Information-geometric adaptive sampling for graph diffusion

Standard diffusion models for graph generation rely on uniform time-stepping, which ignores the non-homogeneous dynamics of distributional evolution on complex manifolds. A new paper accepted to ICML 2026 introduces an information-geometric framework that reinterprets the diffusion sampling trajectory as a parametric curve on a Riemannian manifold. The key insight is that the Fisher-Rao metric provides a principled measure of intrinsic distance, leading to the Drift Variation Score (DVS), a geometry-aware indicator that quantifies the instantaneous rate of distributional change.

Unlike heuristic-based adaptive samplers, the DVS solver enforces a constant informational speed on the statistical manifold. This equal arc-length strategy ensures that each discretization step contributes equally to the information speed, automatically maintaining a uniform rate of distributional change along the sampling trajectory. The theoretical analysis verifies that DVS characterizes the local stiffness of the sampling dynamics in the Fisher-Rao sense.

Experimental results on molecule and social network generation demonstrate that DVS significantly improves structural fidelity and sampling efficiency compared to uniform sampling and prior adaptive methods. The code is available on GitHub. This approach offers a principled, geometry-aware alternative for graph diffusion, potentially impacting applications in drug discovery, social network analysis, and material science where high-fidelity graph generation is critical.