Title: DeepGRAND: Deep Graph Neural Diffusion. Abstract: We propose the Deep Graph Neural Diffusion (DeepGRAND), a class of continuous-depth graph neural networks based on the diffusion process on graphs. DeepGRAND leverages a data-dependent scaling term and a perturbation to the graph diffusivity to make the real part of all eigenvalues of the diffusivity matrix become negative, which ensures two favorable theoretical properties: (i) the node representation does not exponentially converge to a constant vector as the model depth increases, thus alleviating the over-smoothing issue; (ii) the stability of the model is guaranteed by controlling the norm of the node representation. Compared to the baseline GRAND, DeepGRAND mitigates the accuracy drop-off with increasing depth and improves the overall accuracy of the model. We empirically corroborate the advantage of DeepGRAND over many existing graph neural networks on various graph deep learning benchmark tasks.