{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,26]],"date-time":"2025-11-26T15:57:37Z","timestamp":1764172657946,"version":"3.32.0"},"reference-count":34,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","funder":[{"name":"SPOT","award":["ANR-20-CE40-0014"],"award-info":[{"award-number":["ANR-20-CE40-0014"]}]},{"DOI":"10.13039\/100012112","name":"Isaac Newton Institute for Mathematical Sciences","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100012112","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100013237","name":"European Union","doi-asserted-by":"publisher","award":["ERC-2022-SYG-OCEAN-101071601"],"award-info":[{"award-number":["ERC-2022-SYG-OCEAN-101071601"]}],"id":[{"id":"10.13039\/100013237","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Paris Ile-de-France R\u00e9gion","award":["DIM AI4IDF"],"award-info":[{"award-number":["DIM AI4IDF"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM Journal on Mathematics of Data Science"],"published-print":{"date-parts":[[2025,3,31]]},"DOI":"10.1137\/23m1613670","type":"journal-article","created":{"date-parts":[[2025,1,3]],"date-time":"2025-01-03T09:00:49Z","timestamp":1735894849000},"page":"86-109","source":"Crossref","is-referenced-by-count":2,"title":["KL Convergence Guarantees for Score Diffusion Models under Minimal Data Assumptions"],"prefix":"10.1137","volume":"7","author":[{"given":"Giovanni","family":"Conforti","sequence":"first","affiliation":[{"name":"Dipartimento di Matematica, Universi\u00e9 degli Studi di Padova, Padova, Padova 35131, Italy."}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2086-8611","authenticated-orcid":true,"given":"Alain","family":"Durmus","sequence":"additional","affiliation":[{"name":"CMAP, Ecole Polytechnique, Palaiseau 91120, France."}]},{"given":"Marta Gentiloni","family":"Silveri","sequence":"additional","affiliation":[{"name":"\u00c9cole Polytechnique, Palaiseau 91120, France."}]}],"member":"351","published-online":{"date-parts":[[2025,1,3]]},"reference":[{"key":"ref1","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1016\/0304-4149(82)90051-5","volume":"12","author":"Anderson B. D.","year":"1982","journal-title":"Stochastic Process. Appl."},{"key":"ref2","series-title":"Grundlehren Math. Wiss. 348","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-319-00227-9","volume-title":"Analysis and Geometry of Markov Diffusion Operators","author":"Bakry D.","year":"2014"},{"key":"ref3","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-319-62226-2","volume-title":"Stochastic Calculus","author":"Baldi P.","year":"2017"},{"key":"ref6","author":"Bortoli V. De","year":"2022","journal-title":"Trans. Mach. Learn. Res."},{"key":"ref7","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/s41781-020-0035-2","volume":"4","author":"Brehmer J.","year":"2020","journal-title":"Comput. Software Big Sci."},{"key":"ref8","doi-asserted-by":"crossref","first-page":"045002","DOI":"10.1103\/RevModPhys.91.045002","volume":"91","author":"Carleo G.","year":"2019","journal-title":"Rev. Modern Phys."},{"key":"ref9","doi-asserted-by":"crossref","first-page":"1844","DOI":"10.1214\/22-AIHP1320","volume":"59","author":"Cattiaux P.","year":"2023","journal-title":"Ann. Inst. Henri Poincar\u00e9 Probab. Stat."},{"key":"ref12","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1214\/22-EJP850","volume":"27","author":"Chiarini A.","year":"2022","journal-title":"Electron. J. Probab."},{"key":"ref17","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1007\/s11222-014-9511-z","volume":"25","author":"Durmus A.","year":"2015","journal-title":"Stat. Comput."},{"key":"ref18","series-title":"Cambridge Ser. Statist. Probab. Math. 49","doi-asserted-by":"crossref","DOI":"10.1017\/9781108591034","volume-title":"Probability: Theory and Examples","author":"Durrett R.","year":"2019"},{"key":"ref19","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1007\/BF01442207","volume":"13","author":"Fleming W. H.","year":"1985","journal-title":"Appl. Math. Optim."},{"key":"ref21","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1145\/3422622","volume":"63","author":"Goodfellow I.","year":"2020","journal-title":"Commun. ACM"},{"key":"ref22","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1007\/BF00275475","volume":"5","author":"Haj\u0142asz P.","year":"1996","journal-title":"Potential Anal."},{"key":"ref23","doi-asserted-by":"crossref","first-page":"1188","DOI":"10.1214\/aop\/1176992362","volume":"14","author":"Haussmann U. G.","year":"1986","journal-title":"Ann. Probab."},{"key":"ref25","first-page":"6840","volume-title":"Advances in Neural Information Processing Systems","volume":"33","author":"Ho J.","year":"2020"},{"key":"ref27","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1007\/978-3-030-98519-6_10","volume-title":"Stochastic Analysis, Filtering, and Stochastic Optimization: A Commemorative Volume to Honor Mark HA Davis\u2019s Contributions","author":"Karatzas I.","year":"2022"},{"key":"ref29","series-title":"Stoch. Model. Appl. Probab. 14","volume-title":"Controlled Diffusion Processes","author":"Krylov N. V.","year":"2008"},{"key":"ref30","doi-asserted-by":"crossref","first-page":"758","DOI":"10.1016\/j.jfa.2009.09.009","volume":"258","author":"Kusuoka S.","year":"2010","journal-title":"J. Funct. Anal."},{"key":"ref34","series-title":"Stoch. Model. Appl. Probab. 5","volume-title":"Statistics of Random Processes: I. General Theory","author":"Liptser R.","year":"2013"},{"key":"ref35","volume-title":"NeurIPS 2022 Workshop on Score-Based Methods","author":"Liu X.","year":"2022"},{"key":"ref36","doi-asserted-by":"crossref","first-page":"eaaw1147","DOI":"10.1126\/science.aaw1147","volume":"365","author":"No\u00e9 F.","year":"2019","journal-title":"Science"},{"key":"ref37","series-title":"Lecture notes","volume-title":"Introduction to Entropic Optimal Transport","author":"Nutz M.","year":"2021"},{"key":"ref39","first-page":"1","volume":"22","author":"Papamakarios G.","year":"2021","journal-title":"J. Mach. Learn. Res."},{"key":"ref40","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1007\/BF01448198","volume":"19","author":"Pavon M.","year":"1989","journal-title":"Appl. Math. Optim."},{"key":"ref41","author":"Pedrotti F.","year":"2024","journal-title":"Trans. Mach. Learn. Res."},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.1137\/1129093"},{"key":"ref43","doi-asserted-by":"crossref","first-page":"672","DOI":"10.1038\/s41586-021-03854-z","volume":"597","author":"Ravuri S.","year":"2021","journal-title":"Nature"},{"key":"ref44","doi-asserted-by":"crossref","first-page":"e202100008","DOI":"10.1002\/gamm.202100008","volume":"44","author":"Ruthotto L.","year":"2021","journal-title":"GAMM-Mitt."},{"key":"ref45","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1146\/annurev-statistics-010814-020120","volume":"2","author":"Salakhutdinov R.","year":"2015","journal-title":"Annu. Rev. Stat. Appl."},{"key":"ref46","doi-asserted-by":"crossref","first-page":"16884","DOI":"10.1038\/s41598-019-52737-x","volume":"9","author":"Sandfort V.","year":"2019","journal-title":"Sci. Rep."},{"key":"ref52","doi-asserted-by":"crossref","first-page":"3797","DOI":"10.1109\/TIT.2014.2320500","volume":"60","author":"Van Erven T.","year":"2014","journal-title":"IEEE Trans. Inform. Theory"},{"key":"ref53","series-title":"Mem. Amer. Math. Soc. 202","volume-title":"Hypocoercivity","author":"Villani C.","year":"2009"},{"key":"ref54","volume-title":"NeurIPS 2022 Workshop on Score-Based Methods","author":"Yang K. Y.","year":"2022"},{"key":"ref55","series-title":"Stoch. Model. Appl. Probab. 43","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-1466-3","volume-title":"Stochastic Controls: Hamiltonian Systems and HJB Equations","author":"Yong J.","year":"1999"}],"container-title":["SIAM Journal on Mathematics of Data Science"],"original-title":[],"language":"en","deposited":{"date-parts":[[2025,1,3]],"date-time":"2025-01-03T09:01:07Z","timestamp":1735894867000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/23M1613670"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,1,3]]},"references-count":34,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,3,31]]}},"alternative-id":["10.1137\/23M1613670"],"URL":"https:\/\/doi.org\/10.1137\/23m1613670","relation":{},"ISSN":["2577-0187"],"issn-type":[{"value":"2577-0187","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,1,3]]}}}