Local MAP Sampling for Diffusion Models
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916044044500992 |
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| author | Zhang, Shaorong Brekelmans, Rob Steeg, Greg Ver |
| author_facet | Zhang, Shaorong Brekelmans, Rob Steeg, Greg Ver |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_07343 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Local MAP Sampling for Diffusion Models Zhang, Shaorong Brekelmans, Rob Steeg, Greg Ver Graphics Artificial Intelligence Image and Video Processing 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. |
| title | Local MAP Sampling for Diffusion Models |
| topic | Graphics Artificial Intelligence Image and Video Processing |
| url | https://arxiv.org/abs/2510.07343 |