{"id":"https://openalex.org/W7161870436","doi":"https://doi.org/10.48550/arxiv.2605.19391","title":"Tweedie's Formulae and Diffusion Generative Models Beyond Gaussian","display_name":"Tweedie's Formulae and Diffusion Generative Models Beyond Gaussian","publication_year":2026,"publication_date":"2026-05-19","ids":{"openalex":"https://openalex.org/W7161870436","doi":"https://doi.org/10.48550/arxiv.2605.19391"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.19391","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.19391","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.19391","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5136605163","display_name":"Wenpin Tang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tang, Wenpin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5124043115","display_name":"Nizar Touzi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Touzi, Nizar","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5136547585","display_name":"Zikun Zhang","orcid":"https://orcid.org/0009-0009-4787-8957"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Zikun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5136541494","display_name":"Xun Yu Zhou","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhou, Xun Yu","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":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":0.19660000503063202,"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":0.19660000503063202,"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.08460000157356262,"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/T10241","display_name":"Functional Brain Connectivity Studies","score":0.05730000138282776,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.600600004196167},{"id":"https://openalex.org/keywords/brownian-motion","display_name":"Brownian motion","score":0.5121999979019165},{"id":"https://openalex.org/keywords/diffusion-process","display_name":"Diffusion process","score":0.4970000088214874},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4943000078201294},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.4909000098705292},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.4902999997138977},{"id":"https://openalex.org/keywords/noise-reduction","display_name":"Noise reduction","score":0.48489999771118164},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.4361000061035156},{"id":"https://openalex.org/keywords/bessel-function","display_name":"Bessel function","score":0.42910000681877136}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7172999978065491},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.600600004196167},{"id":"https://openalex.org/C112401455","wikidata":"https://www.wikidata.org/wiki/Q178036","display_name":"Brownian motion","level":2,"score":0.5121999979019165},{"id":"https://openalex.org/C68710425","wikidata":"https://www.wikidata.org/wiki/Q5275442","display_name":"Diffusion process","level":3,"score":0.4970000088214874},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4943000078201294},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.4909000098705292},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.4902999997138977},{"id":"https://openalex.org/C163294075","wikidata":"https://www.wikidata.org/wiki/Q581861","display_name":"Noise reduction","level":2,"score":0.48489999771118164},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4797999858856201},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.4361000061035156},{"id":"https://openalex.org/C107706756","wikidata":"https://www.wikidata.org/wiki/Q219637","display_name":"Bessel function","level":2,"score":0.42910000681877136},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4068000018596649},{"id":"https://openalex.org/C4199805","wikidata":"https://www.wikidata.org/wiki/Q2725903","display_name":"Gaussian noise","level":2,"score":0.4020000100135803},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.38119998574256897},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3513000011444092},{"id":"https://openalex.org/C177769412","wikidata":"https://www.wikidata.org/wiki/Q278090","display_name":"Prior probability","level":3,"score":0.3497999906539917},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.3490999937057495},{"id":"https://openalex.org/C108819105","wikidata":"https://www.wikidata.org/wiki/Q1143293","display_name":"Fractional Brownian motion","level":3,"score":0.3400999903678894},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.33629998564720154},{"id":"https://openalex.org/C207201462","wikidata":"https://www.wikidata.org/wiki/Q182505","display_name":"Bayes' theorem","level":3,"score":0.33500000834465027},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.33070001006126404},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.31690001487731934},{"id":"https://openalex.org/C101615488","wikidata":"https://www.wikidata.org/wiki/Q1503307","display_name":"Geometric Brownian motion","level":4,"score":0.3156999945640564},{"id":"https://openalex.org/C167966045","wikidata":"https://www.wikidata.org/wiki/Q5532625","display_name":"Generative model","level":3,"score":0.31529998779296875},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.30079999566078186},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.2856000065803528},{"id":"https://openalex.org/C118532472","wikidata":"https://www.wikidata.org/wiki/Q4896405","display_name":"Bessel process","level":5,"score":0.272599995136261},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.26660001277923584},{"id":"https://openalex.org/C2779664328","wikidata":"https://www.wikidata.org/wiki/Q6311158","display_name":"Jump diffusion","level":3,"score":0.2574999928474426}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.19391","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.19391","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.19391","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.19391","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"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],"models":[1,19,59],"have":[2,64,69],"achieved":[3],"remarkable":[4],"success":[5],"in":[6],"generating":[7],"samples":[8,53],"from":[9,54],"unknown":[10],"data":[11],"distributions.":[12],"Most":[13],"popular":[14],"stochastic":[15],"differential":[16],"equation-based":[17],"diffusion":[18,58,62,122],"perturb":[20],"the":[21,47,70,100,108,130,138],"target":[22],"distribution":[23],"by":[24],"adding":[25],"Gaussian":[26],"noise,":[27],"transforming":[28],"it":[29],"into":[30],"a":[31,40],"simple":[32],"prior,":[33],"and":[34,50,94,113,120,124],"then":[35,106],"use":[36],"denoising":[37,102],"score":[38,48],"matching,":[39],"consequence":[41],"of":[42,140],"Tweedie's":[43,72,79],"formula,":[44],"to":[45,81,111,125],"learn":[46],"function":[49],"generate":[51],"clean":[52],"noise.":[55],"However,":[56],"non-Gaussian":[57,83,141],"with":[60],"state-dependent":[61],"coefficient":[63],"been":[65],"largely":[66],"underexplored,":[67],"as":[68],"corresponding":[71,101],"formulae.":[73],"In":[74],"this":[75],"work,":[76],"we":[77],"extend":[78],"formula":[80],"important":[82],"processes,":[84,93,97],"including":[85],"geometric":[86],"Brownian":[87],"motion":[88],"(GBM),":[89],"squared":[90],"Bessel":[91],"(BESQ)":[92],"Cox-Ingersoll-Ross":[95],"(CIR)":[96],"thereby":[98],"yielding":[99],"score-matching":[103],"objectives.":[104],"We":[105],"apply":[107],"derived":[109],"formulae":[110],"image":[112],"financial":[114],"time":[115],"series":[116],"generation":[117],"using":[118],"GBM-":[119],"CIR-based":[121],"models,":[123],"empirical":[126],"Bayes":[127],"estimation":[128],"under":[129],"BESQ":[131],"setting.":[132],"The":[133],"reported":[134],"experimental":[135],"results":[136],"demonstrate":[137],"potential":[139],"models.":[142]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-05-21T00:00:00"}
