{"id":"https://openalex.org/W7212149694","doi":"https://doi.org/10.48550/arxiv.2609.09905","title":"FlowCPO: A Unified Divergence View of Preference Alignment for Flow Models","display_name":"FlowCPO: A Unified Divergence View of Preference Alignment for Flow Models","publication_year":2026,"publication_date":"2026-09-09","ids":{"openalex":"https://openalex.org/W7212149694","doi":"https://doi.org/10.48550/arxiv.2609.09905"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.09905","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.09905","pdf_url":"https://arxiv.org/pdf/2609.09905","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.09905","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5133641401","display_name":"Yansen Han","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I3133055985","display_name":"Westlake University","ror":"https://ror.org/05hfa4n20","country_code":"CN","type":"education","lineage":["https://openalex.org/I3133055985"]},{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Han, Yansen","raw_affiliation_strings":["Westlake University","Zhejiang University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Westlake University","institution_ids":["https://openalex.org/I3133055985"]},{"raw_affiliation_string":"Zhejiang University","institution_ids":["https://openalex.org/I76130692"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109738424","display_name":"Shengyi Liao","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4401726859","display_name":"Kuaishou (China)","ror":"https://ror.org/0258as409","country_code":"CN","type":"company","lineage":["https://openalex.org/I4401726859"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liao, Shengyi","raw_affiliation_strings":["Kling Team , Kuaishou Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Kling Team , Kuaishou Technology","institution_ids":["https://openalex.org/I4401726859"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003997054","display_name":"Peng Sun","orcid":"https://orcid.org/0000-0002-2105-4636","observed_orcids":["https://orcid.org/0000-0002-2105-4636","https://orcid.org/0000-0002-4850-1870"]},"institutions":[{"id":"https://openalex.org/I3133055985","display_name":"Westlake University","ror":"https://ror.org/05hfa4n20","country_code":"CN","type":"education","lineage":["https://openalex.org/I3133055985"]},{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Sun, Peng","raw_affiliation_strings":["Westlake University","Zhejiang University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Westlake University","institution_ids":["https://openalex.org/I3133055985"]},{"raw_affiliation_string":"Zhejiang University","institution_ids":["https://openalex.org/I76130692"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049282010","display_name":"Deyuan Liu","orcid":"https://orcid.org/0000-0001-5764-8754","observed_orcids":["https://orcid.org/0000-0001-5764-8754"]},"institutions":[{"id":"https://openalex.org/I3133055985","display_name":"Westlake University","ror":"https://ror.org/05hfa4n20","country_code":"CN","type":"education","lineage":["https://openalex.org/I3133055985"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liu, Deyuan","raw_affiliation_strings":["Westlake University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Westlake University","institution_ids":["https://openalex.org/I3133055985"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5143204482","display_name":"Yuanxing Zhang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4401726859","display_name":"Kuaishou (China)","ror":"https://ror.org/0258as409","country_code":"CN","type":"company","lineage":["https://openalex.org/I4401726859"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhang, Yuanxing","raw_affiliation_strings":["Kling Team , Kuaishou Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Kling Team , Kuaishou Technology","institution_ids":["https://openalex.org/I4401726859"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101928510","display_name":"Pengfei Wan","orcid":"https://orcid.org/0000-0001-7225-565X","observed_orcids":["https://orcid.org/0000-0001-7225-565X","https://orcid.org/0000-0001-5371-1867","https://orcid.org/0000-0001-9281-1529"]},"institutions":[{"id":"https://openalex.org/I4401726859","display_name":"Kuaishou (China)","ror":"https://ror.org/0258as409","country_code":"CN","type":"company","lineage":["https://openalex.org/I4401726859"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wan, Pengfei","raw_affiliation_strings":["Kling Team , Kuaishou Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Kling Team , Kuaishou Technology","institution_ids":["https://openalex.org/I4401726859"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5147773196","display_name":"Tao Lin","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I3133055985","display_name":"Westlake University","ror":"https://ror.org/05hfa4n20","country_code":"CN","type":"education","lineage":["https://openalex.org/I3133055985"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lin, Tao","raw_affiliation_strings":["Westlake University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Westlake University","institution_ids":["https://openalex.org/I3133055985"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.6820999979972839,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.6820999979972839,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10028","display_name":"Topic Modeling","score":0.04690000042319298,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10462","display_name":"Reinforcement Learning in Robotics","score":0.043299999088048935,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/preference-alignment","display_name":"preference alignment","score":0.9869999885559082},{"id":"https://openalex.org/keywords/flow-model","display_name":"flow model","score":0.890999972820282},{"id":"https://openalex.org/keywords/diffusion-models","display_name":"diffusion models","score":0.859000027179718},{"id":"https://openalex.org/keywords/preference-pairs","display_name":"preference pairs","score":0.3199999928474426},{"id":"https://openalex.org/keywords/out-of-domain-evaluation","display_name":"out-of-domain evaluation","score":0.4950000047683716}],"concepts":[{"id":"https://openalex.org/C2781249084","wikidata":"https://www.wikidata.org/wiki/Q908656","display_name":"Preference","level":2,"score":0.6577000021934509},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6324999928474426},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.5708000063896179},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5473999977111816},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.5412999987602234},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5245000123977661},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.5134000182151794},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43070000410079956},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.4007999897003174},{"id":"https://openalex.org/C148043351","wikidata":"https://www.wikidata.org/wiki/Q4456944","display_name":"Current (fluid)","level":2,"score":0.3752000033855438},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.37070000171661377},{"id":"https://openalex.org/C48921125","wikidata":"https://www.wikidata.org/wiki/Q10861030","display_name":"Linear regression","level":2,"score":0.35899999737739563},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.3564000129699707},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.35089999437332153},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33880001306533813},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.3334999978542328},{"id":"https://openalex.org/C152877465","wikidata":"https://www.wikidata.org/wiki/Q208042","display_name":"Regression analysis","level":2,"score":0.32519999146461487},{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.322299987077713},{"id":"https://openalex.org/C2780490138","wikidata":"https://www.wikidata.org/wiki/Q7079636","display_name":"Offline learning","level":3,"score":0.31869998574256897},{"id":"https://openalex.org/C148483581","wikidata":"https://www.wikidata.org/wiki/Q446488","display_name":"Feature selection","level":2,"score":0.31369999051094055},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.29580000042915344},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.2939000129699707},{"id":"https://openalex.org/C2780102126","wikidata":"https://www.wikidata.org/wiki/Q10928179","display_name":"Online and offline","level":2,"score":0.29089999198913574},{"id":"https://openalex.org/C2777062324","wikidata":"https://www.wikidata.org/wiki/Q25036211","display_name":"Preference relation","level":3,"score":0.27950000762939453},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.274399995803833},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.27300000190734863},{"id":"https://openalex.org/C2986087404","wikidata":"https://www.wikidata.org/wiki/Q15946010","display_name":"Online learning","level":2,"score":0.27140000462532043},{"id":"https://openalex.org/C196921405","wikidata":"https://www.wikidata.org/wiki/Q786431","display_name":"Online algorithm","level":2,"score":0.26669999957084656},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.25850000977516174},{"id":"https://openalex.org/C93959086","wikidata":"https://www.wikidata.org/wiki/Q6888345","display_name":"Model selection","level":2,"score":0.25209999084472656}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.09905","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.09905","pdf_url":"https://arxiv.org/pdf/2609.09905","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.09905","doi":"https://doi.org/10.48550/arxiv.2609.09905","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.09905","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.09905","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.09905","pdf_url":"https://arxiv.org/pdf/2609.09905","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7212149694.pdf","grobid_xml":"https://content.openalex.org/works/W7212149694.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W2799151646","https://openalex.org/W4283070712","https://openalex.org/W4288099666","https://openalex.org/W4293327156","https://openalex.org/W4300980573","https://openalex.org/W4303647933","https://openalex.org/W4377121527","https://openalex.org/W4380994608","https://openalex.org/W4387430844","https://openalex.org/W4391506302","https://openalex.org/W4405917844","https://openalex.org/W4406810917","https://openalex.org/W4414742673","https://openalex.org/W4414968315","https://openalex.org/W4415058126","https://openalex.org/W4415130457","https://openalex.org/W4415337568","https://openalex.org/W4416052723","https://openalex.org/W4416070669","https://openalex.org/W4417093930","https://openalex.org/W4417516997","https://openalex.org/W6910716039","https://openalex.org/W6929355313","https://openalex.org/W6967046348","https://openalex.org/W6967052438","https://openalex.org/W7101722927","https://openalex.org/W7114793404","https://openalex.org/W7138064046","https://openalex.org/W7160960000","https://openalex.org/W7204800592"],"related_works":["https://openalex.org/W7138378969","https://openalex.org/W7203886273","https://openalex.org/W7160945880","https://openalex.org/W7164143790","https://openalex.org/W4414968315","https://openalex.org/W4407308992","https://openalex.org/W4391709950","https://openalex.org/W7160597965","https://openalex.org/W4404782630","https://openalex.org/W4414819931"],"abstract_inverted_index":{"Preference":[0],"alignment":[1,28],"for":[2,151],"flow":[3,97],"and":[4,12,62,73,136,145,149],"diffusion":[5],"models":[6],"now":[7],"spans":[8],"online":[9,77],"reinforcement":[10],"learning":[11],"offline":[13,38,66],"preference":[14,43],"optimization,":[15],"but":[16,169],"the":[17,34,89,116,128,140,157,160,165],"relation":[18],"between":[19],"these":[20,56],"methods":[21,29,39],"remains":[22],"unclear.":[23],"In":[24,127,156],"particular,":[25],"existing":[26],"forward-process":[27],"require":[30],"fresh":[31],"samples":[32,75],"from":[33],"current":[35],"model,":[36],"while":[37],"based":[40],"on":[41,47,104,175],"fixed":[42,105],"pairs":[44],"rely":[45],"primarily":[46],"positive-only":[48],"fine-tuning":[49],"or":[50],"DPO-style":[51],"likelihood-ratio":[52],"surrogates.":[53],"We":[54,107],"organize":[55],"approaches":[57],"through":[58],"a":[59,95,101],"divergence-based":[60],"framework":[61],"introduce":[63],"FlowCPO,":[64],"an":[65],"forward-KL":[67,90],"objective":[68,91],"that":[69,88,110],"uses":[70],"both":[71],"preferred":[72],"dispreferred":[74],"without":[76],"rollouts.":[78],"For":[79],"linear":[80],"interpolation,":[81],"we":[82],"show":[83,109],"under":[84],"explicit":[85],"regularity":[86],"conditions":[87],"is":[92,113],"bounded":[93],"by":[94],"contrastive":[96],"matching":[98],"loss,":[99],"yielding":[100],"tractable":[102],"surrogate":[103],"data.":[106],"further":[108],"this":[111],"loss":[112,119],"nonnegative,":[114],"whereas":[115],"signed":[117],"regression":[118],"of":[120],"simplified":[121],"FlowDPO":[122,152],"can":[123],"be":[124],"unbounded":[125],"below.":[126],"in-domain":[129],"setting,":[130,159],"FlowCPO":[131],"achieves":[132],"higher":[133],"mean":[134],"GenEval":[135,167],"OCR":[137],"scores":[138,172],"than":[139,173],"evaluated":[141],"baselines,":[142],"reaching":[143],"0.84":[144],"0.87":[146],"versus":[147],"0.81":[148],"0.74":[150],"at":[153],"CFG":[154],"3.0.":[155],"out-of-domain":[158],"results":[161],"are":[162],"mixed,":[163],"with":[164],"best":[166],"result":[168],"lower":[170],"reward":[171],"RFT":[174],"several":[176],"metrics.":[177]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-11T00:00:00"}