Bayesian Conditioned Diffusion Models for Inverse Problems
This addresses the problem of inaccurate image reconstruction for applications in medical imaging or computer vision, offering a rigorous improvement over heuristic methods.
The paper tackles the suboptimal performance of diffusion models in image reconstruction inverse problems by proposing a Bayesian conditioning technique (BCDM) that uses conditional score-functions, achieving state-of-the-art results in tasks like dealiasing, deblurring, super-resolution, and inpainting.
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.