ICML 2025

DeFoG: Discrete Flow Matching for Graph Generation
Yiming Qin * 1 Manuel Madeira * 1 Dorina Thanou 1 Pascal Frossard 1
Abstract
Graph generative models are essential across
diverse scientific domains by capturing complex
distributions over relational data. Among them,
graph diffusion models achieve superior perfor-
mance but face inefficient sampling and limited
flexibility due to the tight coupling between
training and sampling stages.
We introduce
DeFoG, a novel graph generative framework that
disentangles sampling from training, enabling
a broader design space for more effective and
efficient model optimization. DeFoG employs a
discrete flow-matching formulation that respects
the inherent symmetries of graphs.
We theo-
retically ground this disentangled formulation
by explicitly relating the training loss to the
sampling algorithm and showing that DeFoG
faithfully replicates the ground truth graph
distribution. Building on these foundations, we
thoroughly investigate DeFoG’s design space
and propose novel sampling methods that sig-
nificantly enhance performance and reduce the
required number of refinement steps. Extensive
experiments demonstrate state-of-the-art perfor-
mance across synthetic, molecular, and digital
pathology datasets, covering both unconditional
and conditional generation settings.
It also
outperforms most diffusion-based models with
just 5–10% of their sampling steps.
1. Introduction
Graph generation has become a fundamental task across
diverse fields, from molecular chemistry to social net-
work analysis, due to graphs’ capacity to represent com-
plex relationships and generate realistic structured data.
Diffusion-based graph generative models (Niu et al., 2020;
Jo et al., 2022), particularly those tailored for discrete data
(Vignac et al., 2022), have emerged as compelling ap-
*Equal contribution
1EPFL, Lausanne, Switzerland.
Cor-
respondence to: Yiming Qin <yiming.qin@epfl.ch>, Manuel
Madeira <manuel.madeira@epfl.ch>.
Proceedings of the 42 ...