{"id":"https://openalex.org/W7161970802","doi":"https://doi.org/10.48550/arxiv.2605.21123","title":"Linear-DPO: Linear Direct Preference Optimization for Diffusion and Flow-Matching Generative Models","display_name":"Linear-DPO: Linear Direct Preference Optimization for Diffusion and Flow-Matching Generative Models","publication_year":2026,"publication_date":"2026-05-20","ids":{"openalex":"https://openalex.org/W7161970802","doi":"https://doi.org/10.48550/arxiv.2605.21123"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2605.21123","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2605.21123","pdf_url":"https://arxiv.org/pdf/2605.21123","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":"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/2605.21123","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5136664956","display_name":"Kesong Li","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]},{"id":"https://openalex.org/I45928872","display_name":"Alibaba Group (China)","ror":"https://ror.org/00k642b80","country_code":"CN","type":"company","lineage":["https://openalex.org/I45928872"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Li, Kesong","raw_affiliation_strings":["Alibaba Group , Hangzhou , Zhejiang , China","School of Computer Science and Technology , Harbin Institute of Technology , Shenzhen , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Alibaba Group , Hangzhou , Zhejiang , China","institution_ids":["https://openalex.org/I45928872"]},{"raw_affiliation_string":"School of Computer Science and Technology , Harbin Institute of Technology , Shenzhen , China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068152351","display_name":"Yixuan Xu","orcid":"https://orcid.org/0000-0002-2411-2715","observed_orcids":["https://orcid.org/0000-0002-2411-2715","https://orcid.org/0009-0008-2131-6975","https://orcid.org/0009-0008-9756-6380"]},"institutions":[{"id":"https://openalex.org/I45928872","display_name":"Alibaba Group (China)","ror":"https://ror.org/00k642b80","country_code":"CN","type":"company","lineage":["https://openalex.org/I45928872"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xu, Yixuan","raw_affiliation_strings":["Alibaba Group , Hangzhou , Zhejiang , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Alibaba Group , Hangzhou , Zhejiang , China","institution_ids":["https://openalex.org/I45928872"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017727521","display_name":"Kuo-Kun Tseng","orcid":"https://orcid.org/0000-0002-3340-8710","observed_orcids":["https://orcid.org/0000-0002-3340-8710"]},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tseng, Kuo-kun","raw_affiliation_strings":["School of Computer Science and Technology , Harbin Institute of Technology , Shenzhen , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science and Technology , Harbin Institute of Technology , Shenzhen , China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133387453","display_name":"Weiyi Lu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I45928872","display_name":"Alibaba Group (China)","ror":"https://ror.org/00k642b80","country_code":"CN","type":"company","lineage":["https://openalex.org/I45928872"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lu, Weiyi","raw_affiliation_strings":["Alibaba Group , Hangzhou , Zhejiang , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Alibaba Group , Hangzhou , Zhejiang , China","institution_ids":["https://openalex.org/I45928872"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5136674737","display_name":"Kan Liu","orcid":"https://orcid.org/0009-0006-0477-4814","observed_orcids":["https://orcid.org/0009-0006-0477-4814"]},"institutions":[{"id":"https://openalex.org/I45928872","display_name":"Alibaba Group (China)","ror":"https://ror.org/00k642b80","country_code":"CN","type":"company","lineage":["https://openalex.org/I45928872"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liu, Kan","raw_affiliation_strings":["Alibaba Group , Hangzhou , Zhejiang , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Alibaba Group , Hangzhou , Zhejiang , China","institution_ids":["https://openalex.org/I45928872"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5133359474","display_name":"Tao Lan","orcid":"https://orcid.org/0009-0004-4363-8888","observed_orcids":["https://orcid.org/0009-0004-4363-8888"]},"institutions":[{"id":"https://openalex.org/I45928872","display_name":"Alibaba Group (China)","ror":"https://ror.org/00k642b80","country_code":"CN","type":"company","lineage":["https://openalex.org/I45928872"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lan, Tao","raw_affiliation_strings":["Alibaba Group , Hangzhou , Zhejiang , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Alibaba Group , Hangzhou , Zhejiang , China","institution_ids":["https://openalex.org/I45928872"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":4,"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":0.9970999956130981,"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":0.9970999956130981,"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/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.000699999975040555,"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/T11307","display_name":"Domain Adaptation and Few-Shot Learning","score":0.00019999999494757503,"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/direct-preference-optimization","display_name":"direct preference optimization","score":0.8529999852180481},{"id":"https://openalex.org/keywords/text-to-image-generation","display_name":"text-to-image generation","score":0.8539999723434448},{"id":"https://openalex.org/keywords/diffusion-models","display_name":"diffusion models","score":0.9639999866485596},{"id":"https://openalex.org/keywords/flow-matching","display_name":"flow matching","score":0.7749999761581421},{"id":"https://openalex.org/keywords/linear-utility-function","display_name":"linear utility function","score":0.9110000133514404}],"concepts":[{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.6097000241279602},{"id":"https://openalex.org/C2781249084","wikidata":"https://www.wikidata.org/wiki/Q908656","display_name":"Preference","level":2,"score":0.5631999969482422},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.5600000023841858},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5224000215530396},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.49459999799728394},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4903999865055084},{"id":"https://openalex.org/C39890363","wikidata":"https://www.wikidata.org/wiki/Q36108","display_name":"Generative grammar","level":2,"score":0.4749000072479248},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4708999991416931},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4180999994277954},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39590001106262207},{"id":"https://openalex.org/C167966045","wikidata":"https://www.wikidata.org/wiki/Q5532625","display_name":"Generative model","level":3,"score":0.39010000228881836},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3880000114440918},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.35929998755455017},{"id":"https://openalex.org/C163175372","wikidata":"https://www.wikidata.org/wiki/Q3339222","display_name":"Linear model","level":2,"score":0.35679998993873596},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35409998893737793},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.34709998965263367},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.3034000098705292},{"id":"https://openalex.org/C163294075","wikidata":"https://www.wikidata.org/wiki/Q581861","display_name":"Noise reduction","level":2,"score":0.2906000018119812},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.2904999852180481},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.2849999964237213},{"id":"https://openalex.org/C68710425","wikidata":"https://www.wikidata.org/wiki/Q5275442","display_name":"Diffusion process","level":3,"score":0.27160000801086426},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.2651999890804291},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.2578999996185303},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.25049999356269836}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2605.21123","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2605.21123","pdf_url":"https://arxiv.org/pdf/2605.21123","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2605.21123","doi":"https://doi.org/10.48550/arxiv.2605.21123","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.21123","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:2605.21123","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2605.21123","pdf_url":"https://arxiv.org/pdf/2605.21123","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":"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/W7161970802.pdf","grobid_xml":"https://content.openalex.org/works/W7161970802.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W2736601468","https://openalex.org/W2908510526","https://openalex.org/W3110257065","https://openalex.org/W4283388932","https://openalex.org/W4288099666","https://openalex.org/W4297676498","https://openalex.org/W4300980573","https://openalex.org/W4303647933","https://openalex.org/W4327673663","https://openalex.org/W4378464471","https://openalex.org/W4380994608","https://openalex.org/W4383472654","https://openalex.org/W4391631327","https://openalex.org/W4396945138","https://openalex.org/W4414968315","https://openalex.org/W4416070669","https://openalex.org/W4417517408","https://openalex.org/W6966874861"],"related_works":["https://openalex.org/W7104271315","https://openalex.org/W4413157670","https://openalex.org/W4412598373","https://openalex.org/W7129103793","https://openalex.org/W7160838488","https://openalex.org/W7218568891","https://openalex.org/W7131263071","https://openalex.org/W7127363472","https://openalex.org/W6966766647","https://openalex.org/W7117703275"],"abstract_inverted_index":{"Direct":[0],"Preference":[1],"Optimization":[2],"(DPO)":[3],"is":[4,76],"successful":[5],"for":[6,78],"alignment":[7],"in":[8,14],"LLMs":[9],"but":[10],"still":[11],"faces":[12],"challenges":[13],"text-to-image":[15,79],"generation.":[16,80],"Existing":[17],"studies":[18],"are":[19],"confined":[20],"to":[21,39],"denoising":[22],"diffusion":[23,55,108],"models":[24,109],"while":[25],"overlooking":[26],"flow-matching,":[27],"and":[28,56,64,97,104,112],"suffer":[29],"from":[30,67],"an":[31,99],"objective":[32,51,75],"mismatch":[33],"when":[34],"applying":[35],"discrete":[36],"NLP-based":[37],"DPO":[38,50,74],"regression-based":[40],"generative":[41],"tasks.\\":[42],"In":[43],"this":[44],"paper,":[45],"we":[46,82],"derive":[47],"a":[48,59,68,93],"generalized":[49],"that":[52,71],"covers":[53],"both":[54],"flow-matching":[57,113],"via":[58],"unified":[60],"reverse-time":[61],"SDE":[62],"framework,":[63],"point":[65],"out":[66],"gradient":[69],"perspective":[70],"the":[72,87,117],"standard":[73],"suboptimal":[77],"Consequently,":[81],"propose":[83],"Linear-DPO,":[84],"which":[85],"replaces":[86],"aggressive":[88],"sigmoid-based":[89],"utility":[90,96],"function":[91],"with":[92],"sustained":[94],"linear":[95],"incorporates":[98],"EMA-updated":[100],"reference":[101],"model.":[102],"Qualitative":[103],"quantitative":[105],"experiments":[106],"on":[107],"(SD1.5,":[110],"SDXL)":[111],"model":[114],"(SD3-Medium)":[115],"demonstrate":[116],"superiority":[118],"of":[119],"our":[120],"approach":[121],"over":[122],"existing":[123],"baselines.":[124]},"counts_by_year":[{"year":2026,"cited_by_count":4}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-05-22T00:00:00"}
