Graph Generation with Destination-Predicting Diffusion Mixture

Generation of graphs is a major challenge for real-world tasks that require understanding the complex nature of their non-Euclidean structures. Although diffusion models have achieved notable success in graph generation recently, they are ill-suited for modeling the structural information of graphs since learning to denoise the noisy samples does not explicitly capture the graph topology. To tackle this limitation, we propose a novel generative framework that models the topology of graphs by predicting the destination of the diffusion process, which is the original graph that has the correct topology information, as a weighted mean of data. Specifically, we design the generative process as a mixture of diffusion processes conditioned on the endpoint in the data distribution, which drives the process toward the predicted destination, resulting in rapid convergence. We introduce new simulation-free training objectives for predicting the destination, and further discuss the advantages of our framework that can explicitly model the graph topology and exploit the inductive bias of the data. Through extensive experimental validation on general graph and 2D/3D molecule generation tasks, we show that our method outperforms previous generative models, generating graphs with correct topology with both continuous (e.g. 3D coordinates) and discrete (e.g. atom types) features.