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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2018-12-04</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>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>125799</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2018-12-04</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
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                <transactionFormType>4</transactionFormType>
                <transactionCode>C</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>3806083</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
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                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>3913649</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Trust</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2018-12-04</value>
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            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
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                </transactionShares>
                <transactionPricePerShare>
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                </transactionPricePerShare>
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                </transactionAcquiredDisposedCode>
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            <postTransactionAmounts>
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                <natureOfOwnership>
                    <value>By Trust</value>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

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            <transactionTimeliness>
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            <transactionAmounts>
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                <transactionPricePerShare>
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            <expirationDate>
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            <underlyingSecurity>
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                </underlyingSecurityTitle>
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                </underlyingSecurityShares>
            </underlyingSecurity>
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                </sharesOwnedFollowingTransaction>
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            <ownershipNature>
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                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Trust</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
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        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
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            <transactionTimeliness>
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            <transactionAmounts>
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                <transactionPricePerShare>
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            <expirationDate>
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                </underlyingSecurityTitle>
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                <sharesOwnedFollowingTransaction>
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                </sharesOwnedFollowingTransaction>
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            <ownershipNature>
                <directOrIndirectOwnership>
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                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Trust</value>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Stock Option (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>2.98</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2018-12-04</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
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                <footnoteId id="F4"/>
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            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>600000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F5"/>
            </exerciseDate>
            <expirationDate>
                <value>2024-03-27</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class B Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>600000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
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            <ownershipNature>
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                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
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            </securityTitle>
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            </conversionOrExercisePrice>
            <transactionDate>
                <value>2018-12-04</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
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                <footnoteId id="F4"/>
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            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
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                </transactionShares>
                <transactionPricePerShare>
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                <transactionAcquiredDisposedCode>
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            <expirationDate>
                <value>2024-03-27</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
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                </underlyingSecurityTitle>
                <underlyingSecurityShares>
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                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
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                </sharesOwnedFollowingTransaction>
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        <derivativeTransaction>
            <securityTitle>
                <value>Stock Option (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>17.00</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2018-12-04</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
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                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F4"/>
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            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
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                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
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            <exerciseDate>
                <footnoteId id="F6"/>
            </exerciseDate>
            <expirationDate>
                <value>2025-09-22</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class B Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>83333</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
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                </sharesOwnedFollowingTransaction>
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                <directOrIndirectOwnership>
                    <value>D</value>
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        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Stock Option (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>17.00</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2018-12-04</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
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                <footnoteId id="F4"/>
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            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
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                <transactionPricePerShare>
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                <transactionAcquiredDisposedCode>
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                </underlyingSecurityTitle>
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        <derivativeTransaction>
            <securityTitle>
                <value>Stock Option (right to buy)</value>
            </securityTitle>
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            <transactionDate>
                <value>2018-12-04</value>
            </transactionDate>
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                <transactionCode>J</transactionCode>
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                <footnoteId id="F4"/>
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            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>125000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
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            <exerciseDate>
                <footnoteId id="F7"/>
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            <expirationDate>
                <value>2025-09-22</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class B Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>125000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
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                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
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            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Stock Option (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>17.00</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2018-12-04</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
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                <footnoteId id="F4"/>
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            <transactionTimeliness>
                <value></value>
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            <transactionAmounts>
                <transactionShares>
                    <value>125000</value>
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                <transactionPricePerShare>
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                <transactionAcquiredDisposedCode>
                    <value>A</value>
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                <footnoteId id="F7"/>
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            <expirationDate>
                <value>2025-09-22</value>
            </expirationDate>
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                <underlyingSecurityTitle>
                    <value>Class A Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>125000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
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                <sharesOwnedFollowingTransaction>
                    <value>125000</value>
                </sharesOwnedFollowingTransaction>
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        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">On December 4, 2018, the Issuer's outstanding shares of Class B Common Stock ceased to represent at least 10% of all outstanding shares of Class A Common Stock and Class B Common Stock.  As a result, each share of the Issuer's Class B Common Stock automatically converted into one share of Class A Common Stock pursuant to the Issuer's amended and restated certificate of incorporation.</footnote>
        <footnote id="F2">Shares are held by Scott Dietzen and Katherine Dietzen, Co-Trustees of the Dietzen Living Trust, dated January 16, 2009.</footnote>
        <footnote id="F3">Shares are held by JP Morgan Trust Company of Delaware, as Trustee of the Dietzen Family Irrevocable Trust GST Exempt Trust under agreement dated March 25, 2014.</footnote>
        <footnote id="F4">In connection with the automatic conversion described in footnote (1), outstanding Class B Common Stock options that were issued under the Issuer's 2009 Equity Incentive Plan remain unchanged, except that the underlying shares are now Class A Common Stock.</footnote>
        <footnote id="F5">The option vests in twenty-four (24) equal monthly installments beginning one month from April 1, 2018. The option shall be subject to accelerated vesting as set forth in optionee's employment agreement with the Issuer.</footnote>
        <footnote id="F6">The option vests in twelve (12) equal monthly installments beginning one month from January 1, 2020. The option shall be subject to accelerated vesting in accordance with the terms of the Issuer's change in control severance benefit plan.</footnote>
        <footnote id="F7">The option vests in twelve (12) equal monthly installments beginning one month from January 1, 2021. The option shall be subject to accelerated vesting in accordance with the terms of the Issuer's change in control severance benefit plan.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Joseph T. FitzGerald, attorney-in-fact</signatureName>
        <signatureDate>2018-12-07</signatureDate>
    </ownerSignature>
</ownershipDocument>
