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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2013-05-20</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001558785</issuerCik>
        <issuerName>CVR Refining, LP</issuerName>
        <issuerTradingSymbol>CVRR</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0000921669</rptOwnerCik>
            <rptOwnerName>ICAHN CARL C</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O ICAHN ASSOCIATES HOLDING LLC</rptOwnerStreet1>
            <rptOwnerStreet2>767 FIFTH AVE., SUITE 4700</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10153</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Units</value>
            </securityTitle>
            <transactionDate>
                <value>2013-05-20</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>12000000</value>
                    <footnoteId id="F5"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>29.8275</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>112000000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>please see footnotes</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Units</value>
            </securityTitle>
            <transactionDate>
                <value>2013-05-20</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>2000000</value>
                    <footnoteId id="F6"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>30.75</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>112000000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>please see footnotes</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Call Option (obligaiton to sell)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>29.8275</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2013-05-20</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>1800000</value>
                    <footnoteId id="F7"/>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F7"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F7"/>
            </exerciseDate>
            <expirationDate>
                <value>2013-06-13</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Units</value>
                </underlyingSecurityTitle>
                <underlyingSecurityValue>
                    <value>1800000</value>
                </underlyingSecurityValue>
            </underlyingSecurity>
            <postTransactionAmounts>
                <valueOwnedFollowingTransaction>
                    <value>1800000</value>
                </valueOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>please see footnotes</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">CVR Refining Holdings, LLC, a Delaware limited liability company (&quot;Holdings&quot;), is (i) the direct beneficial owner of 105,988,000 common units representing limited partner interests of the Issuer (the &quot;Common Units&quot;) and (ii) the indirect beneficial owner of 12,000 Common Units owned of record by its wholly subsidiary, CVR Refining Holdings Sub, LLC (&quot;Holdings Sub&quot;).</footnote>
        <footnote id="F2">Holdings is the sole member of CVR Refining GP, LLC, a Delaware limited liability company which serves as the general partner of the Issuer (the &quot;General Partner&quot;). CVR Energy, Inc., a Delaware corporation (&quot;CVR&quot;), through subsidiaries is the beneficial owner of Holdings. Icahn Enterprises L.P., a Delaware limited partnership (&quot;IEP&quot;), through subsidiaries is the beneficial owner of (i) 6,000,000 Common Units (including the 2,000,000 Common Units purchased as described in footnote (6) below) and (ii) approximately 82% of the outstanding shares of common stock of CVR. Carl C. Icahn through subsidiaries is the beneficial owner of (i) the general partner of IEP and (ii) approximately 90.5% of the outstanding depositary units representing limited partnership interests in IEP.</footnote>
        <footnote id="F3">Each of the General Partner, CVR and IEP (by virtue of their relationship to Holdings and Holdings Sub) and Mr. Icahn (by virtue of his relationship to IEP) may be deemed to indirectly beneficially own (as that term is defined in Rule 13d-3 under the Act) the Common Units which Holdings and Holdings Sub beneficially own. Each of the General Partner, CVR, IEP and Mr. Icahn disclaims beneficial ownership of such Common Units except to the extent of their pecuniary interest therein. Mr. Icahn (by virtue of his relationship to IEP) may be deemed to indirectly beneficially own (as that term is defined in Rule 13d-3 under the Act) the Common Units which IEP beneficially owns. Mr. Icahn disclaims beneficial ownership of such Common Units except to the extent of his pecuniary interest therein.</footnote>
        <footnote id="F4">Does not include 20,000 Common Units owned by Gail Golden, the spouse of Mr. Icahn. Mr. Icahn, by virtue of his relationship to Ms. Golden, may be deemed to beneficially own such Common Units. Mr. Icahn disclaims beneficial ownership of such Common Units for all purposes.</footnote>
        <footnote id="F5">Holdings disposed of these Common Units to the Issuer in connection with the Issuer's public offering of Common Units which closed on May 20, 2013 (the &quot;Offering&quot;). This disposition to the Issuer was exempt from the operation of Section 16(b) of the Exchange Act pursuant to Rule 16-3(e) thereunder.</footnote>
        <footnote id="F6">Icahn Enterprises through subsidiaries purchased these Common Units from Holdings in a privately negotiated transaction conducted concurrently with the Offering.</footnote>
        <footnote id="F7">Under the underwriting agreement entered into in connection with the Offering, the Issuer granted the underwriters a 30-day over-allotment option to purchase additional Common Units. Holdings incurred a conditional obligation to deliver Common Units to the Issuer equal to the number of Common Units purchased by the underwriters upon exercise of such over-allotment option. Holdings' disposition of such Common Units to the Issuer is exempt from the operation of Section 16(b) of the Exchange Act pursuant to Rule 16-3(e) thereunder.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>CARL C. ICAHN</signatureName>
        <signatureDate>2013-05-20</signatureDate>
    </ownerSignature>
</ownershipDocument>
