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, GraphBFNemploys 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.

How can computers better generate realistic graphs like social networks or molecular structures? Graphs are everywhere-from Facebook connections to the atoms and bonds in medicines. Creating new graphs artificially is challenging because they have complex patterns and relationships.Our paper presents Graph Bayesian Flow Networks (GraphBFN), a new method that generates graphs by treating their structure as continuous information rather than discrete combinations of pieces. Think of it as the difference between a smooth water flow versus individual water droplets - our approach captures the "flow" of how graphs could be generated.Traditional methods work with graphs as separate nodes and connections, like building with LEGO blocks. Instead, GraphBFN leverages advanced mathematical concepts inspired by graph spectral theory to represent graph patterns more smoothly—analogous to how artists blend colors gradually from coarse to fine, rather than relying on distinct dots. This allows our method to generate more realistic graphs much faster. Our findings show that GraphBFN creates better-quality graphs while being significantly more efficient than existing methods. This could accelerate drug discovery by generating new molecular structures or help understand complex networks in biology and social sciences.