Smooth Interpolation for Improved Discrete Graph Generative Models

Though typically represented by the discrete node and edge attributes, the graph topological information can be sufficiently captured by the graph spectrum in a continuous space. It is believed that incorporating the continuity of graph topological information into the generative process design could establish a superior paradigm for graph generative modeling. Motivated by such prior and recent advancements in the generative paradigm, we propose Graph Bayesian Flow Networks (GraphBFN) in this paper, a principled generative framework that designs an alternative generative process emphasizing the dynamics of topological information. Unlike recent discrete-diffusion-based methods, GraphBFN employs the continuous counts derived from sampling infinite times from a categorical distribution as latent to facilitate a smooth decomposition of topological information, demonstrating enhanced effectiveness. To effectively realize the concept, we further develop an advanced sampling strategy and new time-scheduling techniques to overcome practical barriers and boost performance. Through extensive experimental validation on both generic graph and molecular graph generation tasks, GraphBFN could consistently achieve superior or competitive performance with significantly higher training and sampling efficiency. The code is available at https: //github.com/AlgoMole/GraphBFN .