Diffusion Model Based Posterior Sampling for Noisy Linear Inverse Problems

Xiangming Meng, Yoshiyuki Kabashima
Proceedings of the 16th Asian Conference on Machine Learning, PMLR 260:623-638, 2025.

Abstract

With the rapid development of diffusion models and flow-based generative models, there has been a surge of interests in solving noisy linear inverse problems, e.g., super-resolution, deblurring, denoising, colorization, etc, with generative models. However, while remarkable reconstruction performances have been achieved, their inference time is typically too slow since most of them rely on the seminal diffusion posterior sampling (DPS) framework and thus to approximate the intractable likelihood score, time-consuming gradient calculation through back-propagation is needed. To address this issue, this paper provides a fast and effective solution by proposing a simple closed-form approximation to the likelihood score. For both diffusion and flow-based models, extensive experiments are conducted on various noisy linear inverse problems such as noisy super-resolution, denoising, deblurring, and colorization. In all these tasks, our method (namely DMPS) demonstrates highly competitive or even better reconstruction performances while being significantly faster than all the baseline methods.

Cite this Paper

BibTeX
@InProceedings{pmlr-v260-meng25a, title = {Diffusion Model Based Posterior Sampling for Noisy Linear Inverse Problems}, author = {Meng, Xiangming and Kabashima, Yoshiyuki}, booktitle = {Proceedings of the 16th Asian Conference on Machine Learning}, pages = {623--638}, year = {2025}, editor = {Nguyen, Vu and Lin, Hsuan-Tien}, volume = {260}, series = {Proceedings of Machine Learning Research}, month = {05--08 Dec}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v260/main/assets/meng25a/meng25a.pdf}, url = {https://proceedings.mlr.press/v260/meng25a.html}, abstract = {With the rapid development of diffusion models and flow-based generative models, there has been a surge of interests in solving noisy linear inverse problems, e.g., super-resolution, deblurring, denoising, colorization, etc, with generative models. However, while remarkable reconstruction performances have been achieved, their inference time is typically too slow since most of them rely on the seminal diffusion posterior sampling (DPS) framework and thus to approximate the intractable likelihood score, time-consuming gradient calculation through back-propagation is needed. To address this issue, this paper provides a fast and effective solution by proposing a simple closed-form approximation to the likelihood score. For both diffusion and flow-based models, extensive experiments are conducted on various noisy linear inverse problems such as noisy super-resolution, denoising, deblurring, and colorization. In all these tasks, our method (namely DMPS) demonstrates highly competitive or even better reconstruction performances while being significantly faster than all the baseline methods.} }
Endnote
%0 Conference Paper %T Diffusion Model Based Posterior Sampling for Noisy Linear Inverse Problems %A Xiangming Meng %A Yoshiyuki Kabashima %B Proceedings of the 16th Asian Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Vu Nguyen %E Hsuan-Tien Lin %F pmlr-v260-meng25a %I PMLR %P 623--638 %U https://proceedings.mlr.press/v260/meng25a.html %V 260 %X With the rapid development of diffusion models and flow-based generative models, there has been a surge of interests in solving noisy linear inverse problems, e.g., super-resolution, deblurring, denoising, colorization, etc, with generative models. However, while remarkable reconstruction performances have been achieved, their inference time is typically too slow since most of them rely on the seminal diffusion posterior sampling (DPS) framework and thus to approximate the intractable likelihood score, time-consuming gradient calculation through back-propagation is needed. To address this issue, this paper provides a fast and effective solution by proposing a simple closed-form approximation to the likelihood score. For both diffusion and flow-based models, extensive experiments are conducted on various noisy linear inverse problems such as noisy super-resolution, denoising, deblurring, and colorization. In all these tasks, our method (namely DMPS) demonstrates highly competitive or even better reconstruction performances while being significantly faster than all the baseline methods.
APA
Meng, X. & Kabashima, Y.. (2025). Diffusion Model Based Posterior Sampling for Noisy Linear Inverse Problems. Proceedings of the 16th Asian Conference on Machine Learning, in Proceedings of Machine Learning Research 260:623-638 Available from https://proceedings.mlr.press/v260/meng25a.html.

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