{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T17:26:11Z","timestamp":1777569971113,"version":"3.51.4"},"reference-count":24,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","funder":[{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/T00097X\/1"],"award-info":[{"award-number":["EP\/T00097X\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/V046527\/1"],"award-info":[{"award-number":["EP\/V046527\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/R018472\/1"],"award-info":[{"award-number":["EP\/R018472\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM Rev."],"published-print":{"date-parts":[[2025,8,7]]},"DOI":"10.1137\/23m1626232","type":"journal-article","created":{"date-parts":[[2025,8,7]],"date-time":"2025-08-07T07:16:50Z","timestamp":1754551010000},"page":"607-623","source":"Crossref","is-referenced-by-count":3,"title":["Diffusion Models for Generative Artificial Intelligence: An Introduction for Applied Mathematicians"],"prefix":"10.1137","volume":"67","author":[{"given":"Catherine","family":"Higham","sequence":"first","affiliation":[{"name":"School of Computing Science, University of Glasgow, Glasgow, G12 8RZ, United Kingdom."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Desmond J.","family":"Higham","sequence":"additional","affiliation":[{"name":"School of Mathematics, University of Edinburgh, Edinburgh, EH9 3FD, United Kingdom."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peter","family":"Grindrod","sequence":"additional","affiliation":[{"name":"Mathematical Institute, University of Oxford, Oxford, United Kingdom."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"351","published-online":{"date-parts":[[2025,8,7]]},"reference":[{"key":"ref3","series-title":"Inform. Sci. Statist.","volume-title":"Pattern Recognition and Machine Learning","author":"Bishop C. M.","year":"2007"},{"key":"ref4","first-page":"125:1","volume":"5","author":"Cao Y.","year":"2025","journal-title":"ACM Comput. Surv."},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2023.3261988"},{"key":"ref7","first-page":"8780","volume-title":"Advances in Neural Information Processing Systems","volume":"34","author":"Dhariwal P.","year":"2021"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1007\/s12599-023-00834-7"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1561\/2200000089"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.3844\/jcssp.2024.801.818"},{"key":"ref11","volume-title":"CVPR Workshop on Ethical Considerations in Creative applications of Computer Vision","author":"Hao S.","year":"2023"},{"key":"ref12","first-page":"6626","volume-title":"Advances in Neural Information Processing Systems","author":"Heusel M.","year":"2017"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1137\/18M1165748"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611976434"},{"key":"ref16","first-page":"1","volume":"23","author":"Ho J.","year":"2022","journal-title":"J. Mach. Learn. Res."},{"key":"ref17","volume-title":"NeurIPS. 2021 Workshop on Deep Generative Models and Downstream Applications","author":"Ho J.","year":"2021"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1016\/j.cosrev.2023.100553"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1016\/j.media.2023.102846"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4471-0597-8"},{"key":"ref28","volume-title":"Probabilistic Machine Learning: An Introduction","author":"Murphy K. P.","year":"2022"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1016\/j.patter.2021.100336"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.15063"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-24574-4_28"},{"key":"ref35","first-page":"36479","volume-title":"Advances in Neural Information Processing Systems, Vol. 35","author":"Saharia C.","year":"2022"},{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1016\/j.neunet.2024.106711"},{"key":"ref40","first-page":"109","volume":"55","author":"Tay Y.","year":"2022","journal-title":"ACM Comput. Surv."},{"key":"ref43","first-page":"16782","volume-title":"Advances in Neural Information Processing Systems, Vol. 35","author":"Xu Y.","year":"2022"}],"container-title":["SIAM Review"],"original-title":[],"language":"en","deposited":{"date-parts":[[2025,8,7]],"date-time":"2025-08-07T07:17:02Z","timestamp":1754551022000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/23M1626232"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,7]]},"references-count":24,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2025,8,7]]}},"alternative-id":["10.1137\/23M1626232"],"URL":"https:\/\/doi.org\/10.1137\/23m1626232","relation":{},"ISSN":["0036-1445","1095-7200"],"issn-type":[{"value":"0036-1445","type":"print"},{"value":"1095-7200","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,8,7]]}}}