Recent studies reveal the connection between GNNs and the diffusion process, which motivates many diffusion-based GNNs to be proposed. However, since these two mechanisms are closely related, one fundamental question naturally arises: Is there a general diffusion framework that can formally unify these GNNs? The answer to this question can not only deepen our understanding of the learning process of GNNs, but also may open a new door to design a broad new class of GNNs. In this paper, we propose a general diffusion equation framework with the fidelity term, which formally establishes the relationship between the diffusion process with more GNNs. Meanwhile, with this framework, we identify one characteristic of graph diffusion networks, i.e., the current neural diffusion process only corresponds to the first-order diffusion equation. However, by an experimental investigation, we show that the labels of high-order neighbors actually exhibit monophily property, which induces the similarity based on labels among high-order neighbors without requiring the similarity among first-order neighbors. This discovery motives to design a new high-order neighbor-aware diffusion equation, and derive a new type of graph diffusion network (HiD-Net) based on the framework. With the high-order diffusion equation, HiD-Net is more robust against attacks and works on both homophily and heterophily graphs. We not only theoretically analyze the relation between HiD-Net with high-order random walk, but also provide a theoretical convergence guarantee. Extensive experimental results well demonstrate the effectiveness of HiD-Net over state-of-the-art graph diffusion networks.

翻译：最新研究表明，图神经网络与扩散过程存在内在联系，这推动了众多基于扩散的图神经网络被提出。然而，由于这两种机制紧密相关，一个根本性问题自然浮现：是否存在一个统一的扩散框架能够正式统一这些图神经网络？这个问题的答案不仅能加深我们对图神经网络学习过程的理解，更可能为设计全新类别的图神经网络打开新的大门。本文提出一个包含保真项的通用扩散方程框架，正式建立了扩散过程与更多图神经网络之间的关联。同时，借助该框架，我们识别出图扩散网络的一个特性：当前神经扩散过程仅对应一阶扩散方程。但通过实验研究，我们发现高阶邻居的标签实际上表现出了同性相似性，这种性质使得基于标签的相似性在高阶邻居间得以形成，而不需要一阶邻居间存在相似性。这一发现启发我们设计了一种新的高阶邻居感知扩散方程，并基于该框架推导出新型图扩散网络(HiD-Net)。借助高阶扩散方程，HiD-Net对攻击具有更强的鲁棒性，且能同时处理同配性与异配性图。我们不仅从理论上分析了HiD-Net与高阶随机游走的关系，还提供了理论收敛保证。大量实验结果表明，HiD-Net相较于当前最先进的图扩散网络具有显著优势。