Diffusion models have been recently studied as powerful generative inverse problem solvers, owing to their high quality reconstructions and the ease of combining existing iterative solvers. However, most works focus on solving simple linear inverse problems in noiseless settings, which significantly under-represents the complexity of real-world problems. In this work, we extend diffusion solvers to efficiently handle general noisy (non)linear inverse problems via approximation of the posterior sampling. Interestingly, the resulting posterior sampling scheme is a blended version of diffusion sampling with the manifold constrained gradient without a strict measurement consistency projection step, yielding a more desirable generative path in noisy settings compared to the previous studies. Our method demonstrates that diffusion models can incorporate various measurement noise statistics such as Gaussian and Poisson, and also efficiently handle noisy nonlinear inverse problems such as Fourier phase retrieval and non-uniform deblurring. Code available at https://github.com/DPS2022/diffusion-posterior-sampling

翻译：扩散模型因其高质量重建能力以及易于集成现有迭代求解器的特点，近期被研究作为强大的生成式逆问题求解器。然而，大多数工作聚焦于无噪声环境下的简单线性逆问题，这显著低估了现实世界问题的复杂性。在本工作中，我们通过后验采样的近似，将扩散求解器扩展至能够高效处理一般含噪（非线性）逆问题。有趣的是，所得后验采样方案是扩散采样与流形约束梯度的混合版本，无需严格的测量一致性投影步骤，从而在含噪环境下产生比以往研究更理想的生成路径。我们的方法表明，扩散模型能够融入多种测量噪声统计特性（如高斯噪声和泊松噪声），并高效处理含噪非线性逆问题（如傅里叶相位恢复和非均匀去模糊）。代码见 https://github.com/DPS2022/diffusion-posterior-sampling