用后验最大估计法提升图像逆问题的生成效果。
MAP-based Problem-Agnostic diffusion model for Inverse Problems
- 基于贝叶斯规则分解得分函数，用MAP方法估计引导项。
- 在超分辨率和图像修复中更好保留物体结构与邻域连贯性。
- 无需针对具体任务微调，适合通用图像逆问题求解。
扩散模型在图像处理的逆问题中展现出巨大潜力。本文提出一种新型、问题无关的扩散模型——基于最大后验（MAP）的引导项估计方法。为利用无条件预训练的扩散模型解决条件生成任务，我们根据贝叶斯规则将条件得分函数分解为两部分：由预训练得分网络近似的无条件得分函数，以及通过新提出的MAP方法估计的引导项，该方法引入自然图像的高斯型先验。这一创新使模型更准确捕捉数据内在特性，从而提升性能。数值结果表明，相比现有最先进方法，本方法在保持内容完整性方面表现更优——例如在超分辨率任务中更好地保留眼镜结构，在修补任务中显著改善掩码区域周围的连贯性。
原文摘要 · Abstract (English)
Diffusion models have indeed shown great promise in solving inverse problems in image processing. In this paper, we propose a novel, problem-agnostic diffusion model called the maximum a posteriori (MAP)-based guided term estimation method for inverse problems. To leverage unconditionally pretrained diffusion models to address conditional generation tasks, we divide the conditional score function into two terms according to Bayes' rule: an unconditional score function (approximated by a pretrained score network) and a guided term, which is estimated using a novel MAP-based method that incorporates a Gaussian-type prior of natural images. This innovation allows us to better capture the intrinsic properties of the data, leading to improved performance. Numerical results demonstrate that our method preserves contents more effectively compared to state-of-the-art methods--for example, maintaining the structure of glasses in super-resolution tasks and producing more coherent results in the neighborhood of masked regions during inpainting.
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