{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,2]],"date-time":"2026-01-02T08:41:21Z","timestamp":1767343281363,"version":"3.48.0"},"reference-count":48,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","funder":[{"name":"Austrian Science Fund","award":["10.55776\/COE12"],"award-info":[{"award-number":["10.55776\/COE12"]}]},{"name":"Austrian Science Fund","award":["10.55776\/F100800"],"award-info":[{"award-number":["10.55776\/F100800"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Imaging Sci."],"published-print":{"date-parts":[[2026,3,31]]},"DOI":"10.1137\/25m1745830","type":"journal-article","created":{"date-parts":[[2026,1,2]],"date-time":"2026-01-02T08:40:16Z","timestamp":1767343216000},"page":"35-77","source":"Crossref","is-referenced-by-count":0,"title":["Diffusion at Absolute Zero: Langevin Sampling Using Successive Moreau Envelopes"],"prefix":"10.1137","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1201-5782","authenticated-orcid":true,"given":"Andreas","family":"Habring","sequence":"first","affiliation":[{"name":"Institute of Visual Computing, Graz University of Technology, Graz, Austria."}]},{"given":"Alexander","family":"Falk","sequence":"additional","affiliation":[{"name":"Institute of Visual Computing, Graz University of Technology, Graz, Austria."}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1941-875X","authenticated-orcid":true,"given":"Martin","family":"Zach","sequence":"additional","affiliation":[{"name":"Biomedical Imaging Group, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, 1015 Lausanne, Switzerland and Center for Biomedical Imaging, 1015 Lausanne, Switzerland."}]},{"given":"Thomas","family":"Pock","sequence":"additional","affiliation":[{"name":"Institute of Visual Computing, Graz University of Technology, Graz, Austria."}]}],"member":"351","published-online":{"date-parts":[[2026,1,2]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-00227-9_1"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511804441"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1137\/090769521"},{"key":"ref4","unstructured":"M. Burger, M. J. Ehrhardt, L. Kuger, and L. Weigand, Coupling Analysis of the Asymptotic Behaviour of a Primal-Dual Langevin Algorithm, https:\/\/arxiv.org\/abs\/2405.18098, 2024."},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1007\/s10851-010-0251-1"},{"key":"ref6","unstructured":"X. Cheng, N. S. Chatterji, Y. Abbasi-Yadkori, P. L. Bartlett, and M. I. Jordan, Sharp Convergence Rates for Langevin Dynamics in the Nonconvex Setting, https:\/\/arxiv.org\/abs\/1805.01648, 2018."},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1984-0744921-8"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1111\/rssb.12183"},{"key":"ref9","unstructured":"Y. Du, S. Li, J. Tenenbaum, and I. Mordatch, Improved contrastive divergence training of energy-based models, in Proceedings of the 38th International Conference on Machine Learning, Proc. Mach. Learn. Res., 2021, pp. 2837\u20132848,\u00a0https:\/\/proceedings.mlr.press\/v139\/du21b.html."},{"key":"ref10","first-page":"2666","volume":"20","author":"Durmus A.","year":"2019","journal-title":"J. Mach. Learn. Res."},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1214\/16-AAP1238"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.3150\/18-BEJ1073"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1137\/16M1108340"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1137\/23M1593565"},{"key":"ref15","series-title":"Grad. Stud. Math. 19","volume-title":"Partial Differential Equations","author":"Evans L. C.","year":"2022"},{"key":"ref16","unstructured":"L. Fruehwirth and A. Habring, Ergodicity of Langevin Dynamics and Its Discretizations for Non-Smooth Potentials, preprint, arXiv:2411.12051, 2024."},{"key":"ref17","doi-asserted-by":"crossref","unstructured":"A. Habring, A. Falk, and T. Pock, Diffusion at absolute zero: Langevin sampling using successive moreau envelopes, in 2025 IEEE Statistical Signal Processing Workshop (SSP), 2025, pp. 61\u201365, https:\/\/doi.org\/10.1109\/SSP64130.2025.11073434.","DOI":"10.1109\/SSP64130.2025.11073434"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1137\/23M1591451"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1007\/s42967-022-00239-5"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1137\/S0036141096303359"},{"key":"ref21","doi-asserted-by":"crossref","unstructured":"P. Knobelreiter, C. Sormann, A. Shekhovtsov, F. Fraundorfer, and T. Pock, Belief propagation reloaded: Learning BP-layers for labeling problems, in Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, 2020, pp. 7900\u20137909.","DOI":"10.1109\/CVPR42600.2020.00792"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1148\/ryai.2020190007"},{"key":"ref23","doi-asserted-by":"crossref","unstructured":"E. Kobler, A. Effland, K. Kunisch, and T. Pock, Total deep variation for linear inverse problems, in Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2020.","DOI":"10.1109\/CVPR42600.2020.00757"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1137\/15M1010257"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1142\/S0219493703000838"},{"key":"ref26","unstructured":"T. T.K. Lau and H. Liu, Bregman proximal Langevin Monte Carlo via Bregman-Moreau envelopes, in Proceedings of the International Conference on Machine Learning, Proc. Mach. Learn. Res., 2022, pp. 12049\u201312077."},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1002\/mrm.29624"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1007\/s11009-020-09809-7"},{"key":"ref29","doi-asserted-by":"crossref","unstructured":"D. Martin, C. Fowlkes, D. Tal, and J. Malik, A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics, in Proceedings of the 8th IEEE International Conference on Computer Vision, IEEE, 2001, pp. 416\u2013423.","DOI":"10.1109\/ICCV.2001.937655"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.2307\/1427522"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1137\/19M1298007"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1137\/23M1546129"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1609\/aaai.v34i04.5973"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2220469120"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1007\/s11222-015-9567-4"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1137\/16M1071249"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1137\/19M1283719"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.2307\/3318418"},{"key":"ref39","volume-title":"Variational Analysis","author":"Rockafellar T.","year":"2009"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(92)90242-F"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1134\/S0965542511070165"},{"key":"ref42","volume-title":"Proceedings of the 32nd Advances in Neural Information Processing Systems","author":"Song Y."},{"key":"ref43","unstructured":"Y. Song, J. Sohl-Dickstein, D. P. Kingma, A. Kumar, S. Ermon, and B. Poole, Score-based generative modeling through stochastic differential equations, in Proceedings of the International Conference on Learning Representations, 2021."},{"key":"ref44","doi-asserted-by":"crossref","unstructured":"M. F. Tappen and W. T. Freeman, Comparison of graph cuts with belief propagation for stereo, using identical MRF parameters, in Proceedings of the 9th IEEE International Conference on Computer Vision, Vol. 2, 2003, pp. 900\u2013906.","DOI":"10.1109\/ICCV.2003.1238444"},{"key":"ref45","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-71050-9"},{"key":"ref46","unstructured":"A. Wibisono, Proximal Langevin Algorithm: Rapid Convergence Under Isoperimetry, preprint, arXiv:1911.01469, 2019."},{"key":"ref47","doi-asserted-by":"publisher","DOI":"10.1109\/TMI.2023.3311345"},{"key":"ref48","first-page":"52","volume-title":"Proceedings of the OAGM Workshop 2021","author":"Zach M.","year":"2021"}],"container-title":["SIAM Journal on Imaging Sciences"],"original-title":[],"language":"en","deposited":{"date-parts":[[2026,1,2]],"date-time":"2026-01-02T08:40:19Z","timestamp":1767343219000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/25M1745830"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,2]]},"references-count":48,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,3,31]]}},"alternative-id":["10.1137\/25M1745830"],"URL":"https:\/\/doi.org\/10.1137\/25m1745830","relation":{},"ISSN":["1936-4954"],"issn-type":[{"value":"1936-4954","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1,2]]}}}