{"id":"https://openalex.org/W7154138424","doi":"https://doi.org/10.48550/arxiv.2604.09181","title":"MixFlow: Mixed Source Distributions Improve Rectified Flows","display_name":"MixFlow: Mixed Source Distributions Improve Rectified Flows","publication_year":2026,"publication_date":"2026-04-10","ids":{"openalex":"https://openalex.org/W7154138424","doi":"https://doi.org/10.48550/arxiv.2604.09181"},"language":"en","primary_location":{"id":"pmh:oai:pure.mpg.de:item_3718236","is_oa":true,"landing_page_url":"https://hdl.handle.net/21.11116/0000-0013-4724-3","pdf_url":"https://hdl.handle.net/21.11116/0000-0013-472D-A","source":{"id":"https://openalex.org/S4306400654","display_name":"MPG.PuRe (Max Planck Society)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149899117","host_organization_name":"Max Planck Society","host_organization_lineage":["https://openalex.org/I149899117"],"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":"2nd Workshop on Deep Generative Model in Machine Learning: Theory, Principle and Efficacy","raw_type":"info:eu-repo/semantics/conferenceObject"},"type":"conference-paper","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hdl.handle.net/21.11116/0000-0013-472D-A","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075882081","display_name":"Nazir Nayal","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nayal, Nazir","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035497974","display_name":"Christopher Wewer","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wewer, Christopher","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5073462022","display_name":"Jan Eric Lenssen","orcid":"https://orcid.org/0000-0003-4093-9840"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lenssen, Jan Eric","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.38527781,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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":0.9103000164031982,"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":0.9103000164031982,"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/T11019","display_name":"Image Enhancement Techniques","score":0.01979999989271164,"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/T10531","display_name":"Advanced Vision and Imaging","score":0.007199999876320362,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.5817999839782715},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5562000274658203},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.5101000070571899},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.49869999289512634},{"id":"https://openalex.org/keywords/independence","display_name":"Independence (probability theory)","score":0.4945000112056732},{"id":"https://openalex.org/keywords/importance-sampling","display_name":"Importance sampling","score":0.44920000433921814},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.4300999939441681},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.3894999921321869},{"id":"https://openalex.org/keywords/source-code","display_name":"Source code","score":0.34769999980926514}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6137999892234802},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.5817999839782715},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5562000274658203},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.5101000070571899},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.49869999289512634},{"id":"https://openalex.org/C35651441","wikidata":"https://www.wikidata.org/wiki/Q625303","display_name":"Independence (probability theory)","level":2,"score":0.4945000112056732},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4812999963760376},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.462799996137619},{"id":"https://openalex.org/C52740198","wikidata":"https://www.wikidata.org/wiki/Q1539564","display_name":"Importance sampling","level":3,"score":0.44920000433921814},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4480000138282776},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.4300999939441681},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.3894999921321869},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35850000381469727},{"id":"https://openalex.org/C43126263","wikidata":"https://www.wikidata.org/wiki/Q128751","display_name":"Source code","level":2,"score":0.34769999980926514},{"id":"https://openalex.org/C167966045","wikidata":"https://www.wikidata.org/wiki/Q5532625","display_name":"Generative model","level":3,"score":0.34310001134872437},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.33329999446868896},{"id":"https://openalex.org/C177769412","wikidata":"https://www.wikidata.org/wiki/Q278090","display_name":"Prior probability","level":3,"score":0.33149999380111694},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3305000066757202},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.33000001311302185},{"id":"https://openalex.org/C2779530757","wikidata":"https://www.wikidata.org/wiki/Q1207505","display_name":"Quality (philosophy)","level":2,"score":0.31769999861717224},{"id":"https://openalex.org/C77170095","wikidata":"https://www.wikidata.org/wiki/Q1753188","display_name":"Linearity","level":2,"score":0.303600013256073},{"id":"https://openalex.org/C190839683","wikidata":"https://www.wikidata.org/wiki/Q2448197","display_name":"Train","level":2,"score":0.2849999964237213},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.2847999930381775},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.2840999960899353},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.27720001339912415},{"id":"https://openalex.org/C108882938","wikidata":"https://www.wikidata.org/wiki/Q274506","display_name":"Uniform distribution (continuous)","level":2,"score":0.26170000433921814},{"id":"https://openalex.org/C20326153","wikidata":"https://www.wikidata.org/wiki/Q7049638","display_name":"Nonuniform sampling","level":3,"score":0.25619998574256897}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:pure.mpg.de:item_3718236","is_oa":true,"landing_page_url":"https://hdl.handle.net/21.11116/0000-0013-4724-3","pdf_url":"https://hdl.handle.net/21.11116/0000-0013-472D-A","source":{"id":"https://openalex.org/S4306400654","display_name":"MPG.PuRe (Max Planck Society)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149899117","host_organization_name":"Max Planck Society","host_organization_lineage":["https://openalex.org/I149899117"],"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":"2nd Workshop on Deep Generative Model in Machine Learning: Theory, Principle and Efficacy","raw_type":"info:eu-repo/semantics/conferenceObject"},{"id":"doi:10.48550/arxiv.2604.09181","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.09181","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,"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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:pure.mpg.de:item_3718236","is_oa":true,"landing_page_url":"https://hdl.handle.net/21.11116/0000-0013-4724-3","pdf_url":"https://hdl.handle.net/21.11116/0000-0013-472D-A","source":{"id":"https://openalex.org/S4306400654","display_name":"MPG.PuRe (Max Planck Society)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149899117","host_organization_name":"Max Planck Society","host_organization_lineage":["https://openalex.org/I149899117"],"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":"2nd Workshop on Deep Generative Model in Machine Learning: Theory, Principle and Efficacy","raw_type":"info:eu-repo/semantics/conferenceObject"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7154138424.pdf","grobid_xml":"https://content.openalex.org/works/W7154138424.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Diffusion":[0],"models":[1],"and":[2,11,51,117,135,148,159,183],"their":[3],"variations,":[4],"such":[5],"as":[6,38],"rectified":[7,181],"flows,":[8],"generate":[9],"diverse":[10],"high-quality":[12],"images,":[13],"but":[14,107],"they":[15,30],"are":[16],"still":[17],"hindered":[18],"by":[19,24,40,62,77,174],"slow":[20],"iterative":[21],"sampling":[22,120,157,192],"caused":[23],"the":[25,46,52,73,85,98,113,143,146,161,171],"highly":[26],"curved":[27],"generative":[28,114],"paths":[29],"learn.":[31],"An":[32],"important":[33],"cause":[34],"of":[35,130],"high":[36],"curvature,":[37],"shown":[39],"previous":[41,187],"work,":[42,57],"is":[43],"independence":[44],"between":[45,145],"source":[47,86,147],"distribution":[48,87,134],"(standard":[49],"Gaussian)":[50],"data":[53,99],"distribution.":[54,100,138],"In":[55],"this":[56,60],"we":[58,67,102],"tackle":[59],"limitation":[61],"two":[63],"complementary":[64],"contributions.":[65],"First,":[66],"attempt":[68],"to":[69,179,186],"break":[70],"away":[71],"from":[72],"standard":[74,180],"Gaussian":[75],"assumption":[76],"introducing":[78],"$\u03ba\\texttt{-FC}$,":[79],"a":[80,105,124,131,136,190],"general":[81],"formulation":[82],"that":[83,93,111],"conditions":[84],"on":[88,127],"an":[89],"arbitrary":[90],"signal":[91],"$\u03ba$":[92],"aligns":[94],"it":[95],"better":[96,151],"with":[97,154],"Then,":[101],"present":[103],"MixFlow,":[104],"simple":[106,140],"effective":[108],"training":[109,162,168],"strategy":[110],"reduces":[112],"path":[115],"curvatures":[116],"considerably":[118],"improves":[119,142,170],"efficiency.":[121],"MixFlow":[122],"trains":[123],"flow":[125,182],"model":[126],"linear":[128],"mixtures":[129],"fixed":[132,191],"unconditional":[133],"$\u03ba\\texttt{-FC}$-based":[137],"This":[139],"mixture":[141],"alignment":[144],"data,":[149],"provides":[150],"generation":[152,172],"quality":[153,173],"less":[155],"required":[156],"steps,":[158],"accelerates":[160],"convergence":[163],"considerably.":[164],"On":[165],"average,":[166],"our":[167],"procedure":[169],"12\\%":[175],"in":[176],"FID":[177],"compared":[178,185],"7\\%":[184],"baselines":[188],"under":[189],"budget.":[193],"Code":[194],"available":[195],"at:":[196],"$\\href{https://github.com/NazirNayal8/MixFlow}{https://github.com/NazirNayal8/MixFlow}$":[197]},"counts_by_year":[],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2026-04-14T00:00:00"}