{"id":"https://openalex.org/W7130724798","doi":"https://doi.org/10.48550/arxiv.2602.17211","title":"MGD: Moment Guided Diffusion for Maximum Entropy Generation","display_name":"MGD: Moment Guided Diffusion for Maximum Entropy Generation","publication_year":2026,"publication_date":"2026-02-19","ids":{"openalex":"https://openalex.org/W7130724798","doi":"https://doi.org/10.48550/arxiv.2602.17211"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2602.17211","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2602.17211","pdf_url":"https://arxiv.org/pdf/2602.17211","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2602.17211","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5097330888","display_name":"Etienne Lempereur","orcid":"https://orcid.org/0009-0005-0257-5697","observed_orcids":["https://orcid.org/0009-0005-0257-5697"]},"institutions":[{"id":"https://openalex.org/I2746051580","display_name":"Universit\u00e9 Paris Sciences et Lettres","ror":"https://ror.org/013cjyk83","country_code":"FR","type":"education","lineage":["https://openalex.org/I2746051580"]},{"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"]},{"id":"https://openalex.org/I4210161954","display_name":"D\u00e9partement d'Informatique","ror":"https://ror.org/05y6rqs46","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I2746051580","https://openalex.org/I29607241","https://openalex.org/I4210159245","https://openalex.org/I4210161954"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Lempereur, Etienne","raw_affiliation_strings":["D\u00e9partement d'informatique , ENS , Universit\u00e9 PSL , Paris , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"D\u00e9partement d'informatique , ENS , Universit\u00e9 PSL , Paris , France","institution_ids":["https://openalex.org/I2746051580","https://openalex.org/I29607241","https://openalex.org/I4210161954"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063233337","display_name":"Nathana\u00ebl Cuvelle-Magar","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I2746051580","display_name":"Universit\u00e9 Paris Sciences et Lettres","ror":"https://ror.org/013cjyk83","country_code":"FR","type":"education","lineage":["https://openalex.org/I2746051580"]},{"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"]},{"id":"https://openalex.org/I4210161954","display_name":"D\u00e9partement d'Informatique","ror":"https://ror.org/05y6rqs46","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I2746051580","https://openalex.org/I29607241","https://openalex.org/I4210159245","https://openalex.org/I4210161954"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Cuvelle--Magar, Nathana\u00ebl","raw_affiliation_strings":["D\u00e9partement d'informatique , ENS , Universit\u00e9 PSL , Paris , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"D\u00e9partement d'informatique , ENS , Universit\u00e9 PSL , Paris , France","institution_ids":["https://openalex.org/I2746051580","https://openalex.org/I29607241","https://openalex.org/I4210161954"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090299192","display_name":"Florentin Coeurdoux","orcid":"https://orcid.org/0000-0002-2100-1438","observed_orcids":["https://orcid.org/0000-0002-2100-1438"]},"institutions":[{"id":"https://openalex.org/I44713367","display_name":"Capital Fund Management (France)","ror":"https://ror.org/01kpwv903","country_code":"FR","type":"company","lineage":["https://openalex.org/I44713367"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Coeurdoux, Florentin","raw_affiliation_strings":["Capital Fund Management , Paris , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Capital Fund Management , Paris , France","institution_ids":["https://openalex.org/I44713367"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065086376","display_name":"St\u00e9phane Mallat","orcid":"https://orcid.org/0000-0001-5263-8960","observed_orcids":["https://orcid.org/0000-0001-5263-8960"]},"institutions":[{"id":"https://openalex.org/I187986737","display_name":"Coll\u00e8ge de France","ror":"https://ror.org/04ex24z53","country_code":"FR","type":"education","lineage":["https://openalex.org/I187986737"]},{"id":"https://openalex.org/I4387153999","display_name":"Flatiron Institute","ror":"https://ror.org/00sekdz59","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I4210107338","https://openalex.org/I4387153999"]}],"countries":["FR","US"],"is_corresponding":false,"raw_author_name":"Mallat, St\u00e9phane","raw_affiliation_strings":["Coll\u00e8ge de France , Paris , France","Flatiron Institute , New York , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Coll\u00e8ge de France , Paris , France","institution_ids":["https://openalex.org/I187986737"]},{"raw_affiliation_string":"Flatiron Institute , New York , USA","institution_ids":["https://openalex.org/I4387153999"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110999758","display_name":"Eric Vanden-Eijnden","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I36672615","display_name":"Courant Institute of Mathematical Sciences","ror":"https://ror.org/037tm7f56","country_code":"US","type":"education","lineage":["https://openalex.org/I36672615","https://openalex.org/I57206974"]},{"id":"https://openalex.org/I44713367","display_name":"Capital Fund Management (France)","ror":"https://ror.org/01kpwv903","country_code":"FR","type":"company","lineage":["https://openalex.org/I44713367"]},{"id":"https://openalex.org/I57206974","display_name":"New York University","ror":"https://ror.org/0190ak572","country_code":"US","type":"education","lineage":["https://openalex.org/I57206974"]}],"countries":["FR","US"],"is_corresponding":false,"raw_author_name":"Vanden-Eijnden, Eric","raw_affiliation_strings":["Courant Institute of Mathematical Sciences , New York University , New York , USA","ML Lab , Capital Fund Management , Paris , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Courant Institute of Mathematical Sciences , New York University , New York , USA","institution_ids":["https://openalex.org/I36672615","https://openalex.org/I57206974"]},{"raw_affiliation_string":"ML Lab , Capital Fund Management , Paris , France","institution_ids":["https://openalex.org/I44713367"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":8,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.36550000309944153,"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":0.36550000309944153,"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/T12261","display_name":"Statistical Mechanics and Entropy","score":0.326200008392334,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.11599999666213989,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/maximum-entropy","display_name":"maximum entropy","score":0.5210000276565552},{"id":"https://openalex.org/keywords/moment-restrictions","display_name":"moment constraints","score":0.7409999966621399},{"id":"https://openalex.org/keywords/diffusion-models","display_name":"diffusion models","score":0.8080000281333923},{"id":"https://openalex.org/keywords/stochastic-differential-equations","display_name":"stochastic differential equations","score":0.7889999747276306},{"id":"https://openalex.org/keywords/entropy-estimation","display_name":"entropy estimation","score":0.7429999709129333},{"id":"https://openalex.org/keywords/negentropy","display_name":"negentropy","score":0.7429999709129333},{"id":"https://openalex.org/keywords/wavelet-scattering","display_name":"wavelet scattering","score":0.6510000228881836},{"id":"https://openalex.org/keywords/financial-time-series","display_name":"financial time series","score":0.7749999761581421},{"id":"https://openalex.org/keywords/turbulence","display_name":"turbulent flow","score":0.9789999723434448},{"id":"https://openalex.org/keywords/uncertainty-quantification","display_name":"uncertainty quantification","score":0.7110000252723694},{"id":"https://openalex.org/keywords/high-dimensional-sampling","display_name":"high-dimensional sampling","score":0.4779999852180481}],"concepts":[{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.7141000032424927},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6078000068664551},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.5425999760627747},{"id":"https://openalex.org/C60507348","wikidata":"https://www.wikidata.org/wiki/Q6795892","display_name":"Maximum entropy probability distribution","level":3,"score":0.5333999991416931},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.516700029373169},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.4650999903678894},{"id":"https://openalex.org/C89735579","wikidata":"https://www.wikidata.org/wiki/Q6795894","display_name":"Maximum entropy spectral estimation","level":3,"score":0.4512999951839447},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.44530001282691956},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4424000084400177},{"id":"https://openalex.org/C166963901","wikidata":"https://www.wikidata.org/wiki/Q287251","display_name":"Kurtosis","level":2,"score":0.4350999891757965},{"id":"https://openalex.org/C118346863","wikidata":"https://www.wikidata.org/wiki/Q252552","display_name":"Negentropy","level":3,"score":0.4090000092983246},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.4065000116825104},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.3970000147819519},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37770000100135803},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.3140000104904175},{"id":"https://openalex.org/C61062188","wikidata":"https://www.wikidata.org/wiki/Q835065","display_name":"Second moment of area","level":2,"score":0.30640000104904175},{"id":"https://openalex.org/C124551494","wikidata":"https://www.wikidata.org/wiki/Q3055345","display_name":"Differential entropy","level":4,"score":0.3052000105381012},{"id":"https://openalex.org/C106752470","wikidata":"https://www.wikidata.org/wiki/Q1364826","display_name":"Joint entropy","level":3,"score":0.30489999055862427},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.29809999465942383},{"id":"https://openalex.org/C75438885","wikidata":"https://www.wikidata.org/wiki/Q3403615","display_name":"Large deviations theory","level":2,"score":0.2921999990940094},{"id":"https://openalex.org/C112401455","wikidata":"https://www.wikidata.org/wiki/Q178036","display_name":"Brownian motion","level":2,"score":0.2833000123500824},{"id":"https://openalex.org/C49775889","wikidata":"https://www.wikidata.org/wiki/Q6795896","display_name":"Maximum entropy thermodynamics","level":4,"score":0.2815000116825104},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.266400009393692},{"id":"https://openalex.org/C52740198","wikidata":"https://www.wikidata.org/wiki/Q1539564","display_name":"Importance sampling","level":3,"score":0.2621000111103058},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.26030001044273376},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.25600001215934753},{"id":"https://openalex.org/C22019652","wikidata":"https://www.wikidata.org/wiki/Q331309","display_name":"Overfitting","level":3,"score":0.2540999948978424},{"id":"https://openalex.org/C39943821","wikidata":"https://www.wikidata.org/wiki/Q506346","display_name":"Semimartingale","level":2,"score":0.2535000145435333},{"id":"https://openalex.org/C201779956","wikidata":"https://www.wikidata.org/wiki/Q5426803","display_name":"Ergodicity","level":2,"score":0.2522999942302704},{"id":"https://openalex.org/C142611142","wikidata":"https://www.wikidata.org/wiki/Q1433083","display_name":"R\u00e9nyi entropy","level":3,"score":0.2517000138759613}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:2602.17211","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2602.17211","pdf_url":"https://arxiv.org/pdf/2602.17211","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":"pmh:oai:HAL:hal-05843010v1","doi":null,"is_oa":true,"landing_page_url":"https://hal.science/hal-05843010","pdf_url":null,"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":"2026","raw_type":"info:eu-repo/semantics/preprint"},{"id":"doi:10.48550/arxiv.2602.17211","doi":"https://doi.org/10.48550/arxiv.2602.17211","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.17211","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:2602.17211","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2602.17211","pdf_url":"https://arxiv.org/pdf/2602.17211","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/G2439744834","display_name":"PR[AI]RIE-PSAI - Paris School of Artificial Intelligence","funder_award_id":"ANR-23-IACL-0008","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G7754151094","display_name":"Data-driven learning of uncertainty in dynamical systems","funder_award_id":"ANR-24-EXMA-0002","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320326256","display_name":"Grand \u00c9quipement National De Calcul Intensif","ror":"https://ror.org/0010d1q40"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7130724798.pdf","grobid_xml":"https://content.openalex.org/works/W7130724798.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4415367204","https://openalex.org/W4392822560","https://openalex.org/W2009990554","https://openalex.org/W4399758765","https://openalex.org/W7172436269","https://openalex.org/W1984321224","https://openalex.org/W2604912240","https://openalex.org/W2906385621","https://openalex.org/W4416967361","https://openalex.org/W2985811395"],"abstract_inverted_index":{"Generating":[0],"samples":[1,85],"from":[2,20,137],"limited":[3,56],"information":[4],"is":[5,64],"a":[6,91,128],"fundamental":[7],"problem":[8],"across":[9],"scientific":[10],"domains.":[11],"Classical":[12],"maximum":[13,86,123],"entropy":[14,87,124,134],"methods":[15],"provide":[16],"principled":[17],"uncertainty":[18],"quantification":[19],"moment":[21],"constraints":[22],"but":[23,54],"require":[24],"sampling":[25],"via":[26],"MCMC":[27],"or":[28],"Langevin":[29],"dynamics,":[30],"which":[31,72],"typically":[32],"exhibit":[33],"exponential":[34],"slowdown":[35],"in":[36,101,108,114],"high":[37],"dimensions.":[38],"In":[39],"contrast,":[40],"generative":[41],"models":[42],"based":[43],"on":[44,79],"diffusion":[45],"and":[46,59,126,147],"flow":[47],"matching":[48],"efficiently":[49],"transport":[50],"noise":[51],"to":[52,121,141],"data":[53,63],"offer":[55],"theoretical":[57],"guarantees":[58],"can":[60],"overfit":[61],"when":[62],"scarce.":[65],"We":[66,111],"introduce":[67],"Moment":[68],"Guided":[69],"Diffusion":[70],"(MGD),":[71],"combines":[73],"elements":[74],"of":[75,119,131,156],"both":[76],"approaches.":[77],"Building":[78],"the":[80,115,122,132,138],"stochastic":[81,92],"interpolant":[82],"framework,":[83],"MGD":[84,120],"distributions":[88],"by":[89],"solving":[90],"differential":[93],"equation":[94],"that":[95],"guides":[96],"moments":[97,153],"toward":[98],"prescribed":[99],"values":[100],"finite":[102],"time,":[103],"thereby":[104],"avoiding":[105],"slow":[106],"mixing":[107],"equilibrium-based":[109],"methods.":[110],"formally":[112],"obtain,":[113],"large-volatility":[116],"limit,":[117],"convergence":[118],"distribution":[125],"derive":[127],"tractable":[129],"estimator":[130],"resulting":[133],"computed":[135],"directly":[136],"dynamics.":[139],"Applications":[140],"financial":[142],"time":[143],"series,":[144],"turbulent":[145],"flows,":[146],"cosmological":[148],"fields":[149],"using":[150],"wavelet":[151],"scattering":[152],"yield":[154],"estimates":[155],"negentropy":[157],"for":[158],"high-dimensional":[159],"multiscale":[160],"processes.":[161]},"counts_by_year":[],"updated_date":"2026-11-05T12:25:35.769452","created_date":"2026-02-21T00:00:00"}
