Related papers: Diffusion Posterior Sampling for General Noisy Inverse Problems

Diffusion Posterior Sampling for General Noisy Inverse Problems

URL: http://arxiv.org/abs/2209.14687v4
Date: Mon, 20 May 2024 04:23:45 GMT
Title: Diffusion Posterior Sampling for General Noisy Inverse Problems
Authors: Hyungjin Chung, Jeongsol Kim, Michael T. Mccann, Marc L. Klasky, Jong Chul Ye,
Abstract summary: We extend diffusion solvers to handle noisy (non)linear inverse problems via approximation of the posterior sampling. Our method demonstrates that diffusion models can incorporate various measurement noise statistics.
Score: 50.873313752797124
License: http://creativecommons.org/licenses/by-nc-nd/4.0/
Abstract: 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

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