# Learning Shortest Paths with Generative Flow Networks

arXiv: https://arxiv.org/abs/2603.01786 · HTML: https://mlsanity.com/paper/2603.01786/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 49 references that are in the map.
- First posted on arXiv 2 Mar 2026.

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

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [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)
- [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)
- [If beam search is the answer, what was the question?](https://mlsanity.com/paper/2010.02650/) (2020)
- [GFlowNets and variational inference](https://mlsanity.com/paper/2210.00580/) (2022)
- [Amortizing intractable inference in large language models](https://mlsanity.com/paper/2310.04363/) (2023)
- [Generative Flow Networks as Entropy-Regularized RL](https://mlsanity.com/paper/2310.12934/) (2023)
- [Ant Colony Sampling with GFlowNets for Combinatorial Optimization](https://mlsanity.com/paper/2403.07041/) (2024)
- [Joint Bayesian Inference of Graphical Structure and Parameters with a Single Generative Flow Network](https://mlsanity.com/paper/2305.19366/) (2023)
- [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)
- [A Variational Perspective on Generative Flow Networks](https://mlsanity.com/paper/2210.07992/) (2022)
- [DynGFN: Towards Bayesian Inference of Gene Regulatory Networks with GFlowNets](https://mlsanity.com/paper/2302.04178/) (2023)
- [SynFlowNet: Design of Diverse and Novel Molecules with Synthesis Constraints](https://mlsanity.com/paper/2405.01155/) (2024)
- [Solving the Rubik's Cube Without Human Knowledge](https://mlsanity.com/paper/1805.07470/) (2018)
- [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)
- [A Theory of Non-Acyclic Generative Flow Networks](https://mlsanity.com/paper/2312.15246/) (2023)
- [A Survey of Shortest-Path Algorithms](https://mlsanity.com/paper/1705.02044/) (2017)
- [Revisiting Non-Acyclic GFlowNets in Discrete Environments](https://mlsanity.com/paper/2502.07735/) (2025)
- [Improving GFlowNets with Monte Carlo Tree Search](https://mlsanity.com/paper/2406.13655/) (2024)
- [CayleyPy RL: Pathfinding and Reinforcement Learning on Cayley Graphs](https://mlsanity.com/paper/2502.18663/) (2025)
- [Self-Supervision is All You Need for Solving Rubik's Cube](https://mlsanity.com/paper/2106.03157/) (2021)
- [gfnx: Fast and Scalable Library for Generative Flow Networks in JAX](https://mlsanity.com/paper/2511.16592/) (2025)

## Built on by (most cited first, 2 of 2)

- [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)

## Abstract (arXiv)

In this paper, we present a novel learning framework for finding shortest paths in graphs utilizing Generative Flow Networks (GFlowNets). First, we examine theoretical properties of GFlowNets in non-acyclic environments in relation to shortest paths. We prove that, if the total flow is minimized, forward and backward policies traverse the environment graph exclusively along shortest paths between the initial and terminal states. Building on this result, we reduce shortest-path finding in an arbitrary unweighted graph to finding a non-acyclic GFlowNet with minimal total flow, and approximate it in practice by training with flow regularization. We experimentally demonstrate the performance of our method in pathfinding in permutation environments and in solving Rubik's Cubes of various sizes. For the latter problems, our approach shows competitive results with state-of-the-art machine learning approaches designed specifically for this task in terms of the solution length, while requiring smaller search budget at test-time.