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.

翻译：我们在线性模型框架下为基于扩散的图像修复方法提供了理论依据。尽管多数修复算法需要针对每种新掩码重新训练，但我们证明基于扩散的修复方法无需重新训练即可很好地泛化到未见过的掩码。我们分析了最近一种流行的基于扩散的修复算法RePaint（Lugmayr等人，2022），并发现在两态扩散过程中，该算法因对齐偏差而影响样本恢复。受此启发，我们提出改进算法RePaint$^+$，该算法能够可靠地恢复真实样本，并具有线性收敛速度。其核心在于修正逆向过程中漂移与扩散项的对齐误差。据我们所知，这是首个针对基于扩散的图像修复算法的线性收敛性证明结果。