ICML 2025

Symmetry-Aware GFlowNets
Hohyun Kim 1 Seunggeun Lee 1 Min-hwan Oh 1
Abstract
Generative Flow Networks (GFlowNets) offer a
powerful framework for sampling graphs in pro-
portion to their rewards. However, existing ap-
proaches suffer from systematic biases due to
inaccuracies in state transition probability com-
putations. These biases, rooted in the inherent
symmetries of graphs, impact both atom-based
and fragment-based generation schemes. To ad-
dress this challenge, we introduce Symmetry-
Aware GFlowNets (SA-GFN), a method that in-
corporates symmetry corrections into the learning
process through reward scaling. By integrating
bias correction directly into the reward structure,
SA-GFN eliminates the need for explicit state
transition computations. Empirical results show
that SA-GFN enables unbiased sampling while
enhancing diversity and consistently generating
high-reward graphs that closely match the target
distribution.
1. Introduction
GFlowNets have emerged as a powerful framework for learn-
ing generative models capable of sampling complex, compo-
sitional objects with probabilities proportional to a given re-
ward. Inspired by reinforcement learning (RL), GFlowNets
generate these objects through a sequence of actions that it-
eratively modify the structure of the object being built. This
approach is particularly well-suited for generating compo-
sitional objects, such as graphs, where there are multiple
paths for constructing an object. A prominent application
of GFlowNets is molecule generation, where molecules are
sequentially constructed as graphs (Bengio et al., 2021; Jain
et al., 2023a).
However, GFlowNet training objectives rely on the accurate
computation of the transition probability of a policy, which
1Graduate School of Data Science, Seoul National University,
Seoul, Republic of Korea. Correspondence to: Seunggeun Lee
<lee7801@snu.ac.kr>, Min-hwan Oh <minoh@snu.ac.kr>.
Proceedings of the 42 nd International Conference on Machine
Learning, Vancouver...