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。

使用去噪扩散概率模型理论上证明图像修复的合理性

A Theoretical Justification for Image Inpainting using Denoising Diffusion Probabilistic Models

Accelerating learning processes for complex tasks by leveraging previously
learned tasks has been one of the most challenging problems in reinforcement
learning, especially when the similarity between source and target tasks is
low. This work proposes REPresentation And INstance Transfer (REPAINT)
algorithm for knowledge transfer in deep reinforcement learning. REPAINT not
only transfers the representation of a pre-trained teacher policy in the
on-policy learning, but also uses an advantage-based experience selection
approach to transfer useful samples collected following the teacher policy in
the off-policy learning. Our experimental results on several benchmark tasks
show that REPAINT significantly reduces the total training time in generic
cases of task similarity. In particular, when the source tasks are dissimilar
to, or sub-tasks of, the target tasks, REPAINT outperforms other baselines in
both training-time reduction and asymptotic performance of return scores.

本研究提出了一种名为 REPAINT 的深度强化学习知识转移算法，它不仅在 On-policy 学习中传递了预训练模型的表征，还使用基于优势的经验选择方法在 Off-policy 学习中传递了遵循预训练模型收集的有用样本，实验结果表明 REPAINT 在任务相似性较低的一般情况下显著缩短了总训练时间，特别当源任务与目标任务不相似或为子任务时， REPAINT 在减少训练时间和返回分数的渐近性能方面都优于其他基线。