提出一种新方法，在扩散模型中逐步求解局部最优，提升图像重建精度。
Local MAP Sampling for Diffusion Models
- 沿扩散轨迹迭代求解局部最大后验估计
- 在多种图像修复任务中达到顶尖性能
- 适合需要高精度重建的科学成像场景
扩散后验采样（DPS）为逆问题提供了一种原则性的贝叶斯方法，通过从 $p(x_0 \ mid y)$ 中采样来建模不确定性与多模态。尽管后验采样有价值，但许多经典和实际的逆问题更关注准确的点估计，尤其是最大后验（MAP）估计器，已在成像与科学应用中长期作为标准重建目标。本文提出局部最大后验采样（LMAPS），一种新的推理框架，沿扩散轨迹迭代求解局部MAP子问题。这一视角阐明了其与全局MAP和DPS的联系，为基于优化的方法提供了统一的概率解释。在此基础上，我们开发了实用算法，采用基于高斯先验假设的协方差近似，并重构目标函数以增强稳定性和可解释性。在广泛的图像恢复与科学任务中，LMAPS实现了最先进的性能。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。