Listening to the Noise: Blind Denoising with Gibbs Diffusion

TL;DR

This paper introduces Gibbs Diffusion, a novel method for blind denoising that jointly estimates signals and unknown noise parameters using a diffusion model and Gibbs sampling, applicable to natural images and cosmology data.

Contribution

The paper presents Gibbs Diffusion, a new approach enabling blind denoising by combining diffusion models with Gibbs sampling to infer both signals and noise parameters.

Findings

Effective blind denoising of natural images with unknown colored noise.

Successful application to cosmology data for Bayesian inference of noise parameters.

Theoretical analysis of Gibbs Diffusion's accuracy and limitations.

Abstract

In recent years, denoising problems have become intertwined with the development of deep generative models. In particular, diffusion models are trained like denoisers, and the distribution they model coincide with denoising priors in the Bayesian picture. However, denoising through diffusion-based posterior sampling requires the noise level and covariance to be known, preventing blind denoising. We overcome this limitation by introducing Gibbs Diffusion (GDiff), a general methodology addressing posterior sampling of both the signal and the noise parameters. Assuming arbitrary parametric Gaussian noise, we develop a Gibbs algorithm that alternates sampling steps from a conditional diffusion model trained to map the signal prior to the family of noise distributions, and a Monte Carlo sampler to infer the noise parameters. Our theoretical analysis highlights potential pitfalls, guides diagnostic usage, and quantifies errors in the Gibbs stationary distribution caused by the diffusion model. We showcase our method for 1) blind denoising of natural images involving colored noises with unknown amplitude and spectral index, and 2) a cosmology problem, namely the analysis of cosmic microwave background data, where Bayesian inference of "noise" parameters means constraining models of the evolution of the Universe.