# Baking Symmetry into GFlowNets

arXiv: https://arxiv.org/abs/2406.05426 · HTML: https://mlsanity.com/paper/2406.05426/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 30 references that are in the map.
- First posted on arXiv 8 Jun 2024.

## Builds on (most cited first, 25 of 25)

- [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)
- [Trajectory balance: Improved credit assignment in GFlowNets](https://mlsanity.com/paper/2201.13259/) (2022)
- [Biological Sequence Design with GFlowNets](https://mlsanity.com/paper/2203.04115/) (2022)
- [Frame Averaging for Invariant and Equivariant Network Design](https://mlsanity.com/paper/2110.03336/) (2021)
- [Bayesian Structure Learning with Generative Flow Networks](https://mlsanity.com/paper/2202.13903/) (2022)
- [Relational Pooling for Graph Representations](https://mlsanity.com/paper/1903.02541/) (2019)
- [Generative Flow Networks for Discrete Probabilistic Modeling](https://mlsanity.com/paper/2202.01361/) (2022)
- [GFlowNets and variational inference](https://mlsanity.com/paper/2210.00580/) (2022)
- [Multi-Objective GFlowNets](https://mlsanity.com/paper/2210.12765/) (2022)
- [Janossy Pooling: Learning Deep Permutation-Invariant Functions for Variable-Size Inputs](https://mlsanity.com/paper/1811.01900/) (2018)
- [Better Training of GFlowNets with Local Credit and Incomplete Trajectories](https://mlsanity.com/paper/2302.01687/) (2023)
- [Robust Scheduling with GFlowNets](https://mlsanity.com/paper/2302.05446/) (2023)
- [ForceNet: A Graph Neural Network for Large-Scale Quantum Calculations](https://mlsanity.com/paper/2103.01436/) (2021)
- [Diffusion Generative Flow Samplers: Improving learning signals through partial trajectory optimization](https://mlsanity.com/paper/2310.02679/) (2023)
- [Rotation Invariant Graph Neural Networks using Spin Convolutions](https://mlsanity.com/paper/2106.09575/) (2021)
- [Generative Augmented Flow Networks](https://mlsanity.com/paper/2210.03308/) (2022)
- [Joint Bayesian Inference of Graphical Structure and Parameters with a Single Generative Flow Network](https://mlsanity.com/paper/2305.19366/) (2023)
- [Let the Flows Tell: Solving Graph Combinatorial Optimization Problems with GFlowNets](https://mlsanity.com/paper/2305.17010/) (2023)
- [Stochastic Generative Flow Networks](https://mlsanity.com/paper/2302.09465/) (2023)
- [Distributional GFlowNets with Quantile Flows](https://mlsanity.com/paper/2302.05793/) (2023)
- [The Exact Sample Complexity Gain from Invariances for Kernel Regression](https://mlsanity.com/paper/2303.14269/) (2023)
- [Improving GFlowNets for Text-to-Image Diffusion Alignment](https://mlsanity.com/paper/2406.00633/) (2024)
- [GFlowOut: Dropout with Generative Flow Networks](https://mlsanity.com/paper/2210.12928/) (2022)
- [Laplacian Canonization: A Minimalist Approach to Sign and Basis Invariant Spectral Embedding](https://mlsanity.com/paper/2310.18716/) (2023)

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

- [FlowRL: Matching Reward Distributions for LLM Reasoning](https://mlsanity.com/paper/2509.15207/) (2025)
- [Flow of Reasoning: Training LLMs for Divergent Reasoning with Minimal Examples](https://mlsanity.com/paper/2406.05673/) (2024)
- [Nabla-R2D3: Effective and Efficient 3D Diffusion Alignment with 2D Rewards](https://mlsanity.com/paper/2506.15684/) (2025)
- [Symmetry-Aware GFlowNets](https://mlsanity.com/paper/2506.02685/) (2025)
- [Partial GFlowNet: Accelerating Convergence in Large State Spaces via Strategic Partitioning](https://mlsanity.com/paper/2602.11498/) (2026)
- [Planning-Augmented Sampling with Early Guidance for High-Reward Discovery](https://mlsanity.com/paper/2510.00805/) (2025)
- [Signal from Structure: Exploiting Submodular Upper Bounds in Generative Flow Networks](https://mlsanity.com/paper/2601.21061/) (2026)

## Abstract (arXiv)

GFlowNets have exhibited promising performance in generating diverse candidates with high rewards. These networks generate objects incrementally and aim to learn a policy that assigns probability of sampling objects in proportion to rewards. However, the current training pipelines of GFlowNets do not consider the presence of isomorphic actions, which are actions resulting in symmetric or isomorphic states. This lack of symmetry increases the amount of samples required for training GFlowNets and can result in inefficient and potentially incorrect flow functions. As a consequence, the reward and diversity of the generated objects decrease. In this study, our objective is to integrate symmetries into GFlowNets by identifying equivalent actions during the generation process. Experimental results using synthetic data demonstrate the promising performance of our proposed approaches.