Information-geometric adaptive sampling for graph diffusion

TL;DR

This paper introduces an information-geometric adaptive sampling method for graph diffusion that maintains a constant informational speed, improving efficiency and fidelity in graph generation tasks.

Contribution

It proposes a novel geometry-aware indicator, DVS, based on Fisher-Rao metric, to adaptively control sampling steps for better graph diffusion performance.

Findings

DVS enforces uniform informational speed along the sampling trajectory.

The method improves structural fidelity in molecule and social network generation.

Experimental results show enhanced sampling efficiency and quality.

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