  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.
