{"id":"https://openalex.org/W4281626548","doi":"https://doi.org/10.48550/arxiv.2205.14987","title":"A Continuous Time Framework for Discrete Denoising Models","display_name":"A Continuous Time Framework for Discrete Denoising Models","publication_year":2022,"publication_date":"2022-05-30","ids":{"openalex":"https://openalex.org/W4281626548","doi":"https://doi.org/10.48550/arxiv.2205.14987"},"language":"en","primary_location":{"id":"pmh:oai:HAL:hal-03945474v1","doi":null,"is_oa":true,"landing_page_url":"https://hal.science/hal-03945474v1","pdf_url":"http://arxiv.org/pdf/2205.14987","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"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":"2023","raw_type":"info:eu-repo/semantics/preprint"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://arxiv.org/pdf/2205.14987","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064857767","display_name":"Andrew Thomas Campbell","orcid":"https://orcid.org/0000-0001-7394-7682","observed_orcids":["https://orcid.org/0000-0001-7394-7682"]},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Campbell, Andrew","raw_affiliation_strings":["Department of Statistics , University of Oxford , UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics , University of Oxford , UK","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056010406","display_name":"Joe Benton","orcid":"https://orcid.org/0000-0002-2103-6112","observed_orcids":["https://orcid.org/0000-0002-2103-6112"]},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Benton, Joe","raw_affiliation_strings":["Department of Statistics , University of Oxford , UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics , University of Oxford , UK","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050614717","display_name":"Valentin De Bortoli","orcid":"https://orcid.org/0000-0002-7163-5391","observed_orcids":["https://orcid.org/0000-0002-7163-5391"]},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I29607241","display_name":"\u00c9cole Normale Sup\u00e9rieure - PSL","ror":"https://ror.org/05a0dhs15","country_code":"FR","type":"other","lineage":["https://openalex.org/I2746051580","https://openalex.org/I29607241"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"De Bortoli, Valentin","raw_affiliation_strings":["CNRS ENS Ulm , Paris , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CNRS ENS Ulm , Paris , France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I29607241"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078631467","display_name":"Tom Rainforth","orcid":"https://orcid.org/0000-0001-7939-4230","observed_orcids":["https://orcid.org/0000-0001-7939-4230"]},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Rainforth, Tom","raw_affiliation_strings":["Department of Statistics , University of Oxford , UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics , University of Oxford , UK","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016007881","display_name":"George Deligiannidis","orcid":"https://orcid.org/0000-0002-0821-4607","observed_orcids":["https://orcid.org/0000-0002-0821-4607"]},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Deligiannidis, George","raw_affiliation_strings":["Department of Statistics , University of Oxford , UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics , University of Oxford , UK","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091677854","display_name":"Arnaud Doucet B","orcid":"https://orcid.org/0000-0002-7662-419X","observed_orcids":["https://orcid.org/0000-0002-7662-419X"]},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Doucet, Arnaud","raw_affiliation_strings":["Department of Statistics , University of Oxford , UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics , University of Oxford , UK","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":65,"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":0.513700008392334,"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":0.513700008392334,"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.2761000096797943,"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":0.07519999891519547,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/denoising-diffusion-probabilistic-models","display_name":"denoising diffusion probabilistic models","score":0.9160000085830688},{"id":"https://openalex.org/keywords/discrete-data","display_name":"discrete data","score":0.9010000228881836},{"id":"https://openalex.org/keywords/continuous-time-markov-chains","display_name":"continuous-time Markov chains","score":0.9710000157356262},{"id":"https://openalex.org/keywords/sampling-methods","display_name":"sampling methods","score":0.6079999804496765}],"concepts":[{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.6474924087524414},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6342825293540955},{"id":"https://openalex.org/C63584917","wikidata":"https://www.wikidata.org/wiki/Q333286","display_name":"Bounding overwatch","level":2,"score":0.5850622653961182},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5284067392349243},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.5145322680473328},{"id":"https://openalex.org/C163294075","wikidata":"https://www.wikidata.org/wiki/Q581861","display_name":"Noise reduction","level":2,"score":0.46671172976493835},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.4481024146080017},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.41835135221481323},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.41593384742736816},{"id":"https://openalex.org/C165696696","wikidata":"https://www.wikidata.org/wiki/Q11287","display_name":"Exploit","level":2,"score":0.4148738384246826},{"id":"https://openalex.org/C10184394","wikidata":"https://www.wikidata.org/wiki/Q5165491","display_name":"Continuous modelling","level":2,"score":0.4139374792575836},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33341777324676514},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.29605090618133545},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.21537813544273376},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.21047711372375488},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.16266599297523499},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:HAL:hal-03945474v1","doi":null,"is_oa":true,"landing_page_url":"https://hal.science/hal-03945474v1","pdf_url":"http://arxiv.org/pdf/2205.14987","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"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":"2023","raw_type":"info:eu-repo/semantics/preprint"},{"id":"pmh:oai:arXiv.org:2205.14987","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2205.14987","pdf_url":"https://arxiv.org/pdf/2205.14987","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.2205.14987","doi":"https://doi.org/10.48550/arxiv.2205.14987","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2205.14987","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-03945474v1","doi":null,"is_oa":true,"landing_page_url":"https://hal.science/hal-03945474v1","pdf_url":"http://arxiv.org/pdf/2205.14987","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"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":"2023","raw_type":"info:eu-repo/semantics/preprint"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1595280774","display_name":"JADE: Joint Academic Data science Endeavour - 2","funder_award_id":"EP/T022205/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G2363103010","display_name":null,"funder_award_id":"JADE2","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G4037990431","display_name":"Semantic Information Pursuit for Multimodal Data Analysis","funder_award_id":"EP/R013616/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G5777727104","display_name":null,"funder_award_id":"EP/R013616/1","funder_id":"https://openalex.org/F4320332972","funder_display_name":"Defence Science and Technology Laboratory"},{"id":"https://openalex.org/G6487001647","display_name":null,"funder_award_id":"T022205/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G8722502606","display_name":null,"funder_award_id":"EP/R034710","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G875582221","display_name":"EPSRC Centre for Doctoral Training in Modern Statistics and Statistical Machine Learning","funder_award_id":"EP/S023151/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G926698369","display_name":null,"funder_award_id":"R034710","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G965103402","display_name":"CoSInES (COmputational Statistical INference for Engineering and Security)","funder_award_id":"EP/R034710/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320306078","display_name":"U.S. Department of Defense","ror":"https://ror.org/0447fe631"},{"id":"https://openalex.org/F4320332972","display_name":"Defence Science and Technology Laboratory","ror":"https://ror.org/04jswqb94"},{"id":"https://openalex.org/F4320333591","display_name":"Multidisciplinary University Research Initiative","ror":null},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"},{"id":"https://openalex.org/F4320335334","display_name":"Defence Science and Technology Group","ror":null},{"id":"https://openalex.org/F4320337003","display_name":"Office of Defense Programs","ror":"https://ror.org/0447fe631"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4281626548.pdf","grobid_xml":"https://content.openalex.org/works/W4281626548.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W3168160162","https://openalex.org/W3202184706","https://openalex.org/W4225319995"],"related_works":["https://openalex.org/W4391631672","https://openalex.org/W7164914441","https://openalex.org/W7155000796","https://openalex.org/W4415795969","https://openalex.org/W7167619806","https://openalex.org/W4408272963","https://openalex.org/W7160125591","https://openalex.org/W7139143455","https://openalex.org/W4414687855","https://openalex.org/W4399401039"],"abstract_inverted_index":{"We":[0,50],"provide":[1],"the":[2,20,48,52,98,101,106],"first":[3],"complete":[4],"continuous":[5,44,65,85],"time":[6,27,45,66,79,86],"framework":[7,67],"for":[8,81],"denoising":[9],"diffusion":[10],"models":[11],"of":[12,47],"discrete":[13,78,82],"data.":[14,83],"This":[15],"is":[16],"achieved":[17],"by":[18],"formulating":[19],"forward":[21],"noising":[22],"process":[23,29],"and":[24,62,105],"corresponding":[25],"reverse":[26],"generative":[28],"as":[30],"Continuous":[31],"Time":[32],"Markov":[33],"Chains":[34],"(CTMCs).":[35],"The":[36,84],"model":[37],"can":[38,76],"be":[39],"efficiently":[40],"trained":[41],"using":[42,56],"a":[43,93],"version":[46],"ELBO.":[49],"simulate":[51],"high":[53,70],"dimensional":[54],"CTMC":[55],"techniques":[57],"developed":[58],"in":[59],"chemical":[60],"physics":[61],"exploit":[63],"our":[64],"to":[68,91],"derive":[69,92],"performance":[71],"samplers":[72],"that":[73],"we":[74],"show":[75],"outperform":[77],"methods":[80],"treatment":[87],"also":[88],"enables":[89],"us":[90],"novel":[94],"theoretical":[95],"result":[96],"bounding":[97],"error":[99],"between":[100],"generated":[102],"sample":[103],"distribution":[104],"true":[107],"data":[108],"distribution.":[109]},"counts_by_year":[{"year":2026,"cited_by_count":13},{"year":2025,"cited_by_count":19},{"year":2024,"cited_by_count":14},{"year":2023,"cited_by_count":16},{"year":2022,"cited_by_count":3}],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2025-10-10T00:00:00"}
