Information-geometric adaptive sampling for graph diffusion

Fuente: arXiv
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Main Authors: Lu, Yuhui, Liu, Wenjing, Zhan, Kun
Format: Preprint
Published: 2026
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author Lu, Yuhui
Liu, Wenjing
Zhan, Kun
author_facet Lu, Yuhui
Liu, Wenjing
Zhan, Kun
contents 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
format Preprint
id arxiv_https___arxiv_org_abs_2605_00250
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Information-geometric adaptive sampling for graph diffusion
Lu, Yuhui
Liu, Wenjing
Zhan, Kun
Machine Learning
Computer Vision and Pattern Recognition
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
title Information-geometric adaptive sampling for graph diffusion
topic Machine Learning
Computer Vision and Pattern Recognition
url https://arxiv.org/abs/2605.00250