[论文] Provable diffusion-based posterior sampling for linear inverse problem...

论文概要

研究领域: ML 作者: Yuchen Jiao, Na Li, Changxiao Cai 发布时间: 2026-07-22 arXiv: 2507.17079

中文摘要

基于扩散的方法在解决逆问题上取得了显著的经验成功。然而，许多现有后验采样器要么缺乏严格的理论保证，要么产生大量计算开销。我们提出一种简单高效的算法\textbf{pDDIM}，通过DDIM类型采样器解决具有扩散先验的线性逆问题。我们的方法仅需要对标准DDIM更新进行轻量级坐标级修改，同时显式结合测量模型。关键思想是沿测量算子的每个奇异方向分别进行后验采样：对每个方向，当观测信噪比（SNR）低于相应扩散SNR时，采样器遵循学习的扩散先验；否则切换到校准的基于测量的预测器。我们证明所提出的采样器收敛于以测量为条件的贝叶斯后验。经验结果表明，所提出的采样器在一系列图像恢复任务上优于现有基于扩散的后验采样器，在大多数评估指标上取得最佳性能。总体而言，我们的结果将噪声线性逆问题的后验采样转化为简单的坐标级DDIM更新，产生了一种高效、易于实现且具有可证明后验一致性的算法。

原文摘要

Diffusion-based methods have achieved remarkable empirical success in solving inverse problems. However, many existing posterior samplers either lack rigorous theoretical guarantees or incur substantial computational overhead. We propose a simple and efficient algorithm, called \pddim, for solving linear inverse problems with diffusion priors via a DDIM-type sampler. Our method requires only lightweight, coordinate-wise modifications to the standard DDIM update, while explicitly incorporating the measurement model. The key idea is to perform posterior sampling separately along each singular direction of the measurement operator: for each direction, the sampler follows the learned diffusion prior when the observation signal-to-noise ratio (SNR) is below the corresponding diffusion SNR, and ...

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