Empirical Bayesian image restoration by Langevin sampling with a denoising diffusion implicit prior

TL;DR

This paper presents a novel and highly computationally efficient image restoration method that carefully embeds a foundational DDPM denoiser within an empirical Bayesian Langevin algorithm, which jointly calibrates key model hyper-parameters as it estimates the model’s posterior mean.

Abstract

Score-based diffusion methods provide a powerful strategy to solve image restoration tasks by flexibly combining a pre-trained foundational prior model with a likelihood function specified during test time. Such methods are predominantly derived from two stochastic processes: reversing Ornstein-Uhlenbeck, which underpins the celebrated denoising diffusion probabilistic models (DDPM) and denoising diffusion implicit models (DDIM), and the Langevin diffusion process. The solutions delivered by DDPM and DDIM are often remarkably realistic, but they are not always consistent with measurements because of likelihood intractability issues and the associated required approximations. Alternatively, using a Langevin process circumvents the intractable likelihood issue, but usually leads to restoration results of inferior quality and longer computing times. This paper presents a novel and highly computationally efficient image restoration method that carefully embeds a foundational DDPM denoiser within an empirical Bayesian Langevin algorithm, which jointly calibrates key model hyper-parameters as it estimates the model's posterior mean. Extensive experimental results on three canonical tasks (image deblurring, super-resolution, and inpainting) demonstrate that the proposed approach improves on state-of-the-art strategies both in image estimation accuracy and computing time.

Figures (13)

• Figure 1: Restoration examples of our method: we present the restored images, corresponding measurements, and ground truth for three common image restoration tasks.
• Figure 2: Sample images from FFHQ 256$\times$256 dataset karras2019style.
• Figure 3: Sample images from ImageNet 256$\times$256 dataset deng2009imagenet.
• Figure 4: Qualitative results on FFHQ 256$\times$256 (first row) and ImageNet 256$\times$256 (second row) datasets - Gaussian deblurring experiment: truth $x$, measurement $y$, DPS chung2022come, DiffPIRzhu2023denoising. From the left to the right, we have truth $x^\star$, measurement $y$, DPS chung2022come, DiffPIRzhu2023denoising, DPIR zhang2021plug, SGS coeurdoux2023plug, and our method ($\eta = 2$). We also report the reconstruction PSNR (dB). Observation noise variance $\sigma = 1/255$.
• Figure 5: Qualitative results on FFHQ 256$\times$256 (first row) and ImageNet 256$\times$256 (second row) datasets - Motion deblurring experiment. From the left to the right, we have truth $x^\star$, measurement $y$, DPS chung2022come, DiffPIRzhu2023denoising, DPIR zhang2021plug, SGS coeurdoux2023plug, and our method ($\eta = 2$). We also report the reconstruction PSNR (dB). Observation noise variance $\sigma = 1/255$.