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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2015-12-09</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001196579</rptOwnerCik>
            <rptOwnerName>BHUSRI ANEEL</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>2550 SAND HILL ROAD, SUITE 200</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>MENLO PARK</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94025</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2015-12-09</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>206887</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>17.95</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1382012</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Mr. Bhusri does not own shares in his individual capacity. Mr. Bhusri is a senior managing member of Greylock XIV GP LLC, the sole general partner of Greylock XIV Limited Partnership (&quot;Greylock XIV&quot;) and Greylock XIV-A Limited Partnership (&quot;Greylock XIV-A&quot;), and as a result may be deemed to share voting and investment power over the shares held by Greylock XIV and Greylock XIV-A. Mr. Bhusri disclaims beneficial ownership of these securities except to the extent of his pecuniary interest therein and the inclusion of these securities in this report shall not be deemed an admission by Mr. Bhusri of beneficial ownership of the reported securities for purposes of Section 16 or for any other purposes.</footnote>
        <footnote id="F2">These shares consist of (i) 195,998 shares held by Greylock XIV and (ii) 10,889 shares held by Greylock XIV-A.</footnote>
        <footnote id="F3">These shares consist of (i) 1,309,275 shares held by Greylock XIV and (ii) 72,737 shares held by Greylock XIV-A.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ John T. McKenna, attorney-in-fact</signatureName>
        <signatureDate>2015-12-10</signatureDate>
    </ownerSignature>
</ownershipDocument>
