Bayesian Conditioned Diffusion Models for Inverse Problems

• URL: http://arxiv.org/abs/2406.09768v1
• Date: Fri, 14 Jun 2024 07:13:03 GMT
• Title: Bayesian Conditioned Diffusion Models for Inverse Problems
• Authors: Alper Güngör, Bahri Batuhan Bilecen, Tolga Çukur,
• Abstract summary: Diffusion models excel in many image reconstruction tasks that involve inverse problems based on a forward measurement operator. We propose a novel Bayesian conditioning technique for diffusion models, BCDM, based on score-functions associated with the conditional distribution of desired images. We show state-of-the-art performance in image dealiasing, deblurring, super-resolution, and inpainting with the proposed technique.
• Score: 11.67269909384503
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• 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.

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