mlsanityData to 14 Oct 2026

Your GFlowNet Secretly Learns an Optimal Transport Plan

arXiv 2606.06272 ↗First posted 4 Jun 2026cs.LG cs.AIcited by 0

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Abstract (arXiv)

Generative Flow Networks (GFlowNets) are a framework for sampling structured objects via stochastic trajectories in a directed graph. In this work, we establish a theoretical connection between non-acyclic GFlowNets and optimal transport (OT). We show that fixing the initial flow distribution in a minimum-flow GFlowNet reduces its objective to a Kantorovich OT problem with graph-induced shortest path costs. At the optimum, the learned GFlowNet policy therefore encodes an optimal transport plan from the source distribution to the target distribution: we show that sampling trajectories from the minimum-flow GFlowNet recovers the corresponding optimal coupling. Our formulation enables applying the GFlowNet learning framework to OT problems on large graphs via edge flows and neural parameterization. Experiments confirm agreement with exact OT solvers and demonstrate that GFlowNets can learn high-quality transport plans.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 33 of its 45 references that are in the map. First posted on arXiv 4 Jun 2026.

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33 of 45 references.

References · 33

  1. 2015Optimal Transport for Domain Adaptationcited by 463
  2. 2021Flow Network based Generative Models for Non-Iterative Diverse Candidate Generationcited by 392
  3. 2017Wasserstein Auto-Encoderscited by 373
  4. 2021GFlowNet Foundationscited by 290
  5. 2022Trajectory balance: Improved credit assignment in GFlowNetscited by 251
  6. 2022Biological Sequence Design with GFlowNetscited by 174
  7. 2022Learning GFlowNets from partial episodes for improved convergence and stabilitycited by 132
  8. 2023A theory of continuous generative flow networkscited by 101
  9. 2024Understanding Reinforcement Learning-Based Fine-Tuning of Diffusion Models: A Tutorial and Reviewcited by 98
  10. 2023Amortizing intractable inference in large language modelscited by 97
  11. 2023Robust Scheduling with GFlowNetscited by 69
  12. 2023Generative Flow Networks as Entropy-Regularized RLcited by 64
21 more
  1. 2024Learning diverse attacks on large language models for robust red-teaming and safety tuningcited by 54
  2. 2024Ant Colony Sampling with GFlowNets for Combinatorial Optimizationcited by 53
  3. 2024Discrete Probabilistic Inference as Control in Multi-path Environmentscited by 44
  4. 2024RGFN: Synthesizable Molecular Generation Using GFlowNetscited by 41
  5. 2025FlowRL: Matching Reward Distributions for LLM Reasoningcited by 40
  6. 2023Maximum entropy GFlowNets with soft Q-learningcited by 30
  7. 2024Improving GFlowNets for Text-to-Image Diffusion Alignmentcited by 27
  8. 2024SynFlowNet: Design of Diverse and Novel Molecules with Synthesis Constraintscited by 26
  9. 2017Quadratically-Regularized Optimal Transport on Graphscited by 19
  10. 2024QGFN: Controllable Greediness with Action Valuescited by 18
  11. 2024Pessimistic Backward Policy for GFlowNetscited by 14
  12. 2024Optimizing Backward Policies in GFlowNets via Trajectory Likelihood Maximizationcited by 14
  13. 2024Improved Off-policy Reinforcement Learning in Biological Sequence Designcited by 13
  14. 2023A Theory of Non-Acyclic Generative Flow Networkscited by 12
  15. 2025Revisiting Non-Acyclic GFlowNets in Discrete Environmentscited by 10
  16. 2024Improving GFlowNets with Monte Carlo Tree Searchcited by 8
  17. 2024GDPO: Learning to Directly Align Language Models with Diversity Using GFlowNetscited by 6
  18. 2024Random Policy Evaluation Uncovers Policies of Generative Flow Networkscited by 5
  19. 2025Ergodic Generative Flowscited by 2
  20. 2025A Theory of Multi-Agent Generative Flow Networkscited by 2
  21. 2026Learning Shortest Paths with Generative Flow Networkscited by 2

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