Bayesian Conditioned Diffusion Models for Inverse Problems

TL;DR

This paper introduces a Bayesian conditioning method for diffusion models that significantly improves image reconstruction tasks like deblurring and super-resolution by rigorously incorporating measured data into the model.

Contribution

The paper proposes a novel Bayesian conditioning technique for diffusion models, enhancing their ability to solve inverse problems with theoretically grounded score-function training.

Findings

State-of-the-art performance in image dealiasing

Superior results in deblurring and super-resolution

Effective inpainting with the proposed method

Abstract

Diffusion models have recently been shown to excel in many image reconstruction tasks that involve inverse problems based on a forward measurement operator. A common framework uses task-agnostic unconditional models that are later post-conditioned for reconstruction, an approach that typically suffers from suboptimal task performance. While task-specific conditional models have also been proposed, current methods heuristically inject measured data as a naive input channel that elicits sampling inaccuracies. Here, we address the optimal conditioning of diffusion models for solving challenging inverse problems that arise during image reconstruction. Specifically, we propose a novel Bayesian conditioning technique for diffusion models, BCDM, based on score-functions associated with the conditional distribution of desired images given measured data. We rigorously derive the theory to express and train the conditional score-function. Finally, we show state-of-the-art performance in image dealiasing, deblurring, super-resolution, and inpainting with the proposed technique.