Diffusion models have demonstrated remarkable efficacy in generating
high-quality samples. Existing diffusion-based image restoration algorithms
exploit pre-trained diffusion models to leverage data priors, yet they still
preserve elements inherited from the unconditional generation paradigm. These
strategies initiate the denoising process with pure white noise and incorporate
random noise at each generative step, leading to over-smoothed results. In this
paper, we introduce a refined paradigm for diffusion-based image restoration.
Specifically, we opt for a sample consistent with the measurement identity at
each generative step, exploiting the sampling selection as an avenue for output
stability and enhancement. Besides, we start the restoration process with an
initialization combined with the measurement signal, providing supplementary
information to better align the generative process. Extensive experimental
results and analyses validate the effectiveness of our proposed approach across
diverse image restoration tasks.

本文介绍了一种通过扩展扩散模型进行图像修复的新方法，该方法利用生成过程中与测量身份一致的样本，并结合测量信号与初始化信息来提高生成过程的效果。实验证明了该方法在不同的图像修复任务中的有效性。

图像恢复的扩散后验近端采样

Diffusion Posterior Proximal Sampling for Image Restoration

The Lipschitz bound, a technique from robust statistics, can limit the
maximum changes in the output concerning the input, taking into account
associated irrelevant biased factors. It is an efficient and provable method
for examining the output stability of machine learning models without incurring
additional computation costs. Recently, Graph Neural Networks (GNNs), which
operate on non-Euclidean data, have gained significant attention. However, no
previous research has investigated the GNN Lipschitz bounds to shed light on
stabilizing model outputs, especially when working on non-Euclidean data with
inherent biases. Given the inherent biases in common graph data used for GNN
training, it poses a serious challenge to constraining the GNN output
perturbations induced by input biases, thereby safeguarding fairness during
training. Recently, despite the Lipschitz constant's use in controlling the
stability of Euclideanneural networks, the calculation of the precise Lipschitz
constant remains elusive for non-Euclidean neural networks like GNNs,
especially within fairness contexts. To narrow this gap, we begin with the
general GNNs operating on an attributed graph, and formulate a Lipschitz bound
to limit the changes in the output regarding biases associated with the input.
Additionally, we theoretically analyze how the Lipschitz constant of a GNN
model could constrain the output perturbations induced by biases learned from
data for fairness training. We experimentally validate the Lipschitz bound's
effectiveness in limiting biases of the model output. Finally, from a training
dynamics perspective, we demonstrate why the theoretical Lipschitz bound can
effectively guide the GNN training to better trade-off between accuracy and
fairness.

通过研究 GNN Lipschitz 界限对非欧几里德数据的作用，调查 GNN 模型输出稳定性，并通过对公平训练中学习到的偏见进行实验验证 Lipschitz 边界的有效性，最终展示理论 Lipschitz 边界在 GNN 训练中如何有效平衡准确性和公平性。