Information-geometric adaptive sampling for graph diffusion

• URL: http://arxiv.org/abs/2605.00250v1
• Date: Thu, 30 Apr 2026 21:32:35 GMT
• Title: Information-geometric adaptive sampling for graph diffusion
• Abstract summary: Drift Variation Score (DVS) is a geometry-aware indicator that quantifies the instantaneous rate of distributional change.<n>Unlike prior-based adaptive samplers, our DVS solver enforces a constant informational speed on the statistical manifold.<n> Experimental results on molecule and social network generation show that DVS significantly improves structural fidelity and sampling efficiency.
• Score: 12.550914083067525
• License: http://creativecommons.org/licenses/by/4.0/
• 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

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