  We present Graph Neural Diffusion (GRAND) that approaches deep learning on
graphs as a continuous diffusion process and treats Graph Neural Networks
(GNNs) as discretisations of an underlying PDE. In our model, the layer
structure and topology correspond to the discretisation choices of temporal and
spatial operators. Our approach allows a principled development of a broad new
class of GNNs that are able to address the common plights of graph learning
models such as depth, oversmoothing, and bottlenecks. Key to the success of our
models are stability with respect to perturbations in the data and this is
addressed for both implicit and explicit discretisation schemes. We develop
linear and nonlinear versions of GRAND, which achieve competitive results on
many standard graph benchmarks.
