# A Theory of Non-Acyclic Generative Flow Networks

arXiv: https://arxiv.org/abs/2312.15246 · HTML: https://mlsanity.com/paper/2312.15246/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 26 references that are in the map.
- First posted on arXiv 23 Dec 2023.

## Builds on (most cited first, 13 of 13)

- [A Distributional Perspective on Reinforcement Learning](https://mlsanity.com/paper/1707.06887/) (2017)
- [A Generalization of Transformer Networks to Graphs](https://mlsanity.com/paper/2012.09699/) (2020)
- [Flow Network based Generative Models for Non-Iterative Diverse Candidate Generation](https://mlsanity.com/paper/2106.04399/) (2021)
- [Trajectory balance: Improved credit assignment in GFlowNets](https://mlsanity.com/paper/2201.13259/) (2022)
- [A theory of continuous generative flow networks](https://mlsanity.com/paper/2301.12594/) (2023)
- [Let the Flows Tell: Solving Graph Combinatorial Optimization Problems with GFlowNets](https://mlsanity.com/paper/2305.17010/) (2023)
- [Local-Global MCMC kernels: the best of both worlds](https://mlsanity.com/paper/2111.02702/) (2021)
- [A Framework for Adaptive MCMC Targeting Multimodal Distributions](https://mlsanity.com/paper/1812.02609/) (2018)
- [CFlowNets: Continuous Control with Generative Flow Networks](https://mlsanity.com/paper/2303.02430/) (2023)
- [Generative Flow Networks: a Markov Chain Perspective](https://mlsanity.com/paper/2307.01422/) (2023)
- [Neural Topological Ordering for Computation Graphs](https://mlsanity.com/paper/2207.05899/) (2022)
- [Generalized Universal Domain Adaptation with Generative Flow Networks](https://mlsanity.com/paper/2305.04466/) (2023)
- [Generative Flow Networks for Precise Reward-Oriented Active Learning on Graphs](https://mlsanity.com/paper/2304.11989/) (2023)

## Built on by (most cited first, 12 of 12)

- [Generative Models in Decision Making: A Survey](https://mlsanity.com/paper/2502.17100/) (2025)
- [Beyond Squared Error: Exploring Loss Design for Enhanced Training of Generative Flow Networks](https://mlsanity.com/paper/2410.02596/) (2024)
- [Revisiting Non-Acyclic GFlowNets in Discrete Environments](https://mlsanity.com/paper/2502.07735/) (2025)
- [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)
- [WINFlowNets: Warm-up Integrated Networks Training of Generative Flow Networks for Robotics and Machine Fault Adaptation](https://mlsanity.com/paper/2603.17301/) (2026)
- [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)

## Abstract (arXiv)

GFlowNets is a novel flow-based method for learning a stochastic policy to generate objects via a sequence of actions and with probability proportional to a given positive reward. We contribute to relaxing hypotheses limiting the application range of GFlowNets, in particular: acyclicity (or lack thereof). To this end, we extend the theory of GFlowNets on measurable spaces which includes continuous state spaces without cycle restrictions, and provide a generalization of cycles in this generalized context. We show that losses used so far push flows to get stuck into cycles and we define a family of losses solving this issue. Experiments on graphs and continuous tasks validate those principles.