Information-geometric adaptive sampling for graph diffusion

2026-04-30

AI Summary

This work addresses the limitation of uniform time stepping in graph diffusion generative models, which fails to capture the non-uniform dynamics of distribution evolution on complex manifolds, thereby compromising sampling efficiency and structural fidelity. The authors model diffusion trajectories as parametric curves on Riemannian manifolds and introduce the Drift Variation Score (DVS)—the first locally rigid metric within an information-geometric framework that quantifies the rate of distributional change via the Fisher–Rao metric. Leveraging DVS, they devise an adaptive sampling strategy that enforces constant information velocity, achieving equi-arc-length discretization. Empirical results on molecular and social network generation demonstrate substantial improvements in both structural fidelity and sampling efficiency, validating the effectiveness and superiority of the proposed geometry-aware, DVS-driven adaptive solver.

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 solver enforces a constant informational speed on the statistical manifold, automatically maintaining a uniform rate of distributional change along the sampling trajectory. This equal arc-length strategy ensures that each discretization step contributes equally to the information speed. 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 show that DVS significantly improves structural fidelity and sampling efficiency. Code is at https://github.com/kunzhan/DVS

Problem

• graph diffusion
• adaptive sampling
• non-homogeneous dynamics
• distributional evolution
• Riemannian manifold

Innovation

• information geometry
• adaptive sampling
• graph diffusion
• Fisher-Rao metric
• Drift Variation Score