{"ID":2859558,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.07343","arxiv_id":"2510.07343","title":"Local MAP Sampling for Diffusion Models","abstract":"Diffusion Posterior Sampling (DPS) provides a principled Bayesian approach to inverse problems by sampling from $p(x_0 \\mid y)$. While posterior sampling is valuable for capturing uncertainty and multi-modality, many classical and practical inverse problem settings ultimately prioritize accurate point estimation -- most notably the MAP estimator, which has long served as a standard reconstruction objective in imaging and scientific applications. We introduce Local MAP Sampling (LMAPS), a new inference framework that iteratively solves local MAP subproblems along the diffusion trajectory. This perspective clarifies their connection to global MAP and DPS, offering a unified probabilistic interpretation for optimization-based methods. Building on this foundation, we develop practical algorithms with a covariance approximation motivated by a Gaussian prior assumption, and a reformulated objective for stability and interpretability. Across a broad set of image restoration and scientific tasks, LMAPS achieves state-of-the-art performance.","short_abstract":"Diffusion Posterior Sampling (DPS) provides a principled Bayesian approach to inverse problems by sampling from $p(x_0 \\mid y)$. While posterior sampling is valuable for capturing uncertainty and multi-modality, many classical and practical inverse problem settings ultimately prioritize accurate point estimation -- mos...","url_abs":"https://arxiv.org/abs/2510.07343","url_pdf":"https://arxiv.org/pdf/2510.07343v3","authors":"[\"Shaorong Zhang\",\"Rob Brekelmans\",\"Greg Ver Steeg\"]","published":"2025-10-07T19:02:32Z","proceeding":"cs.GR","tasks":"[\"cs.GR\",\"cs.AI\",\"eess.IV\"]","methods":"[\"Diffusion Model\"]","has_code":false}