{"id":"https://openalex.org/W7126271724","doi":"https://doi.org/10.48550/arxiv.2601.21943","title":"Entropy-Based Dimension-Free Convergence and Loss-Adaptive Schedules for Diffusion Models","display_name":"Entropy-Based Dimension-Free Convergence and Loss-Adaptive Schedules for Diffusion Models","publication_year":2026,"publication_date":"2026-01-29","ids":{"openalex":"https://openalex.org/W7126271724","doi":"https://doi.org/10.48550/arxiv.2601.21943"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2601.21943","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"Article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020420541","display_name":"Ahmad Aghapour","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Aghapour, Ahmad","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005237318","display_name":"Erhan Bayraktar","orcid":"https://orcid.org/0000-0002-1926-4570"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bayraktar, Erhan","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5124401305","display_name":"Ziqing Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Ziqing","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5020420541"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.5034000277519226,"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":0.5034000277519226,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.1859000027179718,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.1256999969482422,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6549999713897705},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5913000106811523},{"id":"https://openalex.org/keywords/divergence","display_name":"Divergence (linguistics)","score":0.5228000283241272},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.4876999855041504},{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.47999998927116394},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.47209998965263367},{"id":"https://openalex.org/keywords/kullback\u2013leibler-divergence","display_name":"Kullback\u2013Leibler divergence","score":0.4408000111579895},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.4034999907016754}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6549999713897705},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5913000106811523},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5752999782562256},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5491999983787537},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.5228000283241272},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5127000212669373},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.4876999855041504},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.47999998927116394},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.47209998965263367},{"id":"https://openalex.org/C171752962","wikidata":"https://www.wikidata.org/wiki/Q255166","display_name":"Kullback\u2013Leibler divergence","level":2,"score":0.4408000111579895},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4036000072956085},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.4034999907016754},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4007999897003174},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.3765999972820282},{"id":"https://openalex.org/C68387754","wikidata":"https://www.wikidata.org/wiki/Q7271585","display_name":"Schedule","level":2,"score":0.37380000948905945},{"id":"https://openalex.org/C52740198","wikidata":"https://www.wikidata.org/wiki/Q1539564","display_name":"Importance sampling","level":3,"score":0.34630000591278076},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.3222000002861023},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.3061999976634979},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.2955999970436096},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.2872999906539917},{"id":"https://openalex.org/C157709441","wikidata":"https://www.wikidata.org/wiki/Q1411887","display_name":"Uniform convergence","level":3,"score":0.27469998598098755},{"id":"https://openalex.org/C2779530757","wikidata":"https://www.wikidata.org/wiki/Q1207505","display_name":"Quality (philosophy)","level":2,"score":0.27090001106262207},{"id":"https://openalex.org/C167981619","wikidata":"https://www.wikidata.org/wiki/Q1685498","display_name":"Cross entropy","level":3,"score":0.26980000734329224},{"id":"https://openalex.org/C171268870","wikidata":"https://www.wikidata.org/wiki/Q1486676","display_name":"GRASP","level":2,"score":0.2605000138282776},{"id":"https://openalex.org/C2776459999","wikidata":"https://www.wikidata.org/wiki/Q2119376","display_name":"Fidelity","level":2,"score":0.2506999969482422}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2601.21943","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"Article"},{"id":"doi:10.48550/arxiv.2601.21943","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2601.21943","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"article"}],"best_oa_location":{"id":"pmh:doi:10.48550/arxiv.2601.21943","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"Article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Diffusion":[0],"generative":[1],"models":[2,21],"synthesize":[3],"samples":[4],"by":[5,10,78],"discretizing":[6],"reverse-time":[7],"dynamics":[8],"driven":[9],"a":[11,100,108],"learned":[12],"score":[13],"(or":[14],"denoiser).":[15],"Existing":[16],"convergence":[17,55],"analyses":[18],"of":[19,95,102,115],"diffusion":[20],"typically":[22],"scale":[23],"at":[24],"least":[25],"linearly":[26],"with":[27],"the":[28,44,65,73,87,93,103,125],"ambient":[29],"dimension,":[30],"and":[31,75,90,121],"sharper":[32],"rates":[33],"often":[34],"depend":[35],"on":[36,43,64,124],"intrinsic-dimension":[37],"assumptions":[38,63],"or":[39],"other":[40],"geometric":[41,59],"restrictions":[42],"target":[45,66,74],"distribution.":[46],"We":[47],"develop":[48],"an":[49],"alternative,":[50],"information-theoretic":[51],"approach":[52],"to":[53,81],"dimension-free":[54],"that":[56],"avoids":[57],"any":[58],"assumptions.":[60],"Under":[61],"mild":[62],"distribution,":[67],"we":[68,106],"bound":[69],"KL":[70,104],"divergence":[71],"between":[72],"generated":[76],"distributions":[77],"$O(H^2/K)$":[79],"(up":[80],"endpoint":[82],"factors),":[83],"where":[84],"$H$":[85],"is":[86,92,119],"Shannon":[88],"entropy":[89],"$K$":[91],"number":[94],"sampling":[96,136],"steps.":[97],"Moreover,":[98],"using":[99],"reformulation":[101],"divergence,":[105],"propose":[107],"Loss-Adaptive":[109],"Schedule":[110],"(LAS)":[111],"for":[112],"efficient":[113],"discretization":[114],"reverse":[116],"SDE":[117],"which":[118],"lightweight":[120],"relies":[122],"only":[123],"training":[126],"loss,":[127],"requiring":[128],"no":[129],"post-training":[130],"heavy":[131],"computation.":[132],"Empirically,":[133],"LAS":[134],"improves":[135],"quality":[137],"over":[138],"common":[139],"heuristic":[140],"schedules.":[141]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2026-02-01T00:00:00"}