<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2022-09-15</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001659352</issuerCik>
        <issuerName>Codiak BioSciences, Inc.</issuerName>
        <issuerTradingSymbol>CDAK</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001724575</rptOwnerCik>
            <rptOwnerName>Flagship Ventures Fund V General Partner LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>55 CAMBRIDGE PARKWAY, SUITE 800E</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>CAMBRIDGE</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>02142</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001627639</rptOwnerCik>
            <rptOwnerName>Flagship Ventures Fund V, L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>55 CAMBRIDGE PARKWAY, SUITE 800E</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>CAMBRIDGE</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>02142</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001724939</rptOwnerCik>
            <rptOwnerName>Flagship V VentureLabs Rx Fund, L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>55 CAMBRIDGE PARKWAY, SUITE 800E</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>CAMBRIDGE</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>02142</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001222012</rptOwnerCik>
            <rptOwnerName>AFEYAN NOUBAR</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>55 CAMBRIDGE PARKWAY, SUITE 800E</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>CAMBRIDGE</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>02142</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2022-09-15</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>722590</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1865767</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Flagship Ventures Fund V, L.P.</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2022-09-15</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>210743</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1188920</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Flagship V VentureLabs Rx Fund, L.P.</value>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>485949</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>Flagship VentureLabs V LLC</value>
                    <footnoteId id="F4"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Warrants to purchase Common Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>1.875</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2022-09-15</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>722590</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2022-09-15</value>
            </exerciseDate>
            <expirationDate>
                <value>2027-09-15</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>722590</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>722590</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Flagship Ventures Fund V, L.P.</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Warrants to purchase Common Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>1.875</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2022-09-15</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>210743</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2022-09-15</value>
            </exerciseDate>
            <expirationDate>
                <value>2027-09-15</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>210743</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>210743</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Flagship V VentureLabs Rx Fund, L.P.</value>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">On September 15, 2022, pursuant to an underwritten public offering by the Issuer (the &quot;Offering&quot;), Flagship Ventures Fund V, L.P. (&quot;Flagship Fund V&quot;) acquired 722,590 shares of Common Stock and accompanying warrants to purchase 722,590 shares of Common Stock, and Flagship V VentureLabs Rx Fund, L.P. (&quot;Flagship Fund V Rx&quot;) acquired 210,743 shares of Common Stock and accompanying warrants to purchase 210,743 shares of Common Stock. The combined purchase price in the Offering was $1.50 per share of Common Stock and accompanying warrant.</footnote>
        <footnote id="F2">Shares held by Flagship Fund V. Flagship Ventures Fund V General Partner LLC (&quot;Flagship V GP&quot;) is the general partner of Flagship Fund V. Noubar B. Afeyan, Ph.D. is the sole manager of Flagship V GP. Each of the reporting persons except for Flagship Fund V disclaims beneficial ownership of such shares except to the extent of his or its pecuniary interest therein.</footnote>
        <footnote id="F3">Shares held by Flagship Fund V Rx. Flagship V GP is the general partner of Flagship Fund V Rx. Noubar B. Afeyan, Ph.D. is the sole manager of Flagship V GP. Each of the reporting persons except for Flagship Fund V Rx disclaims beneficial ownership of such shares except to the extent of his or its pecuniary interest therein.</footnote>
        <footnote id="F4">Shares held by Flagship VentureLabs V LLC (&quot;VentureLabs V&quot;). Flagship VentureLabs V Manager LLC (&quot;VentureLabs V Manager&quot;) is the manager of VentureLabs V. Flagship Pioneering, Inc. (&quot;Flagship Pioneering&quot;) is the manager of VentureLabs V Manager. Noubar B. Afeyan, Ph.D. is the CEO and sole stockholder of Flagship Pioneering. Each of the reporting persons except for VentureLabs V disclaims beneficial ownership of such shares except to the extent of his or its pecuniary interest therein.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Flagship Ventures Fund V General Partner LLC, By: /s/ Noubar B. Afeyan, Name: Noubar B. Afeyan, Ph.D., Title: Manager</signatureName>
        <signatureDate>2022-09-16</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Flagship Ventures Fund V, L.P., By: Flagship Ventures Fund V General Partner LLC, its general partner, By: /s/ Noubar B. Afeyan, Name: Noubar B. Afeyan, Ph.D., Title: Manager</signatureName>
        <signatureDate>2022-09-16</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Flagship V VentureLabs Rx Fund, L.P., By: Flagship Ventures Fund V General Partner LLC, its general partner, By: /s/ Noubar B. Afeyan, Name: Noubar B. Afeyan, Ph.D., Title: Manager</signatureName>
        <signatureDate>2022-09-16</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Noubar B. Afeyan, Ph.D., By: /s/ Noubar B. Afeyan, Ph.D.</signatureName>
        <signatureDate>2022-09-16</signatureDate>
    </ownerSignature>
</ownershipDocument>
