{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,3]],"date-time":"2026-08-03T16:44:59Z","timestamp":1785775499711,"version":"3.56.0"},"reference-count":15,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12261020"],"award-info":[{"award-number":["12261020"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"award":["12261020"],"award-info":[{"award-number":["12261020"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"publisher"}]},{"name":"Key Project of Guizhou Provincial Basic Research Program","award":["ZD[2026]054"],"award-info":[{"award-number":["ZD[2026]054"]}]},{"name":"Youth Guidance Project of Guizhou Provincial Basic Research Program","award":["Qiankehe Foundation QN[2025]294"],"award-info":[{"award-number":["Qiankehe Foundation QN[2025]294"]}]},{"name":"Research of Zunyi Municipal Science and Technology Plan Project","award":["Zunshi Kehe HZ Zi (2025) No. 103"],"award-info":[{"award-number":["Zunshi Kehe HZ Zi (2025) No. 103"]}]},{"name":"Research of Moutai Institute High-Level Talent Research Startup Funding Project","award":["mygccrc[2024]019"],"award-info":[{"award-number":["mygccrc[2024]019"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Sampling from high-dimensional posterior distributions is a central challenge in Bayesian inference and noisy inverse problems. Standard first-order Langevin-based methods often suffer from slow convergence and sensitivity to step-size hyperparameters, particularly in annealed score-based inverse imaging pipelines. We propose Adaptive Momentum Langevin Dynamics (AMLD), a practical stochastic correction kernel that introduces a momentum variable into the annealed posterior sampling framework and equips it with an annealing-aware momentum retention schedule. The method is fully compatible with the SNIPS framework and retains its coordinate-wise adaptive step structure, acting as a lightweight drop-in replacement for the conventional first-order Langevin correction step. Extensive experiments on three representative image inverse problems\u2014Gaussian deblurring, inpainting, and 4\u00d7 super-resolution\u2014demonstrate that AMLD consistently achieves strong PSNR and LPIPS performance, with competitive FID in most settings, compared to three state-of-the-art baselines (DDRM, DPS, SNIPS) under both nearly noiseless and noisy measurement conditions, while reaching target reconstruction quality using fewer sampling iterations. The proposed momentum-based sampler provides empirically improved exploration and robustness across evolving posterior landscapes, offering a practical and computationally efficient alternative to first-order annealed Langevin samplers in high-dimensional Bayesian inverse problems.<\/jats:p>","DOI":"10.3390\/e28080854","type":"journal-article","created":{"date-parts":[[2026,8,3]],"date-time":"2026-08-03T15:51:23Z","timestamp":1785772283000},"page":"854","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Adaptive Momentum Langevin Dynamics for Efficient Posterior Sampling"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2222-223X","authenticated-orcid":false,"given":"Zhengbo","family":"Li","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China"},{"name":"School of General Education, Moutai Institute, Renhuai 564507, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0350-5528","authenticated-orcid":false,"given":"Jian","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Mathematics, South China University of Technology, Guangzhou 510640, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5632-3050","authenticated-orcid":false,"given":"Dingtao","family":"Peng","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China"},{"name":"Guizhou Provincial Laboratory of Big Data, Guizhou University, Guiyang 550025, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shuang","family":"Hu","sequence":"additional","affiliation":[{"name":"School of General Education, Moutai Institute, Renhuai 564507, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,8,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Brooks, S., Gelman, A., Jones, G., and Meng, X.-L. (2011). MCMC using Hamiltonian dynamics. Handbook of Markov Chain Monte Carlo, Chapman & Hall\/CRC. Chapter 5.","DOI":"10.1201\/b10905"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1017\/S0962492910000061","article-title":"Inverse problems: A Bayesian perspective","volume":"19","author":"Stuart","year":"2010","journal-title":"Acta Numer."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1007\/s11222-008-9110-y","article-title":"A tutorial on adaptive MCMC","volume":"18","author":"Andrieu","year":"2008","journal-title":"Stat. Comput."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"318","DOI":"10.1080\/00949655.2021.1958812","article-title":"Stochastic gradient Langevin dynamics algorithms with adaptive drifts","volume":"92","author":"Kim","year":"2022","journal-title":"J. Stat. Comput. Simul."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Li, C., Chen, C., Carlson, D., and Carin, L. 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A survey on diffusion models for inverse problems. arXiv."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/8\/854\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,3]],"date-time":"2026-08-03T15:52:41Z","timestamp":1785772361000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/8\/854"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,8,1]]},"references-count":15,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2026,8]]}},"alternative-id":["e28080854"],"URL":"https:\/\/doi.org\/10.3390\/e28080854","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,8,1]]}}}