{"id":"https://openalex.org/W7140485343","doi":"https://doi.org/10.48550/arxiv.2603.24594","title":"Polynomial Speedup in Diffusion Models with the Multilevel Euler-Maruyama Method","display_name":"Polynomial Speedup in Diffusion Models with the Multilevel Euler-Maruyama Method","publication_year":2026,"publication_date":"2026-03-25","ids":{"openalex":"https://openalex.org/W7140485343","doi":"https://doi.org/10.48550/arxiv.2603.24594"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.24594","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.24594","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":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.24594","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102318017","display_name":"Arthur Paul Jacot","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Jacot, Arthur","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5102318017"],"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.17829999327659607,"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"}},"topics":[{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.17829999327659607,"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/T10067","display_name":"Stochastic processes and financial applications","score":0.14139999449253082,"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/T11304","display_name":"Advanced Neuroimaging Techniques and Applications","score":0.0957999974489212,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/speedup","display_name":"Speedup","score":0.6468999981880188},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.6360999941825867},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.6207000017166138},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.613099992275238},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.5878000259399414},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.571399986743927}],"concepts":[{"id":"https://openalex.org/C68339613","wikidata":"https://www.wikidata.org/wiki/Q1549489","display_name":"Speedup","level":2,"score":0.6468999981880188},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6360999941825867},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.6207000017166138},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.613099992275238},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.5878000259399414},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.571399986743927},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5552999973297119},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5066999793052673},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48750001192092896},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.47049999237060547},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4122999906539917},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4077000021934509},{"id":"https://openalex.org/C52740198","wikidata":"https://www.wikidata.org/wiki/Q1539564","display_name":"Importance sampling","level":3,"score":0.3982999920845032},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.38580000400543213},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.25609999895095825},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.2535000145435333}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.24594","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.24594","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":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.24594","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.24594","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":"article"},"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":{"We":[0],"introduce":[1],"the":[2,20,35,43,48,52,74,77,84,98,101,109,112,117,137,144,163],"Multilevel":[3],"Euler-Maruyama":[4],"(ML-EM)":[5],"method":[6],"compute":[7,64],"solutions":[8],"of":[9,16,34,42,76,88,108,114,126,139,143,192],"SDEs":[10],"and":[11,26,39,129],"ODEs":[12],"using":[13],"a":[14,31,105,140,172,178],"range":[15],"approximators":[17],"$f^1,\\dots,f^k$":[18],"to":[19,65,96,133,156,167],"drift":[21,49],"$f$":[22],"with":[23,79,136],"increasing":[24,127],"accuracy":[25],"computational":[27],"cost,":[28],"only":[29],"requiring":[30],"few":[32],"evaluations":[33,41],"most":[36],"accurate":[37],"$f^k$":[38],"many":[40],"less":[44],"costly":[45],"$f^1,\\dots,f^{k-1}$.":[46],"If":[47],"lies":[50],"in":[51,186],"so-called":[53],"Harder":[54],"than":[55],"Monte":[56],"Carlo":[57],"(HTMC)":[58],"regime,":[59],"i.e.":[60],"it":[61,93],"requires":[62],"$\u03b5^{-\u03b3}$":[63,80],"be":[66],"$\u03b5$-approximated":[67],"for":[68,159],"some":[69],"$\u03b3>2$,":[70],"then":[71],"ML-EM":[72,130],"$\u03b5$-approximates":[73],"solution":[75],"SDE":[78,99],"compute,":[81],"improving":[82],"over":[83],"traditional":[85],"EM":[86],"rate":[87],"$\u03b5^{-\u03b3-1}$.":[89],"In":[90,111],"other":[91],"terms":[92],"allows":[94,131],"us":[95,132],"solve":[97],"at":[100],"same":[102],"cost":[103],"as":[104],"single":[106,141],"evaluation":[107,142],"drift.":[110],"context":[113],"diffusion":[115],"models,":[116],"different":[118],"levels":[119],"$f^{1},\\dots,f^{k}$":[120],"are":[121],"obtained":[122],"by":[123],"training":[124],"UNets":[125],"sizes,":[128],"perform":[134],"sampling":[135],"equivalent":[138],"largest":[145],"UNet.":[146],"Our":[147],"numerical":[148],"experiments":[149],"confirm":[150],"our":[151],"theory:":[152],"we":[153,170,181],"obtain":[154],"up":[155],"fourfold":[157],"speedups":[158,185],"image":[160],"generation":[161],"on":[162],"CelebA":[164],"dataset":[165],"downscaled":[166],"64x64,":[168],"where":[169],"measure":[171],"$\u03b3\\approx2.5$.":[173],"Given":[174],"that":[175],"this":[176],"is":[177],"polynomial":[179],"speedup,":[180],"expect":[182],"even":[183],"stronger":[184],"practical":[187],"applications":[188],"which":[189],"involve":[190],"orders":[191],"magnitude":[193],"larger":[194],"networks.":[195]},"counts_by_year":[],"updated_date":"2026-03-27T06:05:27.210665","created_date":"2026-03-27T00:00:00"}