SBGD: Improving Graph Diffusion Generative Model via Stochastic Block Diffusion

Graph diffusion generative models (GDGMs) have emerged as powerful tools for generating high-quality graphs. However, their broader adoption faces challenges in scalability and size generalization. GDGMs struggle to scale to large graphs due to their high memory requirements, as they typically operate in the full graph space, requiring the entire graph to be stored in memory during training and inference. This constraint limits their feasibility for large-scale real-world graphs. GDGMs also exhibit poor size generalization, with limited ability to generate graphs of sizes different from those in the training data, restricting their adaptability across diverse applications. To address these challenges, we propose the stochastic block graph diffusion (SBGD) model, which refines graph representations into a block graph space. This space incorporates structural priors based on real-world graph patterns, significantly reducing memory complexity and enabling scalability to large graphs. The block representation also improves size generalization by capturing fundamental graph structures. Empirical results show that SBGD achieves significant memory improvements (up to 6$\times$) while maintaining comparable or even superior graph generation performance relative to state-of-the-art methods. Furthermore, experiments demonstrate that SBGD better generalizes to unseen graph sizes. The significance of SBGD extends beyond being a scalable and effective GDGM; it also exemplifies the principle of modularization in generative modelling, offering a new avenue for exploring generative models by decomposing complex tasks into more manageable components.