{"id":"https://openalex.org/W7128366236","doi":"https://doi.org/10.48550/arxiv.2602.06621","title":"Infinite-dimensional generative diffusions via Doob's h-transform","display_name":"Infinite-dimensional generative diffusions via Doob's h-transform","publication_year":2026,"publication_date":"2026-02-06","ids":{"openalex":"https://openalex.org/W7128366236","doi":"https://doi.org/10.48550/arxiv.2602.06621"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2602.06621","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2602.06621","pdf_url":"https://arxiv.org/pdf/2602.06621","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2602.06621","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5114368264","display_name":"Thorben Pieper-Sethmacher","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pieper-Sethmacher, Thorben","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5041259048","display_name":"Daniel Paulin","orcid":"https://orcid.org/0000-0001-7837-6452","observed_orcids":["https://orcid.org/0000-0001-7837-6452"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Paulin, Daniel","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":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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.2782999873161316,"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":0.2782999873161316,"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":0.2531999945640564,"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.21040000021457672,"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/generative-diffusion-models","display_name":"generative diffusion models","score":0.9729999899864197},{"id":"https://openalex.org/keywords/infinite-dimensional-diffusions","display_name":"infinite-dimensional diffusions","score":0.7929999828338623},{"id":"https://openalex.org/keywords/score-matching","display_name":"score matching","score":0.8759999871253967},{"id":"https://openalex.org/keywords/time-reversal","display_name":"time reversal","score":0.5580000281333923},{"id":"https://openalex.org/keywords/diffusion-approximation","display_name":"diffusion approximation","score":0.36000001430511475}],"concepts":[{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.7573000192642212},{"id":"https://openalex.org/C2780598303","wikidata":"https://www.wikidata.org/wiki/Q65921492","display_name":"Flexibility (engineering)","level":2,"score":0.6269999742507935},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6115999817848206},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.5432000160217285},{"id":"https://openalex.org/C167966045","wikidata":"https://www.wikidata.org/wiki/Q5532625","display_name":"Generative model","level":3,"score":0.5218999981880188},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.5115000009536743},{"id":"https://openalex.org/C68710425","wikidata":"https://www.wikidata.org/wiki/Q5275442","display_name":"Diffusion process","level":3,"score":0.49950000643730164},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4681999981403351},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.46380001306533813},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4291999936103821},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.4239000082015991},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4025999903678894},{"id":"https://openalex.org/C85847156","wikidata":"https://www.wikidata.org/wiki/Q59015987","display_name":"Verifiable secret sharing","level":3,"score":0.382999986410141},{"id":"https://openalex.org/C39890363","wikidata":"https://www.wikidata.org/wiki/Q36108","display_name":"Generative grammar","level":2,"score":0.3774000108242035},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.35120001435279846},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.34860000014305115},{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.3345000147819519},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.32989999651908875},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.3276999890804291},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.3125},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.30869999527931213},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.27869999408721924},{"id":"https://openalex.org/C201779956","wikidata":"https://www.wikidata.org/wiki/Q5426803","display_name":"Ergodicity","level":2,"score":0.2770000100135803},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.2727000117301941},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.26420000195503235},{"id":"https://openalex.org/C177769412","wikidata":"https://www.wikidata.org/wiki/Q278090","display_name":"Prior probability","level":3,"score":0.25870001316070557},{"id":"https://openalex.org/C55350006","wikidata":"https://www.wikidata.org/wiki/Q237193","display_name":"Exponential distribution","level":2,"score":0.25679999589920044},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.251800000667572}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2602.06621","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2602.06621","pdf_url":"https://arxiv.org/pdf/2602.06621","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2602.06621","doi":"https://doi.org/10.48550/arxiv.2602.06621","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.06621","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2602.06621","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2602.06621","pdf_url":"https://arxiv.org/pdf/2602.06621","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1482925484","display_name":null,"funder_award_id":"Tier 1","funder_id":"https://openalex.org/F4320320751","funder_display_name":"Ministry of Education - Singapore"}],"funders":[{"id":"https://openalex.org/F4320320751","display_name":"Ministry of Education - Singapore","ror":"https://ror.org/01kcva023"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7128366236.pdf","grobid_xml":"https://content.openalex.org/works/W7128366236.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W1531413759","https://openalex.org/W1970611947","https://openalex.org/W2138565515","https://openalex.org/W2150662455","https://openalex.org/W3126517808","https://openalex.org/W3207146706","https://openalex.org/W4229459060","https://openalex.org/W4284958228","https://openalex.org/W4294294771","https://openalex.org/W4296957262","https://openalex.org/W4383860788","https://openalex.org/W4389821458","https://openalex.org/W4390214920","https://openalex.org/W4407091863","https://openalex.org/W6967059742","https://openalex.org/W7123501293","https://openalex.org/W7126902350"],"related_works":["https://openalex.org/W4321471992","https://openalex.org/W4411469115","https://openalex.org/W4407091863","https://openalex.org/W4310743572","https://openalex.org/W7126063692","https://openalex.org/W7172511681","https://openalex.org/W7140166243","https://openalex.org/W7221578194","https://openalex.org/W7123501293","https://openalex.org/W4406961433"],"abstract_inverted_index":{"This":[0],"paper":[1],"introduces":[2],"a":[3,24,27,95],"rigorous":[4],"framework":[5],"for":[6],"defining":[7],"generative":[8],"diffusion":[9,29,60],"models":[10],"in":[11,58],"infinite":[12],"dimensions":[13],"via":[14],"Doob's":[15],"h-transform.":[16],"Rather":[17],"than":[18],"relying":[19],"on":[20,102],"time":[21],"reversal":[22],"of":[23,40],"noising":[25],"process,":[26],"reference":[28],"is":[30,64],"forced":[31,84],"towards":[32],"the":[33,51,59,75,83,87],"target":[34,76],"distribution":[35],"by":[36,93],"an":[37],"exponential":[38],"change":[39],"measure.":[41],"Compared":[42],"to":[43,50,74],"existing":[44],"methodology,":[45],"this":[46],"approach":[47],"readily":[48],"generalises":[49],"infinite-dimensional":[52],"setting,":[53],"hence":[54],"offering":[55],"greater":[56],"flexibility":[57],"model.":[61],"The":[62],"construction":[63],"derived":[65],"rigorously":[66],"under":[67,86],"verifiable":[68],"conditions,":[69],"and":[70,98,105],"bounds":[71],"with":[72],"respect":[73],"measure":[77,89],"are":[78],"established.":[79],"We":[80],"show":[81],"that":[82],"process":[85],"changed":[88],"can":[90],"be":[91],"approximated":[92],"minimising":[94],"score-matching":[96],"objective":[97],"validate":[99],"our":[100],"method":[101],"both":[103],"synthetic":[104],"real":[106],"data.":[107]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-02-10T00:00:00"}