# Graph Neural Convection-Diffusion with Heterophily

arXiv: https://arxiv.org/abs/2305.16780 · HTML: https://mlsanity.com/paper/2305.16780/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 61 references that are in the map.
- First posted on arXiv 26 May 2023.

## Builds on (most cited first, 30 of 33)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [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)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [A critical look at the evaluation of GNNs under heterophily: Are we really making progress?](https://mlsanity.com/paper/2302.11640/) (2023)
- [GRAND: Graph Neural Diffusion](https://mlsanity.com/paper/2106.10934/) (2021)
- [Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNs](https://mlsanity.com/paper/2202.04579/) (2022)
- [Graph Neural Networks with Heterophily](https://mlsanity.com/paper/2009.13566/) (2020)
- [Is Homophily a Necessity for Graph Neural Networks?](https://mlsanity.com/paper/2106.06134/) (2021)
- [Finding Global Homophily in Graph Neural Networks When Meeting Heterophily](https://mlsanity.com/paper/2205.07308/) (2022)
- [Revisiting Heterophily For Graph Neural Networks](https://mlsanity.com/paper/2210.07606/) (2022)
- [Graph-Coupled Oscillator Networks](https://mlsanity.com/paper/2202.02296/) (2022)
- [Stable Neural ODE with Lyapunov-Stable Equilibrium Points for Defending Against Adversarial Attacks](https://mlsanity.com/paper/2110.12976/) (2021)
- [Beltrami Flow and Neural Diffusion on Graphs](https://mlsanity.com/paper/2110.09443/) (2021)
- [GBK-GNN: Gated Bi-Kernel Graph Neural Networks for Modeling Both Homophily and Heterophily](https://mlsanity.com/paper/2110.15777/) (2021)
- [ACMP: Allen-Cahn Message Passing with Attractive and Repulsive Forces for Graph Neural Networks](https://mlsanity.com/paper/2206.05437/) (2022)
- [On the Robustness of Graph Neural Diffusion to Topology Perturbations](https://mlsanity.com/paper/2209.07754/) (2022)
- [How does Heterophily Impact the Robustness of Graph Neural Networks? Theoretical Connections and Practical Implications](https://mlsanity.com/paper/2106.07767/) (2021)
- [RobustLoc: Robust Camera Pose Regression in Challenging Driving Environments](https://mlsanity.com/paper/2211.11238/) (2022)
- [Simplified Graph Convolution with Heterophily](https://mlsanity.com/paper/2202.04139/) (2022)

## Built on by (most cited first, 26 of 26)

- [From Continuous Dynamics to Graph Neural Networks: Neural Diffusion and Beyond](https://mlsanity.com/paper/2310.10121/) (2023)
- [Adversarial Robustness in Graph Neural Networks: A Hamiltonian Approach](https://mlsanity.com/paper/2310.06396/) (2023)
- [Unleashing the Potential of Fractional Calculus in Graph Neural Networks with FROND](https://mlsanity.com/paper/2404.17099/) (2024)
- [Graph ODEs and Beyond: A Comprehensive Survey on Integrating Differential Equations with Graph Neural Networks](https://mlsanity.com/paper/2503.23167/) (2025)
- [Node Embedding from Neural Hamiltonian Orbits in Graph Neural Networks](https://mlsanity.com/paper/2305.18965/) (2023)
- [Message-Passing State-Space Models: Improving Graph Learning with Modern Sequence Modeling](https://mlsanity.com/paper/2505.18728/) (2025)
- [Coupling Graph Neural Networks with Fractional Order Continuous Dynamics: A Robustness Study](https://mlsanity.com/paper/2401.04331/) (2024)
- [On The Temporal Domain of Differential Equation Inspired Graph Neural Networks](https://mlsanity.com/paper/2401.11074/) (2024)
- [Supercharging Graph Transformers with Advective Diffusion](https://mlsanity.com/paper/2310.06417/) (2023)
- [Distributed-Order Fractional Graph Operating Network](https://mlsanity.com/paper/2411.05274/) (2024)
- [Neural Variable-Order Fractional Differential Equation Networks](https://mlsanity.com/paper/2503.16207/) (2025)
- [Improving Graph Neural Networks by Learning Continuous Edge Directions](https://mlsanity.com/paper/2410.14109/) (2024)
- [Quadratic Binary Optimization with Graph Neural Networks](https://mlsanity.com/paper/2404.04874/) (2024)
- [Dirac--Bianconi Graph Neural Networks -- Enabling Non-Diffusive Long-Range Graph Predictions](https://mlsanity.com/paper/2407.12419/) (2024)
- [Resolving Oversmoothing with Opinion Dissensus](https://mlsanity.com/paper/2501.19089/) (2025)
- [Graph Neural Networks with a Distribution of Parametrized Graphs](https://mlsanity.com/paper/2310.16401/) (2023)
- [Resilient Graph Neural Networks: A Coupled Dynamical Systems Approach](https://mlsanity.com/paper/2311.06942/) (2023)
- [Link Prediction with Physics-Inspired Graph Neural Networks](https://mlsanity.com/paper/2402.14802/) (2024)
- [HyperAggregation: Aggregating over Graph Edges with Hypernetworks](https://mlsanity.com/paper/2407.11596/) (2024)
- [Hierarchical Uncertainty-Aware Graph Neural Network](https://mlsanity.com/paper/2504.19820/) (2025)
- [Graph Neural Diffusion via Generalized Opinion Dynamics](https://mlsanity.com/paper/2508.11249/) (2025)
- [Simple Graph Contrastive Learning via Fractional-order Neural Diffusion Networks](https://mlsanity.com/paper/2504.16748/) (2025)
- [Adaptive Multi-view Graph Contrastive Learning via Fractional-order Neural Diffusion Networks](https://mlsanity.com/paper/2511.06216/) (2025)
- [Neighbourhood Transformer: Switchable Attention for Monophily-Aware Graph Learning](https://mlsanity.com/paper/2604.08980/) (2026)
- [Graph Navier Stokes Networks](https://mlsanity.com/paper/2605.21247/) (2026)
- [Continuous-Time Quantum Walks based Graph Neural Network](https://mlsanity.com/paper/2608.20738/) (2026)

## Abstract (arXiv)

Graph neural networks (GNNs) have shown promising results across various graph learning tasks, but they often assume homophily, which can result in poor performance on heterophilic graphs. The connected nodes are likely to be from different classes or have dissimilar features on heterophilic graphs. In this paper, we propose a novel GNN that incorporates the principle of heterophily by modeling the flow of information on nodes using the convection-diffusion equation (CDE). This allows the CDE to take into account both the diffusion of information due to homophily and the ``convection'' of information due to heterophily. We conduct extensive experiments, which suggest that our framework can achieve competitive performance on node classification tasks for heterophilic graphs, compared to the state-of-the-art methods. The code is available at urlhttps://github.com/zknus/Graph-Diffusion-CDE.