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 the Laplace 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.
翻译:传播模型最近作为强大的基因反向问题解答器进行了研究,因为其质量高,而且很容易将现有的迭代解答器合并在一起。然而,大多数工作的重点是解决无噪音环境中简单的线性反向问题,这大大低估了现实世界问题的复杂性。在这项工作中,我们扩大扩散解答器,以便通过后继取样的拉普尔近距离有效处理一般的噪音(非线性反向问题)。有趣的是,由此产生的后继取样办法是一个扩散抽样与多层受限梯的混合版本,没有严格的测量一致性预测步骤,在噪音环境中产生比以往研究更可取的基因化路径。我们的方法表明,扩散模型可以纳入诸如高山和普瓦森等各种测量噪音统计,并有效地处理诸如富里叶阶段检索和非单向脱泡器等杂乱的非线性反向问题。