Gibbs Diffusion (GDiff): A New Bayesian Blind Denoising Method with Applications in Image Denoising and Cosmology

Gibbs Diffusion (GDiff) is a novel approach for blind denoising in a Bayesian framework. It combines diffusion models with a Gibbs sampler, addressing the challenges of modeling the prior distribution and sampling the posterior simultaneously3. GDiff allows posterior sampling of both signal and noise parameters, utilizing a pretrained diffusion model and a Hamiltonian Monte Carlo sampler4. This method is effective in applications such as blind denoising of natural images and cosmology problems, outperforming traditional baselines.

Gibbs Diffusion (GDiff) addresses blind denoising by introducing a general methodology for posterior sampling of both signal and noise parameters3. It alternates between two sampling steps: Conditional Diffusion Model Sampling, which maps the signal's prior distribution to a family of noise distributions, and Monte Carlo Sampling, which infers the noise parameters3. This approach allows for the recovery of clean images and noise characterization, overcoming limitations of conventional diffusion-based denoising techniques that require known noise levels and covariance3.