# Information-geometric adaptive sampling for graph diffusion

arXiv: https://arxiv.org/abs/2605.00250 · HTML: https://mlsanity.com/paper/2605.00250/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 36 of its 53 references that are in the map.
- First posted on arXiv 30 Apr 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 30 of 36)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [Fast Sampling of Diffusion Models with Exponential Integrator](https://mlsanity.com/paper/2204.13902/) (2022)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.06503/) (2022)
- [GraphAF: a Flow-based Autoregressive Model for Molecular Graph Generation](https://mlsanity.com/paper/2001.09382/) (2020)
- [Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equations](https://mlsanity.com/paper/2202.02514/) (2022)
- [Permutation Invariant Graph Generation via Score-Based Generative Modeling](https://mlsanity.com/paper/2003.00638/) (2020)
- [Likelihood Training of Schr"odinger Bridge using Forward-Backward SDEs Theory](https://mlsanity.com/paper/2110.11291/) (2021)
- [Fr'echet ChemNet Distance: A metric for generative models for molecules in drug discovery](https://mlsanity.com/paper/1803.09518/) (2018)
- [Learning Fast Samplers for Diffusion Models by Differentiating Through Sample Quality](https://mlsanity.com/paper/2202.05830/) (2022)
- [GraphDF: A Discrete Flow Model for Molecular Graph Generation](https://mlsanity.com/paper/2102.01189/) (2021)
- [On Fast Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2106.00132/) (2021)
- [Graphite: Iterative Generative Modeling of Graphs](https://mlsanity.com/paper/1803.10459/) (2018)
- [Fisher-Rao Metric, Geometry, and Complexity of Neural Networks](https://mlsanity.com/paper/1711.01530/) (2017)
- [SPECTRE: Spectral Conditioning Helps to Overcome the Expressivity Limits of One-shot Graph Generators](https://mlsanity.com/paper/2204.01613/) (2022)
- [Align Your Steps: Optimizing Sampling Schedules in Diffusion Models](https://mlsanity.com/paper/2404.14507/) (2024)
- [DeFoG: Discrete Flow Matching for Graph Generation](https://mlsanity.com/paper/2410.04263/) (2024)
- [Equivariant Energy-Guided SDE for Inverse Molecular Design](https://mlsanity.com/paper/2209.15408/) (2022)
- [Alleviating Exposure Bias in Diffusion Models through Sampling with Shifted Time Steps](https://mlsanity.com/paper/2305.15583/) (2023)
- [Accelerating Diffusion Sampling with Optimized Time Steps](https://mlsanity.com/paper/2402.17376/) (2024)
- [Graph Generation with Diffusion Mixture](https://mlsanity.com/paper/2302.03596/) (2023)

## Abstract (arXiv)

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