# Symmetry-Aware GFlowNets

arXiv: https://arxiv.org/abs/2506.02685 · HTML: https://mlsanity.com/paper/2506.02685/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 36 references that are in the map.
- First posted on arXiv 3 Jun 2025.

## Builds on (most cited first, 29 of 29)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Recipe for a General, Powerful, Scalable Graph Transformer](https://mlsanity.com/paper/2205.12454/) (2022)
- [Reinforcement Learning with Deep Energy-Based Policies](https://mlsanity.com/paper/1702.08165/) (2017)
- [Graph Transformer Networks](https://mlsanity.com/paper/1911.06455/) (2019)
- [GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Models](https://mlsanity.com/paper/1802.08773/) (2018)
- [Flow Network based Generative Models for Non-Iterative Diverse Candidate Generation](https://mlsanity.com/paper/2106.04399/) (2021)
- [Graph Convolutional Policy Network for Goal-Directed Molecular Graph Generation](https://mlsanity.com/paper/1806.02473/) (2018)
- [Graph Neural Networks with Learnable Structural and Positional Representations](https://mlsanity.com/paper/2110.07875/) (2021)
- [GraphAF: a Flow-based Autoregressive Model for Molecular Graph Generation](https://mlsanity.com/paper/2001.09382/) (2020)
- [GFlowNet Foundations](https://mlsanity.com/paper/2111.09266/) (2021)
- [Trajectory balance: Improved credit assignment in GFlowNets](https://mlsanity.com/paper/2201.13259/) (2022)
- [Efficient Graph Generation with Graph Recurrent Attention Networks](https://mlsanity.com/paper/1910.00760/) (2019)
- [Learning Deep Generative Models of Graphs](https://mlsanity.com/paper/1803.03324/) (2018)
- [Labeling Trick: A Theory of Using Graph Neural Networks for Multi-Node Representation Learning](https://mlsanity.com/paper/2010.16103/) (2020)
- [Learning GFlowNets from partial episodes for improved convergence and stability](https://mlsanity.com/paper/2209.12782/) (2022)
- [Generative Flow Networks for Discrete Probabilistic Modeling](https://mlsanity.com/paper/2202.01361/) (2022)
- [Multi-Objective GFlowNets](https://mlsanity.com/paper/2210.12765/) (2022)
- [Better Training of GFlowNets with Local Credit and Incomplete Trajectories](https://mlsanity.com/paper/2302.01687/) (2023)
- [Autoregressive Diffusion Model for Graph Generation](https://mlsanity.com/paper/2307.08849/) (2023)
- [MolecularRNN: Generating realistic molecular graphs with optimized properties](https://mlsanity.com/paper/1905.13372/) (2019)
- [Towards Understanding and Improving GFlowNet Training](https://mlsanity.com/paper/2305.07170/) (2023)
- [Keeping it Simple: Language Models can learn Complex Molecular Distributions](https://mlsanity.com/paper/2112.03041/) (2021)
- [Generative Flow Networks as Entropy-Regularized RL](https://mlsanity.com/paper/2310.12934/) (2023)
- [GFlowNets for AI-Driven Scientific Discovery](https://mlsanity.com/paper/2302.00615/) (2023)
- [Order Matters: Probabilistic Modeling of Node Sequence for Graph Generation](https://mlsanity.com/paper/2106.06189/) (2021)
- [Maximum entropy GFlowNets with soft Q-learning](https://mlsanity.com/paper/2312.14331/) (2023)
- [Learning-Order Autoregressive Models with Application to Molecular Graph Generation](https://mlsanity.com/paper/2503.05979/) (2025)
- [Baking Symmetry into GFlowNets](https://mlsanity.com/paper/2406.05426/) (2024)

## Built on by (most cited first, 7 of 7)

- [Avoid What You Know: Divergent Trajectory Balance for GFlowNets](https://mlsanity.com/paper/2602.17827/) (2026)
- [Path-dependent Discrete Amortized Inference](https://mlsanity.com/paper/2608.08644/) (2026)
- [Terminal Symmetry as a Carrier of Asymmetric Process Knowledge: Statewise Refinement for Anytime Verified Construction](https://mlsanity.com/paper/2608.11318/) (2026)
- [Learning a Mixture of GFlowNets](https://mlsanity.com/paper/2610.07562/) (2026)
- [Beyond Action Entropy: Quotient-Space Exploration for Genome-Scale Metabolic Model Repair](https://mlsanity.com/paper/2610.11627/) (2026)
- [MIPS: Mitigating Mode Collapse in Reinforcement Learning for Large Outcome Spaces](https://mlsanity.com/paper/2610.19457/) (2026)
- [SNACK: A Sequential Notation Framework for Probabilistic Graph Generation](https://mlsanity.com/paper/2610.19781/) (2026)

## Abstract (arXiv)

Generative Flow Networks (GFlowNets) offer a powerful framework for sampling graphs in proportion to their rewards. However, existing approaches suffer from systematic biases due to inaccuracies in state transition probability computations. These biases, rooted in the inherent symmetries of graphs, impact both atom-based and fragment-based generation schemes. To address this challenge, we introduce Symmetry-Aware GFlowNets (SA-GFN), a method that incorporates 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.