First gradient-flow framework for discrete graph diffusion: FEGF trains fast with quadratic loss
FrancescoLocat8 · x · 2026-10-07
A new arXiv paper by Rancati, Maas and Locatello presents the first computational approach framing discrete-space diffusion models as gradient flows.
- Continuous-space diffusion models have long been interpretable via the Wasserstein-2 metric and the JKO scheme, but a parallel theory for discrete diffusion (continuous-time Markov chains) was missing.
- The authors introduce a metric WK on the probability simplex, letting common discrete diffusion paths like the discrete heat equation be seen as gradient flows of free-energy functionals.
- The resulting learning method exploits first-order optimality conditions of the JKO scheme: a simple quadratic loss, extremely fast training, no need for individual sample trajectories, and only numerical preprocessing of WK-geodesics.
- Validated on synthetic data across several graph classes, recovering the underlying functional.
Related event: FEGF Brings Gradient Flow Theory to Graph Discrete Diffusion(2 posts)→
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