A Mixed-Curvature Graph Diffusion Model

Graph generation plays a vital role in a wide range of applications such as traffic analysis, drug discovery and more, for its rapid and efficient generation speed coupled with its precise and stable generation capabilities. And the diffusion model, which is the dominant solution in image generation domain, has shown its potential in graph generation recently. In the literature, existing graph diffusion models trivialize the graph structure, and prioritize the Euclidean space for graph generation, ignoring the intrinsic difference between non-Euclidean graph structures and Euclidean grid-like image/text data. The few graph diffusion models in hyperbolic space separate the embedding and diffusion process, and loose the geometric constraints in the diffusion process. The problem of generating graph structure in a generic Riemannian space largely remains open. It faces several fundamental challenges. On the one hand, navigating and structuring graphs within Riemannian spaces poses greater difficulty. In other words, how to preserve adherence to the constraints of Riemannian geometry has not been touched in the literature. On the other hand, Riemannian operators for graph diffusion models are not available so far, which is inherently different from that in Euclidean space. In light of the aforementioned issues, we restore the notion of product space, and propose a generic graph generation method, called mixed-curvature Product Space Graph Diffusion Model (ProGDM). Specifically, ProGDM includes a Riemannian embedding module based on contrastive learning and a geometric diffusion models across multiple Riemannian sub-spaces. We evaluate the proposed ProGDM with extensive experiments on benchmark datasets, and the empirical results show that ProGDM has achieved superior performance to the state-of-the-art methods.