Sub-graph Based Diffusion Model for Link Prediction

Denoising Diffusion Probabilistic Models (DDPMs) represent a contemporary class of generative models with exceptional qualities in both synthesis and maximizing the data likelihood. These models work by traversing a forward Markov Chain where data is perturbed, followed by a reverse process where a neural network learns to undo the perturbations and recover the original data. There have been increasing efforts exploring the applications of DDPMs in the graph domain. However, most of them have focused on the generative perspective. In this paper, we aim to build a novel generative model for link prediction. In particular, we treat link prediction between a pair of nodes as a conditional likelihood estimation of its enclosing sub-graph. With a dedicated design to decompose the likelihood estimation process via the Bayesian formula, we are able to separate the estimation of sub-graph structure and its node features. Such designs allow our model to simultaneously enjoy the advantages of inductive learning and the strong generalization capability. Remarkably, comprehensive experiments across various datasets validate that our proposed method presents numerous advantages: (1) transferability across datasets without retraining, (2) promising generalization on limited training data, and (3) robustness against graph adversarial attacks.