<?xml version="1.0" encoding="us-ascii"?>
<!-- DFIN ActiveDisclosure(SM) XBRL Schema Document - http://www.dfinsolutions.com/ -->
<!-- Creation Date      : 2021-05-10T19:30:38.9398178+00:00 -->
<!-- Version            : 5.0.1.615 -->
<!-- Package ID         : c67883420a28434288e39cdad078ddd5 -->
<!-- Copyright (c) 2021 Donnelley Financial Solutions, Inc. All Rights Reserved. -->
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  <xsd:element id="kod_AmortizationOfIssuanceCosts" name="AmortizationOfIssuanceCosts" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit" />
  <xsd:element id="kod_IncreaseDecreaseInOperatingLeaseLiability" name="IncreaseDecreaseInOperatingLeaseLiability" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit" />
  <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_ProceedsFromSaleOfFutureRoyaltiesNetOfIssuanceCosts" name="ProceedsFromSaleOfFutureRoyaltiesNetOfIssuanceCosts" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit" />
  <xsd:element id="kod_PrincipalPaymentsOfTenantImprovementAllowancePayable" name="PrincipalPaymentsOfTenantImprovementAllowancePayable" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="kod_TheCompanyTextBlock" name="TheCompanyTextBlock" type="nonnum:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="kod_RiskAndUncertaintiesPolicyTextBlock" name="RiskAndUncertaintiesPolicyTextBlock" type="nonnum:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="kod_ScheduleOfAccruedAndOtherCurrentLiabilitiesTableTextBlock" name="ScheduleOfAccruedAndOtherCurrentLiabilitiesTableTextBlock" type="nonnum:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <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_AccruedResearchAndDevelopmentCurrent" name="AccruedResearchAndDevelopmentCurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="kod_AccruedLegalFeesCurrent" name="AccruedLegalFeesCurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="kod_AvailableForSaleDebtSecuritiesAmortizedCostBasisCurrent" name="AvailableForSaleDebtSecuritiesAmortizedCostBasisCurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit" />
  <xsd:element id="kod_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTaxCurrent" name="AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTaxCurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="kod_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTaxCurrent" name="AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTaxCurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit" />
  <xsd:element id="kod_EstimatedCapitalContributions" name="EstimatedCapitalContributions" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit" />
  <xsd:element id="kod_ContractualObligationDueInSecondYearAndAfter" name="ContractualObligationDueInSecondYearAndAfter" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit" />
  <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_CommitmentsAndContingenciesDisclosureLineItems" name="CommitmentsAndContingenciesDisclosureLineItems" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="kod_CommitmentsAndContingenciesDisclosureTable" name="CommitmentsAndContingenciesDisclosureTable" type="xbrli:stringItemType" substitutionGroup="xbrldt:hypercubeItem" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="kod_ClinicalAndCommercialSupplyMember" name="ClinicalAndCommercialSupplyMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="kod_ManufacturingAgreementMember" name="ManufacturingAgreementMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="kod_LonzaMember" name="LonzaMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="kod_TwoThousandEighteenEquityIncentivePlanMember" name="TwoThousandEighteenEquityIncentivePlanMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="kod_PerformanceBasedStockOptionsMember" name="PerformanceBasedStockOptionsMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="kod_PerformanceBasedEquityAwardsMember" name="PerformanceBasedEquityAwardsMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="kod_TwoThousandEighteenEmployeeSharePurchasePlanMember" name="TwoThousandEighteenEmployeeSharePurchasePlanMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="kod_TwoThousandEighteenAndTwoThousandFifteenEquityIncentivePlanMember" name="TwoThousandEighteenAndTwoThousandFifteenEquityIncentivePlanMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="kod_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsWeightedAverageRemainingContractualTermAbstract" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsWeightedAverageRemainingContractualTermAbstract" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="kod_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsAggregateIntrinsicValueAbstract" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsAggregateIntrinsicValueAbstract" type="xbrli:stringItemType" 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_TermOfOfferingPeriod" name="TermOfOfferingPeriod" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="kod_NumberOfPurchasePeriods" name="NumberOfPurchasePeriods" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="kod_MaximumCapitalContributions" name="MaximumCapitalContributions" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit" />
  <xsd:element id="kod_AnnualSuiteFeesPaymentForNextFiscalYear" name="AnnualSuiteFeesPaymentForNextFiscalYear" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="kod_AnnualSuiteFeesPaymentForEachYearAfterNextFiscalYear" name="AnnualSuiteFeesPaymentForEachYearAfterNextFiscalYear" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="kod_ClinicalAndCommercialDevelopmentAndManufacturingMember" name="ClinicalAndCommercialDevelopmentAndManufacturingMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
</xsd:schema>
