  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
