Geometric Inductive Biases for Diffusion-Based Graph Generation

We view graph generation as the problem of sampling a geometric configuration of nodes in a latent space whose geometry represents the structure of the underlying graph. In this framework, a graph is generated by first sampling node embeddings through a diffusion process defined on the latent geometry, and then recovering edges from the resulting configuration based on geometric relations. The choice of latent geometry acts as the primary inductive bias of the model and determines which graph structures can be represented naturally. By instantiating this process with latent spaces of different curvature, we analyze how geometric assumptions influence generation quality. Experiments on synthetic graph families and molecular graphs show that performance depends systematically on curvature and is highest when the latent geometry matches the structural properties of the data. These results indicate that graph generation can be effectively guided by latent geometry alone, without relying on node features or domain-specific constraints.