用几何方法优化图生成采样步长，让每一步都带来等量信息增量。
Information-geometric adaptive sampling for graph diffusion
- 基于费雪-罗极限度量构建采样轨迹的几何框架
- 提出DVS指标实现自适应步长，提升结构保真度与效率
- 适合需要高质量图生成的研究者和工业应用
图生成的标准扩散模型通常采用均匀时间步长，忽略了复杂流形上分布演化的非均匀性。本文提出一种信息几何框架，将扩散采样轨迹重新解释为黎曼流形上的参数曲线。核心观察是费雪-罗度量能提供内在距离的合理度量。通过分析该度量，我们推导出漂移变化评分（DVS），一个感知几何的指标，用于量化分布变化的瞬时速率。与以往依赖启发式的方法不同，DVS求解器在统计流形上强制保持恒定的信息速度，自动维持采样轨迹上分布变化的均匀速率。这种等弧长策略确保每一步离散化都对信息速度有相等贡献。理论分析表明，DVS刻画了采样动态在费雪-罗意义下的局部刚度。在分子和社交网络生成任务上的实验结果表明，DVS显著提升了结构保真度和采样效率。代码已开源：https://github.com/kunzhan/DVS
原文摘要 · Abstract (English)
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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