{"id":"https://openalex.org/W7216532091","doi":"https://doi.org/10.48550/arxiv.2610.02081","title":"Wasserstein Gradient Flows and Forward-Only Diffusion Are Not Enough for Multimodal Sampling","display_name":"Wasserstein Gradient Flows and Forward-Only Diffusion Are Not Enough for Multimodal Sampling","publication_year":2026,"publication_date":"2026-10-01","ids":{"openalex":"https://openalex.org/W7216532091","doi":"https://doi.org/10.48550/arxiv.2610.02081"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.02081","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02081","pdf_url":"https://arxiv.org/pdf/2610.02081","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":"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/2610.02081","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5139664989","display_name":"Daniel McBride","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I1343871089","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1343871089","https://openalex.org/I198811213","https://openalex.org/I4210120050"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"McBride, Daniel","raw_affiliation_strings":["Los Alamos National Laboratory , Los Alamos , NM 87545 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Los Alamos National Laboratory , Los Alamos , NM 87545 , USA","institution_ids":["https://openalex.org/I1343871089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037158484","display_name":"Pratik Khandagale","orcid":"https://orcid.org/0000-0002-3105-1439","observed_orcids":["https://orcid.org/0000-0002-3105-1439"]},"institutions":[{"id":"https://openalex.org/I1343871089","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1343871089","https://openalex.org/I198811213","https://openalex.org/I4210120050"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Khandagale, Pratik","raw_affiliation_strings":["Los Alamos National Laboratory , Los Alamos , NM 87545 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Los Alamos National Laboratory , Los Alamos , NM 87545 , USA","institution_ids":["https://openalex.org/I1343871089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5154983608","display_name":"Cristina Garcia-Cardona","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I1343871089","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1343871089","https://openalex.org/I198811213","https://openalex.org/I4210120050"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Garcia-Cardona, Cristina","raw_affiliation_strings":["Los Alamos National Laboratory , Los Alamos , NM 87545 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Los Alamos National Laboratory , Los Alamos , NM 87545 , USA","institution_ids":["https://openalex.org/I1343871089"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070331303","display_name":"Yen Ting Lin","orcid":"https://orcid.org/0000-0001-6893-8423","observed_orcids":["https://orcid.org/0000-0001-6893-8423"]},"institutions":[{"id":"https://openalex.org/I1343871089","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1343871089","https://openalex.org/I198811213","https://openalex.org/I4210120050"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lin, Yen Ting","raw_affiliation_strings":["Los Alamos National Laboratory , Los Alamos , NM 87545 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Los Alamos National Laboratory , Los Alamos , NM 87545 , USA","institution_ids":["https://openalex.org/I1343871089"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I1343871089"],"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9980000257492065,"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":0.9980000257492065,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.0006000000284984708,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":9.999999747378752e-05,"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/wasserstein-gradient-flow","display_name":"Wasserstein gradient flow","score":0.9639999866485596},{"id":"https://openalex.org/keywords/metastability","display_name":"metastability","score":0.6830000281333923},{"id":"https://openalex.org/keywords/mixing-time","display_name":"mixing time","score":0.7450000047683716},{"id":"https://openalex.org/keywords/mean-first-passage-time","display_name":"mean first passage time","score":0.8980000019073486},{"id":"https://openalex.org/keywords/spectral-gap","display_name":"spectral gap","score":0.8659999966621399},{"id":"https://openalex.org/keywords/nonequilibrium-statistical-mechanics","display_name":"nonequilibrium statistical mechanics","score":0.7319999933242798},{"id":"https://openalex.org/keywords/sampling-algorithms","display_name":"sampling algorithms","score":0.30300000309944153}],"concepts":[{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.7218000292778015},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.6328999996185303},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.5737000107765198},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.5382999777793884},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5249000191688538},{"id":"https://openalex.org/C138777275","wikidata":"https://www.wikidata.org/wiki/Q6884054","display_name":"Mixing (physics)","level":2,"score":0.47909998893737793},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4767000079154968},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4659999907016754},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.45840001106262207},{"id":"https://openalex.org/C2778114796","wikidata":"https://www.wikidata.org/wiki/Q7575194","display_name":"Spectral gap","level":2,"score":0.4553999900817871},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.39899998903274536},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.39800000190734863},{"id":"https://openalex.org/C89464430","wikidata":"https://www.wikidata.org/wiki/Q849516","display_name":"Metastability","level":2,"score":0.39259999990463257},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37929999828338623},{"id":"https://openalex.org/C52740198","wikidata":"https://www.wikidata.org/wiki/Q1539564","display_name":"Importance sampling","level":3,"score":0.3643999993801117},{"id":"https://openalex.org/C2777317252","wikidata":"https://www.wikidata.org/wiki/Q18393516","display_name":"Rare events","level":2,"score":0.35499998927116394},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.349700003862381},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.34769999980926514},{"id":"https://openalex.org/C206654554","wikidata":"https://www.wikidata.org/wiki/Q5374247","display_name":"Empirical measure","level":2,"score":0.3463999927043915},{"id":"https://openalex.org/C68710425","wikidata":"https://www.wikidata.org/wiki/Q5275442","display_name":"Diffusion process","level":3,"score":0.3292999863624573},{"id":"https://openalex.org/C167879884","wikidata":"https://www.wikidata.org/wiki/Q727568","display_name":"Balanced flow","level":2,"score":0.3116999864578247},{"id":"https://openalex.org/C74859849","wikidata":"https://www.wikidata.org/wiki/Q2466686","display_name":"Non-equilibrium thermodynamics","level":2,"score":0.31029999256134033},{"id":"https://openalex.org/C164602753","wikidata":"https://www.wikidata.org/wiki/Q567544","display_name":"Anomalous diffusion","level":3,"score":0.2948000133037567},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.29339998960494995},{"id":"https://openalex.org/C180188523","wikidata":"https://www.wikidata.org/wiki/Q574576","display_name":"Exponential decay","level":2,"score":0.27230000495910645},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.27149999141693115},{"id":"https://openalex.org/C57945734","wikidata":"https://www.wikidata.org/wiki/Q7977941","display_name":"Weak convergence","level":3,"score":0.26499998569488525},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.263700008392334},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.2556999921798706},{"id":"https://openalex.org/C55350006","wikidata":"https://www.wikidata.org/wiki/Q237193","display_name":"Exponential distribution","level":2,"score":0.2524999976158142},{"id":"https://openalex.org/C68387754","wikidata":"https://www.wikidata.org/wiki/Q7271585","display_name":"Schedule","level":2,"score":0.25119999051094055},{"id":"https://openalex.org/C75438885","wikidata":"https://www.wikidata.org/wiki/Q3403615","display_name":"Large deviations theory","level":2,"score":0.25060001015663147}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.02081","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02081","pdf_url":"https://arxiv.org/pdf/2610.02081","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.02081","doi":"https://doi.org/10.48550/arxiv.2610.02081","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.02081","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:2610.02081","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02081","pdf_url":"https://arxiv.org/pdf/2610.02081","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1017065088","display_name":null,"funder_award_id":"#89233218CNA000001","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G1279347439","display_name":null,"funder_award_id":"89233218CNA 000001","funder_id":"https://openalex.org/F4320338304","funder_display_name":"Los Alamos National Laboratory"},{"id":"https://openalex.org/G2356915424","display_name":null,"funder_award_id":"89233218CNA000001","funder_id":"https://openalex.org/F4320337547","funder_display_name":"Laboratory Directed Research and Development"},{"id":"https://openalex.org/G6410514744","display_name":null,"funder_award_id":"89233218C-NA000001","funder_id":"https://openalex.org/F4320332369","funder_display_name":"National Nuclear Security Administration"},{"id":"https://openalex.org/G6563880843","display_name":null,"funder_award_id":"No.  89233218CNA000001","funder_id":"https://openalex.org/F4320332369","funder_display_name":"National Nuclear Security Administration"}],"funders":[{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320332369","display_name":"National Nuclear Security Administration","ror":"https://ror.org/03sk1we31"},{"id":"https://openalex.org/F4320337547","display_name":"Laboratory Directed Research and Development","ror":"https://ror.org/01e41cf67"},{"id":"https://openalex.org/F4320338304","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7216532091.pdf","grobid_xml":"https://content.openalex.org/works/W7216532091.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W1840847274","https://openalex.org/W4221152681"],"related_works":["https://openalex.org/W4404986219","https://openalex.org/W6958057370","https://openalex.org/W7160320586","https://openalex.org/W7196966431","https://openalex.org/W7129494267","https://openalex.org/W4403816308","https://openalex.org/W2946334818","https://openalex.org/W7220963319","https://openalex.org/W3169190295","https://openalex.org/W7127625476"],"abstract_inverted_index":{"There":[0],"has":[1],"been":[2],"a":[3,200],"proliferation":[4],"of":[5,24,109,166,203,216],"sampling":[6,79,207],"algorithms":[7],"based":[8],"on":[9],"Wasserstein":[10],"gradient":[11],"flows":[12],"(WGF)":[13],"and":[14,70,81,90,96,118,125,141,205,212],"forward-only":[15],"diffusion":[16,84],"processes":[17],"(FODP),":[18],"often":[19,48],"accompanied":[20],"by":[21,50],"theoretical":[22],"guarantees":[23,33],"exponentially":[25,132,185],"fast":[26],"convergence":[27],"to":[28,188],"the":[29,66,76,86,93,146,163,167],"target":[30],"distribution.":[31],"These":[32],"are":[34],"frequently":[35],"interpreted":[36],"as":[37],"evidence":[38],"that":[39,58,75,127,156,197],"such":[40],"methods":[41],"can":[42,130,183],"efficiently":[43],"sample":[44],"complex":[45],"multimodal":[46,222],"distributions,":[47],"supported":[49],"empirical":[51],"results.":[52],"In":[53],"this":[54,59,107,198],"work,":[55],"we":[56,73,154],"argue":[57,196],"interpretation":[60],"is":[61,173],"fundamentally":[62,217],"misleading.":[63],"By":[64],"invoking":[65],"Jordan-Kinderlehrer-Otto":[67],"(JKO)":[68],"scheme":[69],"Otto":[71],"calculus,":[72],"establish":[74],"canonical":[77],"WGF":[78],"dynamics":[80],"overdamped":[82],"forward":[83],"share":[85],"same":[87,94],"density":[88],"evolution":[89],"therefore":[91],"inherit":[92],"metastability":[95],"slow-mixing":[97],"phenomena":[98],"long":[99,133,186],"understood":[100],"in":[101,208],"nonequilibrium":[102],"statistical":[103],"physics.":[104],"We":[105,195],"analyze":[106],"family":[108],"samplers":[110],"using":[111],"two":[112],"complementary":[113],"tools":[114],"--":[115,124],"spectral":[116,139],"analysis":[117,123],"mean":[119],"first-passage":[120],"time":[121],"(MFPT)":[122],"show":[126],"well-separated":[128,193],"multimodality":[129],"induce":[131],"mixing":[134],"times":[135,187],"associated":[136],"with":[137],"small":[138],"gaps":[140],"rare":[142],"inter-mode":[143],"transitions.":[144],"For":[145],"commonly":[147],"adopted":[148],"log-linear":[149],"annealing":[150],"schedule":[151],"studied":[152],"here,":[153],"find":[155],"introducing":[157],"intermediate":[158],"distributions":[159],"does":[160],"not":[161],"remove":[162],"exponential":[164],"scaling":[165],"total":[168],"transport":[169,181,189],"time.":[170],"The":[171],"limitation":[172,202],"structural":[174],"rather":[175],"than":[176],"implementation-specific:":[177],"purely":[178],"local,":[179],"gradient-driven":[180],"mechanisms":[182,219],"require":[184],"probability":[190],"mass":[191],"across":[192],"modes.":[194],"represents":[199],"fundamental":[201],"WGF-":[204],"FODP-based":[206],"their":[209],"standard":[210],"forms,":[211],"motivates":[213],"future":[214],"development":[215],"nonlocal":[218],"for":[220],"efficient":[221],"sampling.":[223]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-03T00:00:00"}