GibbsDDRM: A Partially Collapsed Gibbs Sampler for Solving Blind Inverse Problems with Denoising Diffusion Restoration
This addresses the challenge of applying pre-trained diffusion models to various inverse problems without fine-tuning, though it is incremental as it extends existing DDRM methods to a blind setting.
The paper tackled the problem of solving blind inverse problems where the linear measurement operator is unknown, by proposing GibbsDDRM, an extension of Denoising Diffusion Restoration Models that uses a pre-trained diffusion model as a prior and an efficient Gibbs sampler for posterior sampling, achieving high performance on tasks like blind image deblurring and vocal dereverberation.
Pre-trained diffusion models have been successfully used as priors in a variety of linear inverse problems, where the goal is to reconstruct a signal from noisy linear measurements. However, existing approaches require knowledge of the linear operator. In this paper, we propose GibbsDDRM, an extension of Denoising Diffusion Restoration Models (DDRM) to a blind setting in which the linear measurement operator is unknown. GibbsDDRM constructs a joint distribution of the data, measurements, and linear operator by using a pre-trained diffusion model for the data prior, and it solves the problem by posterior sampling with an efficient variant of a Gibbs sampler. The proposed method is problem-agnostic, meaning that a pre-trained diffusion model can be applied to various inverse problems without fine-tuning. In experiments, it achieved high performance on both blind image deblurring and vocal dereverberation tasks, despite the use of simple generic priors for the underlying linear operators.