ICML 2025

Revisiting Non-Acyclic GFlowNets in Discrete Environments
Nikita Morozov * 1 Ian Maksimov * 1 Daniil Tiapkin 2 3 Sergey Samsonov 1
Abstract
Generative Flow Networks (GFlowNets) are a
family of generative models that learn to sample
objects from a given probability distribution, po-
tentially known up to a normalizing constant. In-
stead of working in the object space, GFlowNets
proceed by sampling trajectories in an appro-
priately constructed directed acyclic graph en-
vironment, greatly relying on the acyclicity of
the graph. In our paper, we revisit the theory
that relaxes the acyclicity assumption and present
a simpler theoretical framework for non-acyclic
GFlowNets in discrete environments. Moreover,
we provide various novel theoretical insights re-
lated to training with fixed backward policies,
the nature of flow functions, and connections be-
tween entropy-regularized RL and non-acyclic
GFlowNets, which naturally generalize the re-
spective concepts and theoretical results from the
acyclic setting. In addition, we experimentally
re-examine the concept of loss stability in non-
acyclic GFlowNet training, as well as validate our
own theoretical findings.
1. Introduction
Generative Flow Networks (GFlowNets, Bengio et al., 2021)
are models that aim to sample discrete objects from distribu-
tions known proportionally up to a constant. They operate
by constructing an object through a sequence of stochastic
transitions defined by a forward policy. GFlowNets have
been successfully applied in various areas, starting from
molecule generation (Bengio et al., 2021; Shen et al., 2024;
Koziarski et al., 2024; Cretu et al., 2025) and biological
sequence design (Jain et al., 2022; Kim et al., 2024) to com-
binatorial optimization (Zhang et al., 2023a;b; Kim et al.,
*Equal contribution 1HSE University, Moscow, Russia 2CMAP
– CNRS – ´Ecole polytechnique – Institut Polytechnique de Paris,
91128, Palaiseau, France 3Universit´e Paris-Saclay, CNRS, LMO,
91405, Orsay, France.
Corr...