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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4/A</documentType>

    <periodOfReport>2017-03-03</periodOfReport>

    <dateOfOriginalSubmission>2017-03-06</dateOfOriginalSubmission>

    <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>C/O PURE STORAGE, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>650 CASTRO ST, SUITE 400</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>2017-03-03</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>52400</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>9.4612</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>52400</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Trust</value>
                    <footnoteId id="F4"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2941</value>
                    <footnoteId id="F3"/>
                    <footnoteId id="F5"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">See remarks below.</footnote>
        <footnote id="F2">The reported price in Column 4 is a weighted average price. These shares were purchased in multiple transactions at prices ranging from $9.34 to $9.64 per share, inclusive. The Reporting Person undertakes to provide to the Issuer, any security holder of the Issuer, or the staff of the Securities and Exchange Commission, upon request, full information regarding the number of shares purchased at each separate price within the range set forth in this footnote.</footnote>
        <footnote id="F3">This amount reflects the correction with respect to the Amount of Securities Beneficially Owned (Directly and Indirectly) Following the Reported Transaction(s) described in the Form 4 filed by the Reporting Person on March 6, 2017.</footnote>
        <footnote id="F4">Shares are held by Scott Dietzen and Katherine Dietzen, Co-Trustees of the Dietzen Living Trust, dated January 16, 2009.</footnote>
        <footnote id="F5">Includes 2,941 shares of Class A Common Stock that were acquired by the Reporting Person on March 15, 2016 pursuant to the Issuer's Employee Stock Purchase Plan.</footnote>
    </footnotes>

    <remarks>This report on Form 4/A amends and replaces in its entirety the Form 4 filed by the Reporting Person on March 6, 2017. This report on Form 4/A (i) corrects an error with respect to the Transaction Code and Ownership Form, (ii) adjusts the Amount of Securities Beneficially Owned Following the Reported Transaction(s), and (iii) also adjusts the Amount of Securities Beneficially Owned Following the Reported Transaction(s) reflected in the filings made between March 6, 2017 and the date of this filing.</remarks>

    <ownerSignature>
        <signatureName>/s/ Joseph T. FitzGerald, attorney-in-fact</signatureName>
        <signatureDate>2020-12-23</signatureDate>
    </ownerSignature>
</ownershipDocument>
