# Learning a Mixture of GFlowNets

arXiv: https://arxiv.org/abs/2610.07562 · HTML: https://mlsanity.com/paper/2610.07562/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 82 references that are in the map.
- First posted on arXiv 6 Oct 2026.

## Builds on (most cited first, 26 of 26)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Better Training of GFlowNets with Local Credit and Incomplete Trajectories](https://mlsanity.com/paper/2302.01687/) (2023)
- [Time Limits in Reinforcement Learning](https://mlsanity.com/paper/1712.00378/) (2017)
- [Amortizing intractable inference in diffusion models for vision, language, and control](https://mlsanity.com/paper/2405.20971/) (2024)
- [Local Search GFlowNets](https://mlsanity.com/paper/2310.02710/) (2023)
- [Discrete Probabilistic Inference as Control in Multi-path Environments](https://mlsanity.com/paper/2402.10309/) (2024)
- [Fast yet Simple Natural-Gradient Descent for Variational Inference in Complex Models](https://mlsanity.com/paper/1807.04489/) (2018)
- [Learning to Scale Logits for Temperature-Conditional GFlowNets](https://mlsanity.com/paper/2310.02823/) (2023)
- [Variational Inference with Continuously-Indexed Normalizing Flows](https://mlsanity.com/paper/2007.05426/) (2020)
- [Generative Flow Networks: a Markov Chain Perspective](https://mlsanity.com/paper/2307.01422/) (2023)
- [Optimizing Backward Policies in GFlowNets via Trajectory Likelihood Maximization](https://mlsanity.com/paper/2410.15474/) (2024)
- [torchgfn: A PyTorch GFlowNet library](https://mlsanity.com/paper/2305.14594/) (2023)
- [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)
- [Symmetry-Aware GFlowNets](https://mlsanity.com/paper/2506.02685/) (2025)
- [GFN-SR: Symbolic Regression with Generative Flow Networks](https://mlsanity.com/paper/2312.00396/) (2023)
- [Generative Marginalization Models](https://mlsanity.com/paper/2310.12920/) (2023)
- [GFlowNet Pretraining with Inexpensive Rewards](https://mlsanity.com/paper/2409.09702/) (2024)
- [Action abstractions for amortized sampling](https://mlsanity.com/paper/2410.15184/) (2024)
- [Avoid What You Know: Divergent Trajectory Balance for GFlowNets](https://mlsanity.com/paper/2602.17827/) (2026)
- [gfnx: Fast and Scalable Library for Generative Flow Networks in JAX](https://mlsanity.com/paper/2511.16592/) (2025)
- [Curriculum-Augmented GFlowNets For mRNA Sequence Generation](https://mlsanity.com/paper/2510.03811/) (2025)
- [Relaxing Bijectivity Constraints with Continuously Indexed Normalising Flows](https://mlsanity.com/paper/1909.13833/) (2019)
- [Exploring Multiple High-Scoring Subspaces in Generative Flow Networks](https://mlsanity.com/paper/2602.11491/) (2026)
- [Partial GFlowNet: Accelerating Convergence in Large State Spaces via Strategic Partitioning](https://mlsanity.com/paper/2602.11498/) (2026)

## Abstract (arXiv)

Learning an ensemble of GFlowNets to sample from a discrete target distribution has become a common approach for achieving better state space exploration and convergence than that of a monolithic sampler. However, these methods often add a substantial runtime overhead to the base model, and their conceptual connection remains elusive. To address this, we first propose a general-purpose theoretical framework for describing a mixture of GFlowNets, which we specialize into continuously (CI) and discretely indexed (DI) collections. On the one hand, we show CI GFlowNets can be interpreted through the lens of a random features expansion, provably boosting the sampler's expressivity in graph-structured tasks and reducing learning instability via spectral shifting. On the other hand, we demonstrate DI GFlowNets encompass prior approaches for GFlowNet training and provide the foundation for the newly proposed Stratum-Conditioned (SC) GFlowNets. This method, which is inspired by the Doob's h-transform of Markov chains, decomposes the state space according to a prescribed modular function and restricts each component to sample from a distinct subset of it. Importantly, SC GFlowNets support centralized and component-wise embarrassingly parallel training, and we show both of them significantly speed up learning convergence and mode coverage without introducing any non-negligible extra computation.