  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 \url{https://github.com/zknus/Graph-Diffusion-CDE}.
