Plug-and-Play Posterior Sampling for Blind Inverse Problems
Anqi Li, Weijie Gan, Ulugbek S. Kamilov
TL;DR
This work tackles blind inverse problems where the forward operator $A(\boldsymbol{\theta})$ is unknown. It introduces Blind-PnPDM, a framework that uses two diffusion-model priors for the image $x$ and the forward-model parameters $\boldsymbol{\theta}$ within a Gibbs sampling scheme to sample from the joint posterior $p(x,\boldsymbol{\theta}|y)$. The method decomposes each sampling step into likelihood and prior substeps, implemented with EDM-based diffusion priors and annealed coupling terms to promote robust convergence. Empirically, Blind-PnPDM achieves state-of-the-art results on blind image deblurring, outperforming several baselines in PSNR, SSIM, and LPIPS while preserving fine textures, highlighting the practicality of joint diffusion-prior modeling for blind inverse problems.
Abstract
We introduce Blind Plug-and-Play Diffusion Models (Blind-PnPDM) as a novel framework for solving blind inverse problems where both the target image and the measurement operator are unknown. Unlike conventional methods that rely on explicit priors or separate parameter estimation, our approach performs posterior sampling by recasting the problem into an alternating Gaussian denoising scheme. We leverage two diffusion models as learned priors: one to capture the distribution of the target image and another to characterize the parameters of the measurement operator. This PnP integration of diffusion models ensures flexibility and ease of adaptation. Our experiments on blind image deblurring show that Blind-PnPDM outperforms state-of-the-art methods in terms of both quantitative metrics and visual fidelity. Our results highlight the effectiveness of treating blind inverse problems as a sequence of denoising subproblems while harnessing the expressive power of diffusion-based priors.