{"id":"https://openalex.org/W4416707190","doi":"https://doi.org/10.1109/lsp.2025.3637667","title":"Gaussian Universality for Diffusion Models","display_name":"Gaussian Universality for Diffusion Models","publication_year":2025,"publication_date":"2025-11-26","ids":{"openalex":"https://openalex.org/W4416707190","doi":"https://doi.org/10.1109/lsp.2025.3637667"},"language":null,"primary_location":{"id":"doi:10.1109/lsp.2025.3637667","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2025.3637667","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Signal Processing Letters","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5093219798","display_name":"Reza Ghane","orcid":null},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Reza Ghane","raw_affiliation_strings":["Electrical Engineering Department, California Institute of Technology, Pasadena, CA, USA"],"raw_orcid":"https://orcid.org/0000-0002-3232-9359","affiliations":[{"raw_affiliation_string":"Electrical Engineering Department, California Institute of Technology, Pasadena, CA, USA","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072466084","display_name":"Anthony Bao","orcid":null},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Anthony Bao","raw_affiliation_strings":["Electrical and Computer Engineering Department, University of Texas, Austin, TX, USA"],"raw_orcid":"https://orcid.org/0000-0003-1162-564X","affiliations":[{"raw_affiliation_string":"Electrical and Computer Engineering Department, University of Texas, Austin, TX, USA","institution_ids":["https://openalex.org/I86519309"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036629613","display_name":"Danil Akhtiamov","orcid":"https://orcid.org/0000-0002-9238-9636"},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Danil Akhtiamov","raw_affiliation_strings":["Computing + Mathematical Sciences Department, California Institute of Technology, Pasadena, CA, USA"],"raw_orcid":"https://orcid.org/0000-0002-9238-9636","affiliations":[{"raw_affiliation_string":"Computing + Mathematical Sciences Department, California Institute of Technology, Pasadena, CA, USA","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002430773","display_name":"Babak Hassibi","orcid":"https://orcid.org/0000-0002-1375-5838"},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Babak Hassibi","raw_affiliation_strings":["Electrical Engineering Department, California Institute of Technology, Pasadena, CA, USA"],"raw_orcid":"https://orcid.org/0000-0002-1375-5838","affiliations":[{"raw_affiliation_string":"Electrical Engineering Department, California Institute of Technology, Pasadena, CA, USA","institution_ids":["https://openalex.org/I122411786"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0182,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.82136658,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"33","issue":null,"first_page":"116","last_page":"120"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11304","display_name":"Advanced Neuroimaging Techniques and Applications","score":0.34470000863075256,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},"topics":[{"id":"https://openalex.org/T11304","display_name":"Advanced Neuroimaging Techniques and Applications","score":0.34470000863075256,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T10241","display_name":"Functional Brain Connectivity Studies","score":0.1265999972820282,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.11990000307559967,"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/universality","display_name":"Universality (dynamical systems)","score":0.7889999747276306},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.7419000267982483},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.5249000191688538},{"id":"https://openalex.org/keywords/gaussian-network-model","display_name":"Gaussian network model","score":0.4146000146865845},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.40290001034736633},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.37400001287460327},{"id":"https://openalex.org/keywords/gaussian-process","display_name":"Gaussian process","score":0.3643999993801117},{"id":"https://openalex.org/keywords/gaussian-noise","display_name":"Gaussian noise","score":0.36070001125335693},{"id":"https://openalex.org/keywords/probability-density-function","display_name":"Probability density function","score":0.3384999930858612}],"concepts":[{"id":"https://openalex.org/C183992945","wikidata":"https://www.wikidata.org/wiki/Q2495574","display_name":"Universality (dynamical systems)","level":2,"score":0.7889999747276306},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.7419000267982483},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5892999768257141},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.5249000191688538},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44429999589920044},{"id":"https://openalex.org/C166550679","wikidata":"https://www.wikidata.org/wiki/Q263400","display_name":"Gaussian network model","level":3,"score":0.4146000146865845},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.40290001034736633},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.391400009393692},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3864000141620636},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.37400001287460327},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.3643999993801117},{"id":"https://openalex.org/C4199805","wikidata":"https://www.wikidata.org/wiki/Q2725903","display_name":"Gaussian noise","level":2,"score":0.36070001125335693},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.3384999930858612},{"id":"https://openalex.org/C7218915","wikidata":"https://www.wikidata.org/wiki/Q1054475","display_name":"Gaussian function","level":3,"score":0.328900009393692},{"id":"https://openalex.org/C16910744","wikidata":"https://www.wikidata.org/wiki/Q7705759","display_name":"Test data","level":2,"score":0.32109999656677246},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.31839999556541443},{"id":"https://openalex.org/C160920958","wikidata":"https://www.wikidata.org/wiki/Q7662746","display_name":"Synthetic data","level":2,"score":0.3172000050544739},{"id":"https://openalex.org/C51267290","wikidata":"https://www.wikidata.org/wiki/Q5527848","display_name":"Gaussian random field","level":4,"score":0.29750001430511475},{"id":"https://openalex.org/C164602753","wikidata":"https://www.wikidata.org/wiki/Q567544","display_name":"Anomalous diffusion","level":3,"score":0.2973000109195709},{"id":"https://openalex.org/C137250428","wikidata":"https://www.wikidata.org/wiki/Q5178897","display_name":"Covariance function","level":3,"score":0.28760001063346863},{"id":"https://openalex.org/C114289077","wikidata":"https://www.wikidata.org/wiki/Q3284399","display_name":"Statistical model","level":2,"score":0.28130000829696655},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.2793000042438507},{"id":"https://openalex.org/C163175372","wikidata":"https://www.wikidata.org/wiki/Q3339222","display_name":"Linear model","level":2,"score":0.2791000008583069},{"id":"https://openalex.org/C2777630202","wikidata":"https://www.wikidata.org/wiki/Q5527840","display_name":"Gaussian measure","level":3,"score":0.2777000069618225},{"id":"https://openalex.org/C87007009","wikidata":"https://www.wikidata.org/wiki/Q210832","display_name":"Statistical hypothesis testing","level":2,"score":0.2605000138282776},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.2581999897956848},{"id":"https://openalex.org/C92224547","wikidata":"https://www.wikidata.org/wiki/Q1673216","display_name":"Probability of error","level":2,"score":0.2513999938964844}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/lsp.2025.3637667","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2025.3637667","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Signal Processing Letters","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W2108598243","https://openalex.org/W4250954493","https://openalex.org/W4281619172","https://openalex.org/W4413147203","https://openalex.org/W4416707190"],"related_works":[],"abstract_inverted_index":{"We":[0],"investigate":[1],"Gaussian":[2,12,52,100],"Universality":[3,13],"for":[4,31,93,131,160,182],"data":[5,38,79,101,113,190,197],"distributions":[6],"generated":[7],"via":[8],"diffusion":[9,37,170],"models.":[10],"By":[11],"we":[14,128,177],"mean":[15],"that":[16,179],"the":[17,36,40,51,64,70,77,81,87,90,106,120,168,192,196,207,211],"test":[18,41,65,91],"error":[19,42,66,92],"of":[20,43,76,89,108,122,195],"a":[21,32,85,115],"generalized":[22],"linear":[23,82,94],"model":[24,171],"<inline-formula":[25,44,137,141,150,161],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[26,45,138,142,151,162],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><tex-math":[27,46,139,143,152,163],"notation=\"LaTeX\">$f(\\bf":[28,47],"{W})$</tex-math></inline-formula>":[29,48],"trained":[30,49,110],"classification":[33],"task":[34],"on":[35,50,69,111],"matches":[39],"Mixture":[53],"with":[54,157],"matching":[55],"means":[56],"and":[57,72],"covariances":[58],"per":[59],"class.":[60,175],"In":[61],"other":[62],"words,":[63],"depends":[67],"only":[68],"first":[71],"second":[73],"order":[74],"statistics":[75],"diffusion-generated":[78,103,189],"in":[80,210],"setting.":[83],"As":[84],"corollary,":[86],"analysis":[88],"classifiers":[95],"can":[96],"be":[97],"reduced":[98],"to":[99,119,149,173,188,199,206],"from":[102,167],"data.":[104],"Analyzing":[105],"performance":[107],"models":[109],"synthetic":[112],"is":[114,147],"pertinent":[116],"problem":[117],"due":[118],"surge":[121],"methods":[123],"such":[124],"as":[125,191,220],"[1].":[126],"Moreover,":[127],"show":[129],"that,":[130],"any":[132],"1-":[133],"Lipschitz":[134],"scalar":[135],"function":[136],"notation=\"LaTeX\">$\\phi$</tex-math></inline-formula>,":[140],"notation=\"LaTeX\">$\\phi":[144],"(\\mathbf":[145],"{x})$</tex-math></inline-formula>":[146,156],"close":[148],"notation=\"LaTeX\">$\\mathbb":[153],"{E}\\phi":[154],"(\\bf":[155],"high":[158],"probability":[159],"notation=\"LaTeX\">$\\bf":[164],"{x}$</tex-math></inline-formula>":[165],"sampled":[166],"conditional":[169],"corresponding":[172],"each":[174],"Finally,":[176],"note":[178],"current":[180],"approaches":[181],"proving":[183],"universality":[184,218],"do":[185],"not":[186],"apply":[187],"covariance":[193],"matrices":[194],"tend":[198],"have":[200],"vanishing":[201],"minimum":[202],"singular":[203],"values,":[204],"contrary":[205],"assumption":[208],"made":[209],"literature.":[212],"This":[213],"leaves":[214],"extending":[215],"previous":[216],"mathematical":[217],"results":[219],"an":[221],"intriguing":[222],"open":[223],"question.":[224]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-11-27T00:00:00"}