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GibbsDDRM: A Partially Collapsed Gibbs Sampler for Solving Blind Inverse Problems with Denoising Diffusion Restoration

Naoki Murata · Koichi Saito · Chieh-Hsin Lai · Yuhta Takida · Toshimitsu Uesaka · Yuki Mitsufuji · Stefano Ermon

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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.

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