Diffusion models (DMs) have recently shown outstanding capabilities in modeling complex image distributions, making them expressive image priors for solving Bayesian inverse problems. However, most existing DM-based methods rely on approximations in the generative process to be generic to different inverse problems, leading to inaccurate sample distributions that deviate from the target posterior defined within the Bayesian framework. To harness the generative power of DMs while avoiding such approximations, we propose a Markov chain Monte Carlo algorithm that performs posterior sampling for general inverse problems by reducing it to sampling the posterior of a Gaussian denoising problem. Crucially, we leverage a general DM formulation as a unified interface that allows for rigorously solving the denoising problem with a range of state-of-the-art DMs. We demonstrate the effectiveness of the proposed method on six inverse problems (three linear and three nonlinear), including a real-world black hole imaging problem. Experimental results indicate that our proposed method offers more accurate reconstructions and posterior estimation compared to existing DM-based imaging inverse methods.

翻译：扩散模型（DMs）近期在建模复杂图像分布方面展现出卓越能力，使其成为解决贝叶斯逆问题的强表达能力图像先验。然而，现有大多数基于扩散模型的方法依赖于生成过程中的近似处理以保持对不同逆问题的通用性，这导致采样分布不准确，偏离了贝叶斯框架内定义的目标后验分布。为充分利用扩散模型的生成能力同时避免此类近似，我们提出一种马尔可夫链蒙特卡洛算法，通过将通用逆问题的后验采样转化为高斯去噪问题的后验采样来实现。关键创新在于，我们采用通用扩散模型表述作为统一接口，能够严格结合多种先进扩散模型求解去噪问题。我们在六个逆问题（三个线性问题和三个非线性问题）上验证了所提方法的有效性，其中包括真实世界的黑洞成像问题。实验结果表明，与现有基于扩散模型的成像逆方法相比，我们提出的方法能提供更准确的重建结果和后验估计。