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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2022-04-11</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001563880</issuerCik>
        <issuerName>Trevi Therapeutics, Inc.</issuerName>
        <issuerTradingSymbol>TRVI</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001277631</rptOwnerCik>
            <rptOwnerName>BASKETT FOREST</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1954 GREENSPRING DRIVE</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 600</rptOwnerStreet2>
            <rptOwnerCity>TIMONIUM</rptOwnerCity>
            <rptOwnerState>MD</rptOwnerState>
            <rptOwnerZipCode>21093</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>2022-04-11</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>2631578</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>1.90</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>10421428</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Note 2</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Acquired from the Issuer on April 11, 2022 pursuant to a Securities Purchase Agreement dated April 6, 2022.</footnote>
        <footnote id="F2">The Reporting Person is a manager of NEA 16 GP, LLC, which is the sole general partner of NEA Partners 16, L.P. (&quot;NEA Partners 16&quot;). NEA
Partners 16 is the sole general partner of New Enterprise Associates 16, L.P. (&quot;NEA 16&quot;), which is the direct beneficial owner of the securities.
The Reporting Person disclaims beneficial ownership within the meaning of Section 16 of the Securities Exchange Act of 1934, as amended, or
otherwise of such portion of the NEA 16 securities in which the Reporting Person has no pecuniary interest.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/Louis Citron, attorney-in-fact</signatureName>
        <signatureDate>2022-04-13</signatureDate>
    </ownerSignature>
</ownershipDocument>
