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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2018-07-19</periodOfReport>

    <notSubjectToSection16>1</notSubjectToSection16>

    <issuer>
        <issuerCik>0001588216</issuerCik>
        <issuerName>RSP Permian, Inc.</issuerName>
        <issuerTradingSymbol>RSPP</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001607482</rptOwnerCik>
            <rptOwnerName>Datla Uma L.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>3141 HOOD STREET, SUITE 500</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>DALLAS</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>75219</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chief Accounting Officer</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2018-07-19</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1957</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>17614</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2018-07-19</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>17614</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F3"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">On July 19, 2018, pursuant to the Agreement and Plan of Merger dated as of March 27, 2018 (the &quot;Merger Agreement&quot;), by and among Concho Resources Inc. (&quot;Concho&quot;), Green Merger Sub Inc. (&quot;Merger Sub&quot;) and RSP Permian, Inc. (&quot;RSP&quot;), Merger Sub merged with and into RSP (the &quot;Merger&quot;), with RSP surviving the Merger as a wholly-owned subsidiary of Concho. Immediately prior to the effective time of the Merger (the &quot;Effective Time&quot;), the outstanding awards of performance-based restricted stock of RSP vested based on RSP's performance through the Effective Time, as determined by the RSP board of directors, and each vested share of performance-based restricted stock was converted into the right to receive 0.320 of a share of Concho common stock.</footnote>
        <footnote id="F2">(Continued from Footnote 1) On July 18, 2018 (the day prior to the Merger), the closing price of one share of Concho common stock was $149.66. Withholding for the payment of tax liabilities in connection with the vesting of restricted stock awards was effectuated following the conversion into shares of Concho common stock.</footnote>
        <footnote id="F3">Pursuant to the Merger Agreement, each share of RSP common stock issued and outstanding immediately prior to the Effective Time (including each outstanding share of time-based restricted stock of RSP that vested in full and was treated as a share of RSP common stock for purposes of the Merger Agreement) was converted into the right to receive 0.320 of a share of Concho common stock. On July 18, 2018 (the day prior to the Merger), the closing price of one share of Concho common stock was $149.66.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/James E. Mutrie, attorney-in-fact for Uma L. Datla</signatureName>
        <signatureDate>2018-07-20</signatureDate>
    </ownerSignature>
</ownershipDocument>
