用退火MCMC改进扩散模型逆问题求解，更准更快。
Think Twice Before You Act: Improving Inverse Problem Solving With MCMC
- 基于退火MCMC构建中间分布，逐步降低噪声采样。
- 在超分辨率、去模糊等任务中，评估次数更少仍更优。
- 适合想用预训练扩散模型高效解逆问题的研究者。
近期研究证明扩散模型可作为求解逆问题的强大先验。典型方法如扩散后验采样（DPS），通过Tweedie公式近似给定观测数据的后验分布。然而，当噪声水平较高时，该后验近似往往不准确，限制了DPS性能。为此，本文提出基于退火MCMC的扩散后验MCMC（DPMC）算法，利用受DPS启发的中间分布序列，在逐级降噪过程中更精确地引导采样路径，减少累积误差。我们在超分辨率、高斯去模糊、运动去模糊、图像修补和相位恢复等多种逆问题上验证该方法，结果表明，相比DPS，DPMC在几乎全部任务中以更少的采样评估次数取得更好效果，且与现有方法相当。
原文摘要 · Abstract (English)
Recent studies demonstrate that diffusion models can serve as a strong prior for solving inverse problems. A prominent example is Diffusion Posterior Sampling (DPS), which approximates the posterior distribution of data given the measure using Tweedie's formula. Despite the merits of being versatile in solving various inverse problems without re-training, the performance of DPS is hindered by the fact that this posterior approximation can be inaccurate especially for high noise levels. Therefore, we propose \textbf{D}iffusion \textbf{P}osterior \textbf{MC}MC (\textbf{DPMC}), a novel inference algorithm based on Annealed MCMC to solve inverse problems with pretrained diffusion models. We define a series of intermediate distributions inspired by the approximated conditional distributions used by DPS. Through annealed MCMC sampling, we encourage the samples to follow each intermediate distribution more closely before moving to the next distribution at a lower noise level, and therefore reduce the accumulated error along the path. We test our algorithm in various inverse problems, including super resolution, Gaussian deblurring, motion deblurring, inpainting, and phase retrieval. Our algorithm outperforms DPS with less number of evaluations across nearly all tasks, and is competitive among existing approaches.
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