# A Generalized Neural Diffusion Framework on Graphs

arXiv: https://arxiv.org/abs/2312.08616 · HTML: https://mlsanity.com/paper/2312.08616/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 35 references that are in the map.
- First posted on arXiv 14 Dec 2023.

## Builds on (most cited first, 24 of 24)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Graph U-Nets](https://mlsanity.com/paper/1905.05178/) (2019)
- [Towards Deeper Graph Neural Networks](https://mlsanity.com/paper/2007.09296/) (2020)
- [GRAND: Graph Neural Diffusion](https://mlsanity.com/paper/2106.10934/) (2021)
- [Learning Discrete Structures for Graph Neural Networks](https://mlsanity.com/paper/1903.11960/) (2019)
- [Iterative Deep Graph Learning for Graph Neural Networks: Better and Robust Node Embeddings](https://mlsanity.com/paper/2006.13009/) (2020)
- [Position-aware Graph Neural Networks](https://mlsanity.com/paper/1906.04817/) (2019)
- [Graph Information Bottleneck](https://mlsanity.com/paper/2010.12811/) (2020)
- [Interpreting and Unifying Graph Neural Networks with An Optimization Framework](https://mlsanity.com/paper/2101.11859/) (2021)
- [A Unified View on Graph Neural Networks as Graph Signal Denoising](https://mlsanity.com/paper/2010.01777/) (2020)
- [DEMO-Net: Degree-specific Graph Neural Networks for Node and Graph Classification](https://mlsanity.com/paper/1906.02319/) (2019)
- [Dissecting the Diffusion Process in Linear Graph Convolutional Networks](https://mlsanity.com/paper/2102.10739/) (2021)
- [On the Robustness of Graph Neural Diffusion to Topology Perturbations](https://mlsanity.com/paper/2209.07754/) (2022)

## Built on by (most cited first, 13 of 13)

- [Graph Fairness Learning under Distribution Shifts](https://mlsanity.com/paper/2401.16784/) (2024)
- [Biologically Plausible Brain Graph Transformer](https://mlsanity.com/paper/2502.08958/) (2025)
- [GCoT: Chain-of-Thought Prompt Learning for Graphs](https://mlsanity.com/paper/2502.08092/) (2025)
- [S-Diff: An Anisotropic Diffusion Model for Collaborative Filtering in Spectral Domain](https://mlsanity.com/paper/2501.00384/) (2024)
- [Infinite-Horizon Graph Filters: Leveraging Power Series to Enhance Sparse Information Aggregation](https://mlsanity.com/paper/2401.09943/) (2024)
- [Resolving Oversmoothing with Opinion Dissensus](https://mlsanity.com/paper/2501.19089/) (2025)
- [Graph Wave Networks](https://mlsanity.com/paper/2505.20034/) (2025)
- [Hyperbolic-PDE GNN: Spectral Graph Neural Networks in the Perspective of A System of Hyperbolic Partial Differential Equations](https://mlsanity.com/paper/2505.23014/) (2025)
- [Physics-Inspired Spatial Temporal Graph Neural Networks for Predicting Industrial Chain Resilience](https://mlsanity.com/paper/2508.16836/) (2025)
- [Towards Pre-trained Graph Condensation via Optimal Transport](https://mlsanity.com/paper/2509.14722/) (2025)
- [An Active Diffusion Neural Network for Graphs](https://mlsanity.com/paper/2510.19202/) (2025)
- [Rethinking Message Passing Neural Networks with Diffusion Distance-guided Stress Majorization](https://mlsanity.com/paper/2511.19984/) (2025)
- [BAED: a New Paradigm for Few-shot Graph Learning with Explanation in the Loop](https://mlsanity.com/paper/2603.01941/) (2026)

## Abstract (arXiv)

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.