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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2018-01-31</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001640313</issuerCik>
        <issuerName>Amplify Snack Brands, INC</issuerName>
        <issuerTradingSymbol>BETR</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001649421</rptOwnerCik>
            <rptOwnerName>Netzky Pamela L.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O AMPLIFY SNACK BRANDS, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>500 WEST 5TH STREET</rptOwnerStreet2>
            <rptOwnerCity>AUSTIN</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>78701</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2018-01-31</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>2313223</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>12.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By P&amp;A Capital LLC</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Disposed of pursuant to the Agreement and Plan of Merger by and among The Hershey Company, Alphabet Merger Sub Inc. and Amplify Snack Brands, Inc. (the &quot;Issuer&quot;) dated as of December 17, 2017, whereby, at the effective time of the merger contemplated therein, all issued and outstanding shares of the Issuer's common stock, par value $0.0001 per share (the &quot;Issuer Common Stock&quot;), including shares of restricted Issuer Common Stock, whether vested or unvested, and all issued and outstanding shares of restricted stock units issued by the Issuer, whether vested or unvested, were automatically cancelled and converted into the right to receive $12.00 per share in cash without interest.</footnote>
        <footnote id="F2">The shares are held directly by P&amp;A Capital LLC in which Ms. Netzky has sole voting and dispositive power.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Bradley C. Weber as Attorney-in-Fact to the Reporting Person</signatureName>
        <signatureDate>2018-01-31</signatureDate>
    </ownerSignature>
</ownershipDocument>
