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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2017-12-29</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001645460</issuerCik>
        <issuerName>Cue Biopharma, Inc.</issuerName>
        <issuerTradingSymbol>CUE</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0000897744</rptOwnerCik>
            <rptOwnerName>MARLETT CHRISTOPHER A</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>2425 CEDAR SPRINGS ROAD</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>DALLAS</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>75201</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Warrants</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>9.375</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2017-12-29</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>416656</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2018-06-12</value>
            </exerciseDate>
            <expirationDate>
                <value>2022-12-14</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>416656</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>416656</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnote</value>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Upon closing of the initial public offering of the Issuer, the Warrants were issued to MDB Capital Group LLC (&quot;MDB&quot;) as partial consideration for
services as underwriter. MDB assigned a portion of the Warrants to certain of its employees effective December 29, 2017.</footnote>
        <footnote id="F2">The Warrants were issued to MDB as partial compensation for its services as underwriter in the Issuer's initial public offering.</footnote>
        <footnote id="F3">The record owner of these securities is MDB. The reporting person is the Chief Executive Officer of MDB. The reporting person disclaims beneficial ownership of these securities except to the extent of his pecuniary interest therein and inclusion of these securities in the report shall not be an admission of beneficial ownership for purposes of section 16 or any other purposes.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Christopher Marlett by Mark Busch, attorney-in-fact</signatureName>
        <signatureDate>2019-01-28</signatureDate>
    </ownerSignature>
</ownershipDocument>
