Diffusion Model Based Posterior Sampling for Noisy Linear Inverse Problems

We consider the ubiquitous linear inverse problems with additive Gaussian noise and propose an unsupervised general-purpose sampling approach called diffusion model based posterior sampling (DMPS) to reconstruct the unknown signal from noisy linear measurements. Specifically, the prior of the unknown signal is implicitly modeled by one pre-trained diffusion model (DM). In posterior sampling, to address the intractability of exact noise-perturbed likelihood score, a simple yet effective noise-perturbed pseudo-likelihood score is introduced under the uninformative prior assumption. While DMPS applies to any kind of DM with proper modifications, we focus on the ablated diffusion model (ADM) as one specific example and evaluate its efficacy on a variety of linear inverse problems such as image super-resolution, denoising, deblurring, colorization. Experimental results demonstrate that, for both in-distribution and out-of-distribution samples, DMPS achieves highly competitive or even better performances on various tasks while being 3 times faster than the leading competitor. The code to reproduce the results is available at https://github.com/mengxiangming/dmps.