Advancing Graph Generation through Beta Diffusion

Diffusion models have demonstrated effectiveness in generating natural images and have been extended to generate diverse data types, including graphs. This new generation of diffusion-based graph generative models has demonstrated significant performance improvements over methods that rely on variational autoencoders or generative adversarial networks. It's important to recognize, however, that most of these models employ Gaussian or categorical diffusion processes, which can struggle with sparse and long-tailed data distributions. In our work, we introduce Graph Beta Diffusion (GBD), a diffusion-based generative model particularly adept at capturing diverse graph structures. GBD utilizes a beta diffusion process, tailored for the sparse and range-bounded characteristics of graph adjacency matrices. Furthermore, we have developed a modulation technique that enhances the realism of the generated graphs by stabilizing the generation of critical graph structures, while preserving flexibility elsewhere. The outstanding performance of GBD across three general graph benchmarks and two biochemical graph benchmarks highlights its capability to effectively capture the complexities of real-world graph data. The code will be made available at https://github.com/YH-UtMSB/Graph_Beta_Diffusion

A Variational Edge Partition Model for Supervised Graph Representation Learning

Graph neural networks (GNNs), which propagate the node features through the edges and learn how to transform the aggregated features under label supervision, have achieved great success in supervised feature extraction for both node-level and graph-level classification tasks. However, GNNs typically treat the graph structure as given and ignore how the edges are formed. This paper introduces a graph generative process to model how the observed edges are generated by aggregating the node interactions over a set of overlapping node communities, each of which contributes to the edges via a logical OR mechanism. Based on this generative model, we partition each edge into the summation of multiple community-specific weighted edges and use them to define community-specific GNNs. A variational inference framework is proposed to jointly learn a GNN based inference network that partitions the edges into different communities, these community-specific GNNs, and a GNN based predictor that combines community-specific GNNs for the end classification task. Extensive evaluations on real-world graph datasets have verified the effectiveness of the proposed method in learning discriminative representations for both node-level and graph-level classification tasks.