{"id":"https://openalex.org/W7221497243","doi":null,"title":"From Score-Based Diffusion Models to Stochastic Flow Maps","display_name":"From Score-Based Diffusion Models to Stochastic Flow Maps","publication_year":2026,"publication_date":"2026-08-06","ids":{"openalex":"https://openalex.org/W7221497243"},"language":"en","primary_location":{"id":"pmh:oai:https://spectrum.library.concordia.ca:997886","doi":null,"is_oa":true,"landing_page_url":"https://spectrum.library.concordia.ca/id/eprint/997886/2/Brahmi_MSc_F2026.pdf","pdf_url":"https://spectrum.library.concordia.ca/id/eprint/997886/2/Brahmi_MSc_F2026.pdf","source":{"id":"https://openalex.org/S4306400871","display_name":"Spectrum Research Repository (Concordia University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I60158472","host_organization_name":"Concordia University","host_organization_lineage":["https://openalex.org/I60158472"],"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":"Thesis"},"volume":null,"type":"dissertation","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://spectrum.library.concordia.ca/id/eprint/997886/2/Brahmi_MSc_F2026.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5158379867","display_name":"Hichem Brahmi","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I60158472","display_name":"Concordia University","ror":"https://ror.org/0420zvk78","country_code":"CA","type":"education","lineage":["https://openalex.org/I60158472"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Brahmi, Hichem","raw_affiliation_strings":["Concordia University , 2026"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Concordia University , 2026","institution_ids":["https://openalex.org/I60158472"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5158379867"],"corresponding_institution_ids":["https://openalex.org/I60158472"],"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/T10067","display_name":"Stochastic processes and financial applications","score":0.33980000019073486,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.33980000019073486,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.22190000116825104,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.20319999754428864,"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/diffusion-models","display_name":"diffusion models","score":0.9399999976158142},{"id":"https://openalex.org/keywords/score-based-diffusion-models","display_name":"score-based diffusion models","score":0.7480000257492065},{"id":"https://openalex.org/keywords/stochastic-differential-equations","display_name":"stochastic differential equations","score":0.9319999814033508},{"id":"https://openalex.org/keywords/denoising-score-matching","display_name":"denoising score matching","score":0.9829999804496765},{"id":"https://openalex.org/keywords/backflow","display_name":"backflow","score":0.8859999775886536},{"id":"https://openalex.org/keywords/ornstein-uhlenbeck-process","display_name":"Ornstein-Uhlenbeck process","score":0.8299999833106995},{"id":"https://openalex.org/keywords/cir-process","display_name":"CIR process","score":0.8360000252723694},{"id":"https://openalex.org/keywords/lamperti-transformation","display_name":"Lamperti transformation","score":0.8980000019073486},{"id":"https://openalex.org/keywords/brownian-paths","display_name":"Brownian paths","score":0.44699999690055847},{"id":"https://openalex.org/keywords/image-generation","display_name":"image generation","score":0.30300000309944153}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7670999765396118},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7009000182151794},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.6671000123023987},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5407000184059143},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.5281000137329102},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.47049999237060547},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.4510999917984009},{"id":"https://openalex.org/C112401455","wikidata":"https://www.wikidata.org/wiki/Q178036","display_name":"Brownian motion","level":2,"score":0.43540000915527344},{"id":"https://openalex.org/C68710425","wikidata":"https://www.wikidata.org/wiki/Q5275442","display_name":"Diffusion process","level":3,"score":0.40389999747276306},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.400299996137619},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3792000114917755},{"id":"https://openalex.org/C108819105","wikidata":"https://www.wikidata.org/wiki/Q1143293","display_name":"Fractional Brownian motion","level":3,"score":0.3492000102996826},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.3273000121116638},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.32429999113082886},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.3192000091075897},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.31790000200271606},{"id":"https://openalex.org/C39943821","wikidata":"https://www.wikidata.org/wiki/Q506346","display_name":"Semimartingale","level":2,"score":0.31380000710487366},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3057999908924103},{"id":"https://openalex.org/C129537906","wikidata":"https://www.wikidata.org/wiki/Q7603913","display_name":"State variable","level":2,"score":0.2777999937534332},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.2745000123977661},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.2687000036239624},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.2685999870300293},{"id":"https://openalex.org/C18015164","wikidata":"https://www.wikidata.org/wiki/Q6935000","display_name":"Multiplicative noise","level":5,"score":0.25870001316070557},{"id":"https://openalex.org/C148043351","wikidata":"https://www.wikidata.org/wiki/Q4456944","display_name":"Current (fluid)","level":2,"score":0.25519999861717224},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.2549999952316284},{"id":"https://openalex.org/C127491075","wikidata":"https://www.wikidata.org/wiki/Q7617825","display_name":"Stochastic modelling","level":2,"score":0.2547999918460846}],"mesh":[],"locations_count":1,"locations":[{"id":"pmh:oai:https://spectrum.library.concordia.ca:997886","doi":null,"is_oa":true,"landing_page_url":"https://spectrum.library.concordia.ca/id/eprint/997886/2/Brahmi_MSc_F2026.pdf","pdf_url":"https://spectrum.library.concordia.ca/id/eprint/997886/2/Brahmi_MSc_F2026.pdf","source":{"id":"https://openalex.org/S4306400871","display_name":"Spectrum Research Repository (Concordia University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I60158472","host_organization_name":"Concordia University","host_organization_lineage":["https://openalex.org/I60158472"],"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":"Thesis"}],"best_oa_location":{"id":"pmh:oai:https://spectrum.library.concordia.ca:997886","doi":null,"is_oa":true,"landing_page_url":"https://spectrum.library.concordia.ca/id/eprint/997886/2/Brahmi_MSc_F2026.pdf","pdf_url":"https://spectrum.library.concordia.ca/id/eprint/997886/2/Brahmi_MSc_F2026.pdf","source":{"id":"https://openalex.org/S4306400871","display_name":"Spectrum Research Repository (Concordia University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I60158472","host_organization_name":"Concordia University","host_organization_lineage":["https://openalex.org/I60158472"],"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":"Thesis"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7221497243.pdf","grobid_xml":"https://content.openalex.org/works/W7221497243.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W1498436455","https://openalex.org/W1677182931","https://openalex.org/W1995140868","https://openalex.org/W2013035813","https://openalex.org/W2092414256","https://openalex.org/W2112796928","https://openalex.org/W2329986772","https://openalex.org/W2948978827","https://openalex.org/W2950899361","https://openalex.org/W3165731524","https://openalex.org/W4238187298"],"related_works":["https://openalex.org/W6960146059","https://openalex.org/W7162104378","https://openalex.org/W4413287696","https://openalex.org/W4367189724","https://openalex.org/W3167139504","https://openalex.org/W4398229957","https://openalex.org/W4283332132","https://openalex.org/W4310558019","https://openalex.org/W7160871043","https://openalex.org/W4389813799"],"abstract_inverted_index":{"This":[0],"thesis":[1],"studies":[2],"diffusion":[3,15],"models":[4,16],"from":[5],"the":[6,30,33,53,61,71,95,104,112,117,125,132,135,140,146,149],"distributional":[7,150],"and":[8,17,64,86,107,151,154],"pathwise":[9,99,152],"viewpoints.":[10],"We":[11,68],"first":[12],"describe":[13],"discrete":[14],"their":[18],"continuous-time":[19],"formulation":[20],"through":[21],"stochastic":[22],"differential":[23],"equations.":[24],"The":[25,89],"reverse-time":[26],"SDE":[27,75],"depends":[28,81],"on":[29,82],"score":[31,41],"of":[32,52,73,97],"evolving":[34],"density,":[35],"which":[36],"is":[37,46,92],"estimated":[38],"using":[39],"denoising":[40],"matching.":[42],"A":[43],"variance-preserving":[44],"implementation":[45],"then":[47,69],"applied":[48],"to":[49,121],"MNIST":[50],"images":[51],"number":[54],"6,":[55],"where":[56],"a":[57],"neural":[58],"network":[59],"estimates":[60],"added":[62],"noise":[63],"produces":[65],"recognizable":[66],"samples.":[67],"study":[70],"solution":[72],"an":[74,77],"as":[76,94],"It\u00f4":[78],"map":[79],"that":[80,111],"its":[83],"starting":[84],"state":[85,119],"Brownian":[87,127],"path.":[88],"backward":[90,114],"flow":[91],"introduced":[93],"inverse":[96],"this":[98],"map.":[100],"Numerical":[101],"examples":[102],"for":[103],"OU,":[105],"variance-preserving,":[106],"CIR":[108,133],"processes":[109],"show":[110,145],"numerical":[113],"equations":[115],"recover":[116],"initial":[118],"up":[120],"discretization":[122],"error":[123],"when":[124],"same":[126],"increments":[128],"are":[129],"used.":[130],"For":[131],"process,":[134],"Lamperti":[136],"transformation":[137],"considerably":[138],"improves":[139],"reconstruction":[141],"error.":[142],"These":[143],"results":[144],"relation":[147],"between":[148],"viewpoints":[153],"how":[155],"they":[156],"answer":[157],"different":[158],"questions.":[159]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-12T00:00:00"}
