Information-Geometric Adaptive Sampling for Graph Diffusion

Abstract

Standard diffusion models for graph generation typically rely on uniform time-stepping, an approach that overlooks the non-homogeneous dynamics of distributional evolution on complex manifolds. In this paper, we present an information-geometric framework that reinterprets the diffusion sampling trajectory as a parametric curve on a Riemannian manifold. Our key observation is that the Fisher-Rao metric provides a principled measure of the intrinsic distance. By analyzing this metric, we derive the Drift Variation Score (DVS), a geometry-aware indicator that quantifies the instantaneous rate of distributional change. Unlike prior heuristic-based adaptive samplers, our DVS Sampler enforces a constant-speed traversal along the manifold, automatically allocating finer steps to regions of high curvature and larger steps to stable phases. This equal arc-length strategy ensures that each discretization step contributes equally to the information gain. Theoretical analysis demonstrates that DVS characterizes the local stiffness of the sampling dynamics in the Fisher-Rao sense. Experimental results on molecule and social network generation show that our method significantly improves structural fidelity and sampling efficiency.