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：近期研究揭示了图神经网络（GNNs）与扩散过程之间的关联，这促使大量基于扩散的GNN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：是否存在一个可统一这些GNN的通用扩散框架？该问题的解答不仅能深化我们对GNN学习过程的理解，还可能为设计全新类型的GNN开辟新途径。本文提出一个包含保真项的广义扩散方程框架，从形式上建立了扩散过程与更多GNN之间的联系。同时，基于该框架，我们发现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。然而，实验研究表明，高阶邻居的标签实际上呈现单亲性（monophily property），即无需一阶邻居的相似性即可产生基于标签的高阶邻居相似性。这一发现促使我们设计新的高阶邻居感知扩散方程，并基于该框架推导出一种新型图扩散网络（HiD-Net）。通过高阶扩散方程，HiD-Net对攻击更具鲁棒性，且在同质性和异质性图上均有效。我们不仅从理论上分析了HiD-Net与高阶随机游走的关系，还提供了理论收敛性保证。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有效性。