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
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:25501-25522, 2023.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-murata23a, title = {{G}ibbs{DDRM}: A Partially Collapsed {G}ibbs Sampler for Solving Blind Inverse Problems with Denoising Diffusion Restoration}, author = {Murata, Naoki and Saito, Koichi and Lai, Chieh-Hsin and Takida, Yuhta and Uesaka, Toshimitsu and Mitsufuji, Yuki and Ermon, Stefano}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {25501--25522}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/murata23a/murata23a.pdf}, url = {https://proceedings.mlr.press/v202/murata23a.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T GibbsDDRM: A Partially Collapsed Gibbs Sampler for Solving Blind Inverse Problems with Denoising Diffusion Restoration %A Naoki Murata %A Koichi Saito %A Chieh-Hsin Lai %A Yuhta Takida %A Toshimitsu Uesaka %A Yuki Mitsufuji %A Stefano Ermon %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-murata23a %I PMLR %P 25501--25522 %U https://proceedings.mlr.press/v202/murata23a.html %V 202 %X 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.
APA
Murata, N., Saito, K., Lai, C., Takida, Y., Uesaka, T., Mitsufuji, Y. & Ermon, S.. (2023). GibbsDDRM: A Partially Collapsed Gibbs Sampler for Solving Blind Inverse Problems with Denoising Diffusion Restoration. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:25501-25522 Available from https://proceedings.mlr.press/v202/murata23a.html.

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