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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2018-02-27</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001474432</issuerCik>
        <issuerName>Pure Storage, Inc.</issuerName>
        <issuerTradingSymbol>PSTG</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001651908</rptOwnerCik>
            <rptOwnerName>Dietzen Scott</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>650 CASTRO ST</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>MOUNTAIN VIEW</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94041</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2018-02-27</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>20001</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>129197</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2018-02-27</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>20001</value>
                    <footnoteId id="F2"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>149198</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2018-02-27</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>20001</value>
                    <footnoteId id="F3"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>169199</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">The shares of Class A Common Stock are to be acquired upon the vesting of a Performance-Based Restricted Stock Unit (&quot;PRSU&quot;) award granted to the Reporting Person. The Issuer's Compensation Committee (the &quot;Committee&quot;) authorized the issuance of the underlying Class A Common Stock based upon the Company's achievement against a financial target set by the Committee on March 30, 2017. The performance period for the award was February 1, 2017 to January 31, 2018, with vesting subject to a determination of performance achievement by the Committee, which was approved on February 27, 2018. As a result, this PRSU award shall vest in full on April 5, 2018, subject to Reporting Person's Continuous Service (as defined in the Issuer's 2015 Equity Incentive Plan) through such date.</footnote>
        <footnote id="F2">The shares of Class A Common Stock are to be acquired upon the vesting of a PRSU award granted to the Reporting Person. The Committee authorized the issuance of the underlying Class A Common Stock based upon the Company's achievement level against a financial target set by the Committee on March 30, 2017. The performance period for the award was February 1, 2017 to January 31, 2018, with vesting subject to a determination of performance achievement by the Committee, which was approved on February 27, 2018. As a result, 1/4th of this PRSU award shall vest on each of July 5, 2018, October 5, 2018, January 5, 2019 and April 5, 2019, subject to the Reporting Person's Continuous Service (as defined in the Issuer's 2015 Equity Incentive Plan) through such dates.</footnote>
        <footnote id="F3">The shares of Class A Common Stock are to be acquired upon the vesting of a PRSU award granted to the Reporting Person. The Committee authorized the issuance of the underlying Class A Common Stock based upon the Company's achievement level against a financial target set by the Committee on March 30, 2017. The performance period for the award was February 1, 2017 to January 31, 2018, with vesting subject to a determination of performance achievement by the Committee, which was approved on February 27, 2018. As a result, 1/4th of this PRSU award shall vest on each of July 5, 2019, October 5, 2019, January 5, 2020 and April 5, 2020, subject to the Reporting Person's Continuous Service (as defined in the Issuer's 2015 Equity Incentive Plan) through such dates.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Joseph T. FitzGerald, attorney-in-fact</signatureName>
        <signatureDate>2018-03-01</signatureDate>
    </ownerSignature>
</ownershipDocument>
