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.

扩散模型在图像重建中表现出优异的性能，提出了一种基于贝叶斯条件技术的扩散模型，通过条件得分函数来解决图像重建中出现的挑战性逆问题，并在图像去混叠、去模糊、超分辨率和修复中展现出最新技术的性能。