# Revisiting Non-Acyclic GFlowNets in Discrete Environments

arXiv: https://arxiv.org/abs/2502.07735 · HTML: https://mlsanity.com/paper/2502.07735/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 43 references that are in the map.
- First posted on arXiv 11 Feb 2025.

## Builds on (most cited first, 30 of 35)

- [Flow Network based Generative Models for Non-Iterative Diverse Candidate Generation](https://mlsanity.com/paper/2106.04399/) (2021)
- [GFlowNet Foundations](https://mlsanity.com/paper/2111.09266/) (2021)
- [A Theory of Regularized Markov Decision Processes](https://mlsanity.com/paper/1901.11275/) (2019)
- [Trajectory balance: Improved credit assignment in GFlowNets](https://mlsanity.com/paper/2201.13259/) (2022)
- [A unified view of entropy-regularized Markov decision processes](https://mlsanity.com/paper/1705.07798/) (2017)
- [Biological Sequence Design with GFlowNets](https://mlsanity.com/paper/2203.04115/) (2022)
- [Bayesian Structure Learning with Generative Flow Networks](https://mlsanity.com/paper/2202.13903/) (2022)
- [Learning GFlowNets from partial episodes for improved convergence and stability](https://mlsanity.com/paper/2209.12782/) (2022)
- [GFlowNets and variational inference](https://mlsanity.com/paper/2210.00580/) (2022)
- [A theory of continuous generative flow networks](https://mlsanity.com/paper/2301.12594/) (2023)
- [Understanding Reinforcement Learning-Based Fine-Tuning of Diffusion Models: A Tutorial and Review](https://mlsanity.com/paper/2407.13734/) (2024)
- [Amortizing intractable inference in large language models](https://mlsanity.com/paper/2310.04363/) (2023)
- [Better Training of GFlowNets with Local Credit and Incomplete Trajectories](https://mlsanity.com/paper/2302.01687/) (2023)
- [Towards Understanding and Improving GFlowNet Training](https://mlsanity.com/paper/2305.07170/) (2023)
- [Amortizing intractable inference in diffusion models for vision, language, and control](https://mlsanity.com/paper/2405.20971/) (2024)
- [Robust Scheduling with GFlowNets](https://mlsanity.com/paper/2302.05446/) (2023)
- [Generative Flow Networks as Entropy-Regularized RL](https://mlsanity.com/paper/2310.12934/) (2023)
- [Learning diverse attacks on large language models for robust red-teaming and safety tuning](https://mlsanity.com/paper/2405.18540/) (2024)
- [Ant Colony Sampling with GFlowNets for Combinatorial Optimization](https://mlsanity.com/paper/2403.07041/) (2024)
- [Discrete Probabilistic Inference as Control in Multi-path Environments](https://mlsanity.com/paper/2402.10309/) (2024)
- [RGFN: Synthesizable Molecular Generation Using GFlowNets](https://mlsanity.com/paper/2406.08506/) (2024)
- [Maximum entropy GFlowNets with soft Q-learning](https://mlsanity.com/paper/2312.14331/) (2023)
- [Improving GFlowNets for Text-to-Image Diffusion Alignment](https://mlsanity.com/paper/2406.00633/) (2024)
- [SynFlowNet: Design of Diverse and Novel Molecules with Synthesis Constraints](https://mlsanity.com/paper/2405.01155/) (2024)
- [Learning Energy Decompositions for Partial Inference of GFlowNets](https://mlsanity.com/paper/2310.03301/) (2023)
- [QGFN: Controllable Greediness with Action Values](https://mlsanity.com/paper/2402.05234/) (2024)
- [Pessimistic Backward Policy for GFlowNets](https://mlsanity.com/paper/2405.16012/) (2024)
- [Optimizing Backward Policies in GFlowNets via Trajectory Likelihood Maximization](https://mlsanity.com/paper/2410.15474/) (2024)
- [Improved Off-policy Reinforcement Learning in Biological Sequence Design](https://mlsanity.com/paper/2410.04461/) (2024)
- [A Theory of Non-Acyclic Generative Flow Networks](https://mlsanity.com/paper/2312.15246/) (2023)

## Built on by (most cited first, 10 of 10)

- [Adaptive Destruction Processes for Diffusion Samplers](https://mlsanity.com/paper/2506.01541/) (2025)
- [gfnx: Fast and Scalable Library for Generative Flow Networks in JAX](https://mlsanity.com/paper/2511.16592/) (2025)
- [Ergodic Generative Flows](https://mlsanity.com/paper/2505.03561/) (2025)
- [Learning Shortest Paths with Generative Flow Networks](https://mlsanity.com/paper/2603.01786/) (2026)
- [Beyond the Proxy: Trajectory-Distilled Guidance for Offline GFlowNet Training](https://mlsanity.com/paper/2505.20110/) (2025)
- [Your GFlowNet Secretly Learns an Optimal Transport Plan](https://mlsanity.com/paper/2606.06272/) (2026)
- [Stop the Sampler! Classifier-Based Adaptive Stopping for Sampling Kernels](https://mlsanity.com/paper/2606.16073/) (2026)
- [Path-dependent Discrete Amortized Inference](https://mlsanity.com/paper/2608.08644/) (2026)
- [Learning a Mixture of GFlowNets](https://mlsanity.com/paper/2610.07562/) (2026)
- [Towards Understanding the Training of GFlowNets: A Theoretical Perspective](https://mlsanity.com/paper/2610.13711/) (2026)

## Abstract (arXiv)

Generative Flow Networks (GFlowNets) are a family of generative models that learn to sample objects from a given probability distribution, potentially known up to a normalizing constant. Instead of working in the object space, GFlowNets proceed by sampling trajectories in an appropriately constructed directed acyclic graph environment, 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 related to training with fixed backward policies, the nature of flow functions, and connections between entropy-regularized RL and non-acyclic GFlowNets, which naturally generalize the respective 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.