{"id":"https://openalex.org/W4416414390","doi":"https://doi.org/10.48550/arxiv.2511.09902","title":"Incremental Generation is Necessary and Sufficient for Universality in Flow-Based Modelling","display_name":"Incremental Generation is Necessary and Sufficient for Universality in Flow-Based Modelling","publication_year":2025,"publication_date":"2025-11-13","ids":{"openalex":"https://openalex.org/W4416414390","doi":"https://doi.org/10.48550/arxiv.2511.09902"},"language":null,"primary_location":{"id":"pmh:oai:arXiv.org:2511.09902","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2511.09902","pdf_url":"https://arxiv.org/pdf/2511.09902","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2511.09902","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5120414859","display_name":"Hossein Rouhvarzi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rouhvarzi, Hossein","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5036113771","display_name":"Anastasis Kratsios","orcid":"https://orcid.org/0000-0001-6791-3371"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kratsios, Anastasis","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":null,"has_fulltext":true,"cited_by_count":0,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.24449999630451202,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.24449999630451202,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10719","display_name":"3D Shape Modeling and Analysis","score":0.2198999971151352,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.1462000012397766,"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/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.675000011920929},{"id":"https://openalex.org/keywords/universality","display_name":"Universality (dynamical systems)","score":0.4575999975204468},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4311000108718872},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.4311000108718872},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.38940000534057617},{"id":"https://openalex.org/keywords/observer","display_name":"Observer (physics)","score":0.3619999885559082},{"id":"https://openalex.org/keywords/probability-measure","display_name":"Probability measure","score":0.3619000017642975},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.3578000068664551}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7888000011444092},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.675000011920929},{"id":"https://openalex.org/C183992945","wikidata":"https://www.wikidata.org/wiki/Q2495574","display_name":"Universality (dynamical systems)","level":2,"score":0.4575999975204468},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.4311000108718872},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4311000108718872},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.38940000534057617},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3817000091075897},{"id":"https://openalex.org/C2780704645","wikidata":"https://www.wikidata.org/wiki/Q9251458","display_name":"Observer (physics)","level":2,"score":0.3619999885559082},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.3619000017642975},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.3578000068664551},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.3237999975681305},{"id":"https://openalex.org/C2776261394","wikidata":"https://www.wikidata.org/wiki/Q315562","display_name":"Impossibility","level":2,"score":0.32030001282691956},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.29510000348091125},{"id":"https://openalex.org/C206654554","wikidata":"https://www.wikidata.org/wiki/Q5374247","display_name":"Empirical measure","level":2,"score":0.27149999141693115},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2662999927997589},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.2653999924659729},{"id":"https://openalex.org/C2777044963","wikidata":"https://www.wikidata.org/wiki/Q5384707","display_name":"Equivalence class (music)","level":2,"score":0.26269999146461487},{"id":"https://openalex.org/C2781067378","wikidata":"https://www.wikidata.org/wiki/Q17027399","display_name":"Interpretability","level":2,"score":0.258899986743927},{"id":"https://openalex.org/C10728891","wikidata":"https://www.wikidata.org/wiki/Q584521","display_name":"Homeomorphism (graph theory)","level":2,"score":0.25760000944137573},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.2565000057220459},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.25440001487731934}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2511.09902","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2511.09902","pdf_url":"https://arxiv.org/pdf/2511.09902","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2511.09902","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2511.09902","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2511.09902","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2511.09902","pdf_url":"https://arxiv.org/pdf/2511.09902","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320309949","display_name":"Canadian Institute for Advanced Research","ror":"https://ror.org/01sdtdd95"},{"id":"https://openalex.org/F4320319880","display_name":"Government of Canada","ror":"https://ror.org/010q4q527"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4416414390.pdf"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Incremental":[0],"flow-based":[1,29],"denoising":[2,42],"models":[3],"have":[4],"reshaped":[5],"generative":[6],"modelling,":[7],"but":[8],"their":[9],"empirical":[10,206],"advantage":[11],"still":[12],"lacks":[13],"a":[14,69,138],"rigorous":[15],"approximation-theoretic":[16],"foundation.":[17],"We":[18],"show":[19,123],"that":[20,124],"incremental":[21],"generation":[22,30],"is":[23,100],"necessary":[24],"and":[25,59,65,102,164,194],"sufficient":[26],"for":[27,191,195],"universal":[28,105,188],"on":[31,55,129,150,198],"the":[32,45,56,79,88,96,107,151,157,171,179,200],"largest":[33],"natural":[34],"class":[35,80,172],"of":[36,38,48,81,87,95,109,112,118,140,205],"self-maps":[37],"$[0,1]^d$":[39,130],"compatible":[40],"with":[41,208],"pipelines,":[43],"namely":[44],"orientation-preserving":[46,110,126],"homeomorphisms":[47,111],"$[0,1]^d$.":[49,113],"All":[50],"our":[51],"guarantees":[52],"are":[53],"uniform":[54],"underlying":[57,97],"maps":[58],"hence":[60],"imply":[61],"approximation":[62,158,189],"both":[63],"samplewise":[64],"in":[66,106],"distribution.":[67],"Using":[68],"new":[70],"topological-dynamical":[71],"argument,":[72],"we":[73,121,185],"first":[74],"prove":[75],"an":[76],"impossibility":[77],"theorem:":[78],"all":[82],"single-step":[83],"autonomous":[84,119],"flows,":[85,120,145],"independently":[86],"architecture,":[89],"width,":[90],"depth,":[91],"or":[92],"Lipschitz":[93,127],"activation":[94],"neural":[98],"network,":[99],"meagre":[101],"therefore":[103],"not":[104],"space":[108],"By":[114],"exploiting":[115],"algebraic":[116],"properties":[117],"conversely":[122],"every":[125],"homeomorphism":[128],"can":[131,160,166],"be":[132,161,167],"approximated":[133],"at":[134,141],"rate":[135,159],"$O(n^{-1/d})$":[136],"by":[137,176],"composition":[139],"most":[142],"$K_d$":[143,147,165],"such":[144],"where":[146],"depends":[148],"only":[149],"dimension.":[152],"Under":[153],"additional":[154],"smoothness":[155],"assumptions,":[156],"made":[162],"dimension-free,":[163],"chosen":[168],"uniformly":[169],"over":[170],"being":[173],"approximated.":[174],"Finally,":[175],"linearly":[177],"lifting":[178],"domain":[180],"into":[181],"one":[182],"higher":[183],"dimension,":[184],"obtain":[186],"structured":[187],"results":[190],"continuous":[192],"functions":[193],"probability":[196],"measures":[197,207],"$[0,1]^d$,":[199],"latter":[201],"realized":[202],"as":[203],"pushforwards":[204],"vanishing":[209],"$1$-Wasserstein":[210],"error.":[211]},"counts_by_year":[],"updated_date":"2026-08-09T07:27:16.801131","created_date":"2025-11-15T00:00:00"}