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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2022-02-21</periodOfReport>

    <noSecuritiesOwned>1</noSecuritiesOwned>

    <issuer>
        <issuerCik>0001661460</issuerCik>
        <issuerName>Poseida Therapeutics, Inc.</issuerName>
        <issuerTradingSymbol>PSTX</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001910914</rptOwnerCik>
            <rptOwnerName>Warner Brent</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O POSEIDA THERAPEUTICS, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>9390 TOWNE CENTRE DRIVE, SUITE 200</rptOwnerStreet2>
            <rptOwnerCity>SAN DIEGO</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>92121</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>President, Gene Therapy</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <footnotes></footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Harry J. Leonhardt, Attorney-in-Fact</signatureName>
        <signatureDate>2022-03-01</signatureDate>
    </ownerSignature>
</ownershipDocument>
