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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2016-10-12</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>2016-10-12</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>10500</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>15.6006</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2529723</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By P&amp;A Capital LLC</value>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">This transaction was effected pursuant to a Rule 10b5-1 trading plan adopted by the Reporting Person.</footnote>
        <footnote id="F2">This transaction was executed in multiple trades at prices ranging from $15.44 to $15.73. The price reported above reflects the weighted average price. The Reporting Person hereby undertakes to provide upon request to the SEC staff, the Issuer or a security holder of the Issuer full information regarding the number of shares and prices at which the transaction was effected.</footnote>
        <footnote id="F3">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/ Brian Goldberg as Attorney-in-Fact to the Reporting Person</signatureName>
        <signatureDate>2016-10-14</signatureDate>
    </ownerSignature>
</ownershipDocument>
