We provide a theoretical justification for sample recovery using diffusion
based image inpainting in a linear model setting. While most inpainting
algorithms require retraining with each new mask, we prove that diffusion based
inpainting generalizes well to unseen masks without retraining. We analyze a
recently proposed popular diffusion based inpainting algorithm called RePaint
(Lugmayr et al., 2022), and show that it has a bias due to misalignment that
hampers sample recovery even in a two-state diffusion process. Motivated by our
analysis, we propose a modified RePaint algorithm we call RePaint$^+$ that
provably recovers the underlying true sample and enjoys a linear rate of
convergence. It achieves this by rectifying the misalignment error present in
drift and dispersion of the reverse process. To the best of our knowledge, this
is the first linear convergence result for a diffusion based image inpainting
algorithm.

本文提出了一种基于扩散的图像修复算法，并针对多数图像修复算法需要反复训练的问题，证明了基于扩散的图像修复算法可以很好地处理未知蒙版，从而避免反复训练。通过分析目前流行的扩散图像修复算法 RePaint 及其存在的偏差问题，本文提出了一种新的修复算法 RePaint+，具有良好的收敛率，并校正了 RePaint 中存在的偏差问题，提升了采样恢复效果，是一种具有线性收敛结果的扩散图像修复算法。