DiPhon: Diffusion on Graphons for Scalable Graph Generation

DiPhon is a diffusion framework for generating graphs at sizes beyond those seen during training. It models a continuous diffusion process in graphon space using a Jacobi stochastic differential equation, then discretizes the process for finite graphs. The reverse process uses a tractable marginal score estimated through graph denoising. The authors prove exact matching of the first moment and a closed-form approximation error for the second moment relative to the graphon dynamics. According to the abstract, models trained on small graphs can generate progressively larger graphs without retraining while preserving core topological properties.