{"id":"https://openalex.org/W4385327881","doi":"https://doi.org/10.3390/e28030351","title":"MCMC Correction of Score-Based Diffusion Models for Model Composition","display_name":"MCMC Correction of Score-Based Diffusion Models for Model Composition","publication_year":2026,"publication_date":"2026-03-20","ids":{"openalex":"https://openalex.org/W4385327881","doi":"https://doi.org/10.3390/e28030351","pmid":"https://pubmed.ncbi.nlm.nih.gov/41900004"},"language":"en","primary_location":{"id":"doi:10.3390/e28030351","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e28030351","pdf_url":"https://www.mdpi.com/1099-4300/28/3/351/pdf","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/28/3/351/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Anders Sj\u00f6berg","orcid":"https://orcid.org/0009-0001-1185-5018"},"institutions":[{"id":"https://openalex.org/I4210139723","display_name":"Fraunhofer Chalmers Research Centre for Industrial Mathematics","ror":"https://ror.org/03tqh5n18","country_code":"SE","type":"nonprofit","lineage":["https://openalex.org/I4210139723","https://openalex.org/I4923324"]},{"id":"https://openalex.org/I66862912","display_name":"Chalmers University of Technology","ror":"https://ror.org/040wg7k59","country_code":"SE","type":"education","lineage":["https://openalex.org/I66862912"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Anders Sj\u00f6berg","raw_affiliation_strings":["Department of Electrical Engineering, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden","Fraunhofer-Chalmers Centre, SE-412 88 Gothenburg, Sweden"],"raw_orcid":"https://orcid.org/0009-0001-1185-5018","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden","institution_ids":["https://openalex.org/I66862912"]},{"raw_affiliation_string":"Fraunhofer-Chalmers Centre, SE-412 88 Gothenburg, Sweden","institution_ids":["https://openalex.org/I4210139723"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032339540","display_name":"Jakob Lindqvist","orcid":"https://orcid.org/0000-0003-2790-8775"},"institutions":[{"id":"https://openalex.org/I66862912","display_name":"Chalmers University of Technology","ror":"https://ror.org/040wg7k59","country_code":"SE","type":"education","lineage":["https://openalex.org/I66862912"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Jakob Lindqvist","raw_affiliation_strings":["Department of Electrical Engineering, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden"],"raw_orcid":"https://orcid.org/0000-0003-2790-8775","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden","institution_ids":["https://openalex.org/I66862912"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032487854","display_name":"Magnus \u00d6nnheim","orcid":"https://orcid.org/0000-0002-5067-704X"},"institutions":[{"id":"https://openalex.org/I4210139723","display_name":"Fraunhofer Chalmers Research Centre for Industrial Mathematics","ror":"https://ror.org/03tqh5n18","country_code":"SE","type":"nonprofit","lineage":["https://openalex.org/I4210139723","https://openalex.org/I4923324"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Magnus \u00d6nnheim","raw_affiliation_strings":["Fraunhofer-Chalmers Centre, SE-412 88 Gothenburg, Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fraunhofer-Chalmers Centre, SE-412 88 Gothenburg, Sweden","institution_ids":["https://openalex.org/I4210139723"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051529023","display_name":"Mats Jirstrand","orcid":"https://orcid.org/0000-0002-6612-8037"},"institutions":[{"id":"https://openalex.org/I4210139723","display_name":"Fraunhofer Chalmers Research Centre for Industrial Mathematics","ror":"https://ror.org/03tqh5n18","country_code":"SE","type":"nonprofit","lineage":["https://openalex.org/I4210139723","https://openalex.org/I4923324"]},{"id":"https://openalex.org/I66862912","display_name":"Chalmers University of Technology","ror":"https://ror.org/040wg7k59","country_code":"SE","type":"education","lineage":["https://openalex.org/I66862912"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Mats Jirstrand","raw_affiliation_strings":["Department of Electrical Engineering, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden","Fraunhofer-Chalmers Centre, SE-412 88 Gothenburg, Sweden"],"raw_orcid":"https://orcid.org/0000-0002-6612-8037","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden","institution_ids":["https://openalex.org/I66862912"]},{"raw_affiliation_string":"Fraunhofer-Chalmers Centre, SE-412 88 Gothenburg, Sweden","institution_ids":["https://openalex.org/I4210139723"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029413988","display_name":"Lennart Svensson","orcid":"https://orcid.org/0000-0003-0206-9186"},"institutions":[{"id":"https://openalex.org/I66862912","display_name":"Chalmers University of Technology","ror":"https://ror.org/040wg7k59","country_code":"SE","type":"education","lineage":["https://openalex.org/I66862912"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Lennart Svensson","raw_affiliation_strings":["Department of Electrical Engineering, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden"],"raw_orcid":"https://orcid.org/0000-0003-0206-9186","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden","institution_ids":["https://openalex.org/I66862912"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00223427,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"28","issue":"3","first_page":"351","last_page":"351"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9455999732017517,"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"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9455999732017517,"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"}},{"id":"https://openalex.org/T11948","display_name":"Machine Learning in Materials Science","score":0.9445000290870667,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/markov-chain-monte-carlo","display_name":"Markov chain Monte Carlo","score":0.8275527358055115},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6441199779510498},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.5586893558502197},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.5556831955909729},{"id":"https://openalex.org/keywords/sample","display_name":"Sample (material)","score":0.5458614230155945},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.5352713465690613},{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.5141065716743469},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4722945988178253},{"id":"https://openalex.org/keywords/importance-sampling","display_name":"Importance sampling","score":0.4329875409603119},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.3666524291038513},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.3638247847557068},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2239525020122528},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07481682300567627}],"concepts":[{"id":"https://openalex.org/C111350023","wikidata":"https://www.wikidata.org/wiki/Q1191869","display_name":"Markov chain Monte Carlo","level":3,"score":0.8275527358055115},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6441199779510498},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.5586893558502197},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.5556831955909729},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.5458614230155945},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.5352713465690613},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.5141065716743469},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4722945988178253},{"id":"https://openalex.org/C52740198","wikidata":"https://www.wikidata.org/wiki/Q1539564","display_name":"Importance sampling","level":3,"score":0.4329875409603119},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3666524291038513},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.3638247847557068},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2239525020122528},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07481682300567627},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.3390/e28030351","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e28030351","pdf_url":"https://www.mdpi.com/1099-4300/28/3/351/pdf","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:41900004","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/41900004","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:arXiv.org:2307.14012","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2307.14012","pdf_url":"https://arxiv.org/pdf/2307.14012","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:doaj.org/article:61ba11e817d743fa87cafd2125e55349","is_oa":true,"landing_page_url":"https://doaj.org/article/61ba11e817d743fa87cafd2125e55349","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 28, Iss 3, p 351 (2026)","raw_type":"article"},{"id":"pmh:oai:pubmedcentral.nih.gov:13025405","is_oa":true,"landing_page_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC13025405/","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"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":"Entropy (Basel)","raw_type":"Text"},{"id":"doi:10.48550/arxiv.2307.14012","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2307.14012","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:10.3390/e28030351","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e28030351","pdf_url":"https://www.mdpi.com/1099-4300/28/3/351/pdf","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Affordable and clean energy","score":0.9100000262260437,"id":"https://metadata.un.org/sdg/7"}],"awards":[{"id":"https://openalex.org/G8869864247","display_name":null,"funder_award_id":"2022-06725","funder_id":"https://openalex.org/F4320322581","funder_display_name":"Vetenskapsr\u00e5det"}],"funders":[{"id":"https://openalex.org/F4320322327","display_name":"Knut och Alice Wallenbergs Stiftelse","ror":"https://ror.org/004hzzk67"},{"id":"https://openalex.org/F4320322581","display_name":"Vetenskapsr\u00e5det","ror":"https://ror.org/03zttf063"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4385327881.pdf","grobid_xml":"https://content.openalex.org/works/W4385327881.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W4311887664","https://openalex.org/W4381332772","https://openalex.org/W4386065790","https://openalex.org/W7133201052","https://openalex.org/W2150884987","https://openalex.org/W2116064496","https://openalex.org/W4312824283","https://openalex.org/W1556278552","https://openalex.org/W2059448777","https://openalex.org/W2056760934","https://openalex.org/W2138309709","https://openalex.org/W2542898981","https://openalex.org/W1983452151","https://openalex.org/W1567512734","https://openalex.org/W1513873506","https://openalex.org/W2007339694","https://openalex.org/W2108598243","https://openalex.org/W3034429256"],"related_works":["https://openalex.org/W2151689585","https://openalex.org/W2380816257","https://openalex.org/W3087071515","https://openalex.org/W4283726152","https://openalex.org/W1525770572","https://openalex.org/W1485888979","https://openalex.org/W2742914308","https://openalex.org/W2330004501","https://openalex.org/W2017089693","https://openalex.org/W2703295919"],"abstract_inverted_index":{"Diffusion":[0],"models":[1,60,137],"can":[2,46],"be":[3],"parameterized":[4],"in":[5,52,93],"terms":[6],"of":[7,55,86,126,134,152,171],"either":[8],"score":[9,113,128],"or":[10],"energy":[11,14,39,98,183],"function.":[12,129],"The":[13],"parameterization":[15,114],"is":[16],"attractive":[17],"as":[18,24,149],"it":[19],"enables":[20],"sampling":[21,49,102],"procedures":[22],"such":[23],"Markov":[25],"Chain":[26],"Monte":[27],"Carlo":[28],"(MCMC)":[29],"that":[30,164],"incorporates":[31],"a":[32,83,117],"Metropolis-Hastings":[33],"(MH)":[34],"correction":[35],"step":[36],"based":[37,122],"on":[38,72,123,157],"differences":[40],"between":[41],"proposed":[42],"samples.":[43],"Such":[44],"corrections":[45],"significantly":[47],"improve":[48],"quality,":[50],"particularly":[51],"the":[53,73,127,132,141],"context":[54],"model":[56],"composition,":[57],"where":[58],"pre-trained":[59,87],"are":[61,76],"combined":[62],"to":[63,174],"generate":[64],"samples":[65],"from":[66],"novel":[67,118],"distributions.":[68],"Score-based":[69],"diffusion":[70,136],"models,":[71,179],"other":[74],"hand,":[75],"more":[77],"widely":[78],"adopted":[79],"and":[80,115,159],"come":[81],"with":[82,144,177],"rich":[84],"ecosystem":[85],"models.":[88],"However,":[89],"they":[90],"do":[91],"not,":[92],"general,":[94],"define":[95],"an":[96,150],"underlying":[97],"function,":[99],"making":[100],"MH-based":[101],"inapplicable.":[103],"In":[104],"this":[105,109],"work,":[106],"we":[107,162],"address":[108],"limitation":[110],"by":[111],"retaining":[112],"introducing":[116],"MH-like":[119,166],"acceptance":[120],"rule":[121],"line":[124],"integration":[125],"This":[130],"allows":[131],"reuse":[133],"existing":[135],"while":[138],"still":[139],"combining":[140],"reverse":[142],"process":[143],"various":[145],"MCMC":[146],"techniques,":[147],"viewed":[148],"instance":[151],"annealed":[153],"MCMC.":[154],"Through":[155],"experiments":[156],"synthetic":[158],"real-world":[160],"data,":[161],"show":[163],"our":[165],"samplers":[167],"yield":[168],"relative":[169],"improvements":[170],"similar":[172],"magnitude":[173],"those":[175],"observed":[176],"energy-based":[178],"without":[180],"requiring":[181],"explicit":[182],"parameterization.":[184]},"counts_by_year":[],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2023-07-28T00:00:00"}