreementInitialTerm_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Manufacturing agreement, initial term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_ManufacturingAgreementInitialTerm_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Manufacturing agreement initial term.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_ManufacturingAgreementInitialTerm_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Manufacturing Agreement Initial Term</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash flows from financing activities</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_LonzaMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Lonza.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_LonzaMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lonza [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_LonzaMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Lonza</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementEquityComponentsAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Equity Components</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementEquityComponentsAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity Components [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EquityComponentDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity Component [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EquityComponentDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Equity Component</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueByAssetClassAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Asset Class</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueByAssetClassAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Asset Class [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeaseholdImprovementsGross_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Leasehold improvements and machinery and equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeaseholdImprovementsGross_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Leasehold Improvements, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_CommonStockSharesReservedForFutureGrantsAward_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock Shares Reserved For Future Grants Award</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_CommonStockSharesReservedForFutureGrantsAward_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Common Stock Shares Reserved For Future Grants Award</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_CommonStockSharesReservedForFutureGrantsAward_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Reserved for future award grants</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_ScheduleOfExpenseSegmentReportingInformationTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule Of Expense Segment Reporting Information Table Text Block</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_ScheduleOfExpenseSegmentReportingInformationTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Schedule Of Expense Segment Reporting Information Table Text Block</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_ScheduleOfExpenseSegmentReportingInformationTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule Of research and development expenses have been disaggregated</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_CommonStockShareReservedForFutureIssuanceESPP_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock ShareReserved For Future Issuance ESPP</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_CommonStockShareReservedForFutureIssuanceESPP_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Common Stock ShareReserved For Future Issuance ESPP</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_CommonStockShareReservedForFutureIssuanceESPP_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Reserved for future ESPP</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardNetOfForfeitures_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Stock Issued During Period, Shares, Restricted Stock Award, Net of Forfeitures, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardNetOfForfeitures_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Shares, Restricted Stock Award, Net of Forfeitures</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardNetOfForfeitures_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Restricted stock units vested, shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesEmployeeStockPurchasePlans_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Issuance of common stock pursuant to employee stock purchase plan, shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesEmployeeStockPurchasePlans_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Shares, Employee Stock Purchase Plans</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesEmployeeStockPurchasePlans_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Proceeds from ESPP , Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MaximumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Maximum [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MaximumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Maximum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MaximumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Maximum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_ShareBasedCompensationArrangementByShareBasedPaymentAwardVestingPeriodForAchievementOfSpecificMilestone_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Share based compensation arrangement by share based payment award vesting period for achievement of specific milestone.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_ShareBasedCompensationArrangementByShareBasedPaymentAwardVestingPeriodForAchievementOfSpecificMilestone_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share Based Compensation Arrangement By Share Based Payment Award Vesting Period For Achievement Of Specific Milestone</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_ShareBasedCompensationArrangementByShareBasedPaymentAwardVestingPeriodForAchievementOfSpecificMilestone_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Vesting period for achievement of specific milestone</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RangeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statistical Measurement [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RangeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Statistical Measurement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangements by Share-Based Payment Award, Options, Exercises in Period, Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Exercised</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Value, Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Common Stock, Value, Issued, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Common Stock, Value, Issued, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Common Stock, Value, Issued, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Common stock, $0.0001 par value, 490,000,000 shares authorized at March 31, 2024 and December 31, 2023; XX and 52,333,850 shares issued and outstanding at March 31, 2024 and December 31, 2023, respectively</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock, $0.0001 par value - 490,000,000 shares authorized; 62,155,685 and 61,758,454 shares issued and outstanding, respectively</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_KSI-101ProgramExpensesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">KSI-101 Program Expenses [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_KSI-101ProgramExpensesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">KSI-101 Program Expenses [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_KSI-101ProgramExpensesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">KSI-101 Program Expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_Long-TermDeposit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-term deposit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_Long-TermDeposit_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Long-term deposit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_Long-TermDeposit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Long-term deposit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ImpairmentOrDisposalOfLongLivedAssetsPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Impairment of Long-Lived Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ImpairmentOrDisposalOfLongLivedAssetsPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Impairment or Disposal of Long-Lived Assets, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MarketableSecuritiesLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Marketable Securities [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MarketableSecuritiesLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Marketable Securities [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_TheCompanyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">The entire disclosure for the company.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_TheCompanyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">The Company [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_TheCompanyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">The Company</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Shares Authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred stock, shares authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finite-Lived Intangible Assets by Major Class [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Finite-Lived Intangible Assets by Major Class</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Employee Stock [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityRegistrantName_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Registrant Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityRegistrantName_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Registrant Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherNonoperatingIncomeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Nonoperating Income (Expense)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherNonoperatingIncomeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Other Nonoperating Income (Expense), Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherNonoperatingIncomeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other income (expense), net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Events [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleDebtSecuritiesGrossUnrealizedLoss_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Unrealized Losses, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleDebtSecuritiesGrossUnrealizedLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale, Unrealized Loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueByMeasurementFrequencyAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Measurement Frequency [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueByMeasurementFrequencyAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Measurement Frequency</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share Based Compensation Arrangement By Share Based Payment Award [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Common Stock, Shares Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Entity Common Stock, Shares Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_TwoThousandTwentyOneLongTermPerformanceIncentivePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Two Thousand Twenty One Long-Term Performance Incentive Plan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_TwoThousandTwentyOneLongTermPerformanceIncentivePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Two Thousand Twenty One Long-Term Performance Incentive Plan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_TwoThousandTwentyOneLongTermPerformanceIncentivePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2021 LTPIP</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments to Acquire Property, Plant, and Equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Purchase of property and equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Payments to Acquire Property, Plant, and Equipment, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_SummaryOfSignificantAccountingPoliciesPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Summary of Significant Accounting Policies [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_SummaryOfSignificantAccountingPoliciesPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Summary of Significant Accounting Policies [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_SummaryOfSignificantAccountingPoliciesPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Significant Accounting Policies</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Grants in Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Granted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Assets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Assets_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeStatementAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Statement [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Vested</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Vested in Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Awards vested</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareDiluted_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share, Diluted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareDiluted_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Earnings Per Share, Diluted, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareDiluted_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net loss per share, diluted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_LesseeOperatingLeaseInitialTermOfContract_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Lessee operating lease initial term of contract.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_LesseeOperatingLeaseInitialTermOfContract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee Operating Lease Initial Term Of Contract</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="kod_LesseeOperatingLeaseInitialTermOfContract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Initial lease term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CityAreaCode_lbl" xlink:role="http://www.xbrl.org/2003/role/label">City Area Code</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CityAreaCode_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">City Area Code</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeaseAgreementsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Lease Agreement</link:label>
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          <link:loc xlink:type="locator" xlink:href="kod-20260331.xsd#kod_AccruedLegalFeesAndProfessionalFees" xlink:label="kod_AccruedLegalFeesAndProfessionalFees"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EmployeeRelatedLiabilitiesCurrent" xlink:label="us-gaap_EmployeeRelatedLiabilitiesCurrent"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherAccruedLiabilitiesCurrent" xlink:label="us-gaap_OtherAccruedLiabilitiesCurrent"/>
        </link:calculationLink>
        <link:calculationLink xlink:type="extended" xlink:role="http://kodiak.com/20260331/taxonomy/role/Role_DisclosureFairValueMeasurementsSummaryOfFairValueHierarchyForAssetsMeasuredAtFairValueOnRecurringBasisDetails">
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="us-gaap_AssetsFairValueDisclosure" xlink:to="us-gaap_CashAndCashEquivalentsFairValueDisclosure" order="0" weight="1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="us-gaap_AssetsFairValueDisclosure" xlink:to="us-gaap_AvailableForSaleSecuritiesDebtSecurities" order="1" weight="1" use="optional"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsFairValueDisclosure" xlink:label="us-gaap_AssetsFairValueDisclosure"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashAndCashEquivalentsFairValueDisclosure" xlink:label="us-gaap_CashAndCashEquivalentsFairValueDisclosure"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtSecurities" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtSecurities"/>
        </link:calculationLink>
      </link:linkbase>
    </xsd:appinfo>
  </xsd:annotation>
  <xsd:element id="kod_ManufacturingAgreementInitialTerm" name="ManufacturingAgreementInitialTerm" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="kod_ManufacturingAgreementTermThatCanBeExtended" name="ManufacturingAgreementTermThatCanBeExtended" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="kod_LesseeOperatingLeaseInitialTermOfContract" name="LesseeOperatingLeaseInitialTermOfContract" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="kod_PaymentForSublease" name="PaymentForSublease" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="kod_ManufacturingAgreementMember" name="ManufacturingAgreementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="kod_ShareBasedCompensationArrangementByShareBasedPaymentAwardVestingPeriodForAchievementOfSpecificMilestone" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardVestingPeriodForAchievementOfSpecificMilestone" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="kod_KSI-101ProgramExpensesMember" name="KSI-101ProgramExpensesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="kod_SummaryOfSignificantAccountingPoliciesPolicyTextBlock" name="SummaryOfSignificantAccountingPoliciesPolicyTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="kod_BuildingTwoMember" name="BuildingTwoMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="kod_JohnBorgesonMember" name="JohnBorgesonMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="kod_LeaseAgreementOnJuneTwoThousandAndTwentyMember" name="LeaseAgreementOnJuneTwoThousandAndTwentyMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="kod_EmployeeStockPurchasePlanMember" name="EmployeeStockPurchasePlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="kod_AccruedLegalFeesAndProfessionalFees" name="AccruedLegalFeesAndProfessionalFees" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="kod_AccruedResearchAndDevelopmentCurrent" name="AccruedResearchAndDevelopmentCurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="kod_NumberOfOptionsToExtendLeaseTerm" name="NumberOfOptionsToExtendLeaseTerm" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="kod_OfficeAndLaboratorySpaceMember" name="OfficeAndLaboratorySpaceMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="kod_SettlementOfDerivativeContracts" name="SettlementOfDerivativeContracts" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="kod_PerformanceBasedStockOptionsMember" name="PerformanceBasedStockOptionsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="kod_RiskAndUncertaintiesPolicyTextBlock" name="RiskAndUncertaintiesPolicyTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="kod_SahreBasedCompensationArrangementByShareBasedPaymentAwardAwardsOutstanding" name="SahreBasedCompensationArrangementByShareBasedPaymentAwardAwardsOutstanding" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="kod_TwoThousandEighteenAndTwoThousandFifteenEquityIncentivePlanAndTwoThousandTwentyOneLongPerformanceIncentivePlanMember" name="TwoThousandEighteenAndTwoThousandFifteenEquityIncentivePlanAndTwoThousandTwentyOneLongPerformanceIncentivePlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="kod_AvailableForSaleDebtSecuritiesNonCurrent" name="AvailableForSaleDebtSecuritiesNonCurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="kod_CommonStockSharesReservedForFutureGrantsAward" name="CommonStockSharesReservedForFutureGrantsAward" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="kod_NonCashLeaseImpairmentExpense" name="NonCashLeaseImpairmentExpense" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="kod_AnnualRentYearOverYearIncreasePercentage" name="AnnualRentYearOverYearIncreasePercentage" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="kod_VariableSubleaseIncome" name="VariableSubleaseIncome" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="kod_LeaseAgreementOnAprilTwoThousandAndTwentyMember" name="LeaseAgreementOnAprilTwoThousandAndTwentyMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="kod_TwoThousandEighteenEquityIncentivePlanMember" name="TwoThousandEighteenEquityIncentivePlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="kod_ClinicalAndCommercialSupplyMember" name="ClinicalAndCommercialSupplyMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="kod_ABCPlatformAndOtherProgramExpensesMember" name="ABCPlatformAndOtherProgramExpensesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="kod_DepositsOnPropertyAndEquipment" name="DepositsOnPropertyAndEquipment" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="kod_AccruedClinicalTrialAndRelatedCostsCurrent" name="AccruedClinicalTrialAndRelatedCostsCurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="kod_TwoThousandEighteenAndTwoThousandFifteenEquityIncentivePlanMember" name="TwoThousandEighteenAndTwoThousandFifteenEquityIncentivePlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="kod_DebtSecuritiesAvailableForSaleUnrealizedGainsNonCurrent" name="DebtSecuritiesAvailableForSaleUnrealizedGainsNonCurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="kod_ScheduleOfExpenseSegmentReportingInformationTableTextBlock" name="ScheduleOfExpenseSegmentReportingInformationTableTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="kod_LTProgramImplementationPlanMember" name="LTProgramImplementationPlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="kod_LiabilityRelatedToSaleOfFutureRoyalties" name="LiabilityRelatedToSaleOfFutureRoyalties" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="kod_TarcocimabProgramExpensesMember" name="TarcocimabProgramExpensesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="kod_PerformanceBasedRestrictedStockUnitsMember" name="PerformanceBasedRestrictedStockUnitsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="kod_TwoThousandTwentyOneLongTermPerformanceIncentivePlanMember" name="TwoThousandTwentyOneLongTermPerformanceIncentivePlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="kod_LesseeOperatingLeaseRentAbatement" name="LesseeOperatingLeaseRentAbatement" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="kod_PerformanceBasedEquityAwardsMember" name="PerformanceBasedEquityAwardsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="kod_TwoThousandEighteenEmployeeSharePurchasePlanMember" name="TwoThousandEighteenEmployeeSharePurchasePlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="kod_CommitmentsAndContingenciesDisclosureLineItems" name="CommitmentsAndContingenciesDisclosureLineItems" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="kod_CommonStockShareReservedForFutureIssuanceESPP" name="CommonStockShareReservedForFutureIssuanceESPP" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="kod_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsPerformancePeriodExpiration" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsPerformancePeriodExpiration" type="xbrli:dateItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="kod_ConsecutiveTradingDays" name="ConsecutiveTradingDays" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="kod_AutomaticRenewalInterval" name="AutomaticRenewalInterval" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="kod_LongTermPerformanceIncentivePlanDescription" name="LongTermPerformanceIncentivePlanDescription" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="kod_TenantImprovementAllowance" name="TenantImprovementAllowance" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="kod_CommitmentsAndContingenciesDisclosureTable" name="CommitmentsAndContingenciesDisclosureTable" type="xbrli:stringItemType" substitutionGroup="xbrldt:hypercubeItem" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="kod_BuildingOneMember" name="BuildingOneMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="kod_BasisOfPresentationAndPrinciplesOfConsolidationPolicyTextBlock" name="BasisOfPresentationAndPrinciplesOfConsolidationPolicyTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="kod_NonCashLeaseImpairmentExpenses" name="NonCashLeaseImpairmentExpenses" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="kod_PayrollAndPersonnelExpensesMember" name="PayrollAndPersonnelExpensesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="kod_LesseeOperatingLeaseMonthlyRentExpense" name="LesseeOperatingLeaseMonthlyRentExpense" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="kod_OperatingLeaseRightOfUseAssetObtainedInExchangeForOperatingLeaseLiability" name="OperatingLeaseRightOfUseAssetObtainedInExchangeForOperatingLeaseLiability" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="kod_KSI-501ProgramExpensesMember" name="KSI-501ProgramExpensesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="kod_ManufacturingAgreementCapitalContributionsFixedAssets" name="ManufacturingAgreementCapitalContributionsFixedAssets" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="kod_PaymentOfPublicOfferingCosts" name="PaymentOfPublicOfferingCosts" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="kod_NumberOfLeasedBuildings" name="NumberOfLeasedBuildings" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="kod_EquityIncentivePlan" name="EquityIncentivePlan" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="kod_DebtSecuritiesAvailableForSaleUnrealizedLossesNonCurrent" name="DebtSecuritiesAvailableForSaleUnrealizedLossesNonCurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="kod_Long-TermDeposit" name="Long-TermDeposit" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="kod_ScheduleOfAccruedAndOtherCurrentLiabilitiesTableTextBlock" name="ScheduleOfAccruedAndOtherCurrentLiabilitiesTableTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="kod_CashCollateralizedLetterOfCredit" name="CashCollateralizedLetterOfCredit" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="kod_LongTermDeposit" name="LongTermDeposit" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="kod_ScheduleOfCommonStockAvailableForIssuanceUnderTheEquityIncentivePlans" name="ScheduleOfCommonStockAvailableForIssuanceUnderTheEquityIncentivePlans" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="kod_ManufacturingAgreementExpense" name="ManufacturingAgreementExpense" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="kod_TermOfOfferingPeriod" name="TermOfOfferingPeriod" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="kod_TheCompanyTextBlock" name="TheCompanyTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="kod_FacilitiesAndOtherResearchAndDevelopmentExpensesMember" name="FacilitiesAndOtherResearchAndDevelopmentExpensesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="kod_NumberOfPurchasePeriods" name="NumberOfPurchasePeriods" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="kod_LonzaMember" name="LonzaMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="kod_NewTaxLawsPolicyTextBlock" name="NewTaxLawsPolicyTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="kod_SalesForecasting" name="SalesForecasting" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
</xsd:schema>
