# Learning Energy Decompositions for Partial Inference of GFlowNets

arXiv: https://arxiv.org/abs/2310.03301 · HTML: https://mlsanity.com/paper/2310.03301/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 30 references that are in the map.
- First posted on arXiv 5 Oct 2023.

## Builds on (most cited first, 22 of 22)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Exploration by Random Network Distillation](https://mlsanity.com/paper/1810.12894/) (2018)
- [When to Trust Your Model: Model-Based Policy Optimization](https://mlsanity.com/paper/1906.08253/) (2019)
- [Junction Tree Variational Autoencoder for Molecular Graph Generation](https://mlsanity.com/paper/1802.04364/) (2018)
- [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)
- [RUDDER: Return Decomposition for Delayed Rewards](https://mlsanity.com/paper/1806.07857/) (2018)
- [Algorithmic Framework for Model-based Deep Reinforcement Learning with Theoretical Guarantees](https://mlsanity.com/paper/1807.03858/) (2018)
- [Learning GFlowNets from partial episodes for improved convergence and stability](https://mlsanity.com/paper/2209.12782/) (2022)
- [GFlowNets and variational inference](https://mlsanity.com/paper/2210.00580/) (2022)
- [Design-Bench: Benchmarks for Data-Driven Offline Model-Based Optimization](https://mlsanity.com/paper/2202.08450/) (2022)
- [Better Training of GFlowNets with Local Credit and Incomplete Trajectories](https://mlsanity.com/paper/2302.01687/) (2023)
- [Towards Understanding and Improving GFlowNet Training](https://mlsanity.com/paper/2305.07170/) (2023)
- [Generative Augmented Flow Networks](https://mlsanity.com/paper/2210.03308/) (2022)
- [Reinforcement Learning with Trajectory Feedback](https://mlsanity.com/paper/2008.06036/) (2020)
- [Let the Flows Tell: Solving Graph Combinatorial Optimization Problems with GFlowNets](https://mlsanity.com/paper/2305.17010/) (2023)
- [Learning Long-Term Reward Redistribution via Randomized Return Decomposition](https://mlsanity.com/paper/2111.13485/) (2021)
- [Learning Guidance Rewards with Trajectory-space Smoothing](https://mlsanity.com/paper/2010.12718/) (2020)
- [Dual Policy Iteration](https://mlsanity.com/paper/1805.10755/) (2018)

## Built on by (most cited first, 24 of 24)

- [Ant Colony Sampling with GFlowNets for Combinatorial Optimization](https://mlsanity.com/paper/2403.07041/) (2024)
- [Improved off-policy training of diffusion samplers](https://mlsanity.com/paper/2402.05098/) (2024)
- [Genetic-guided GFlowNets for Sample Efficient Molecular Optimization](https://mlsanity.com/paper/2402.05961/) (2024)
- [Flow of Reasoning: Training LLMs for Divergent Reasoning with Minimal Examples](https://mlsanity.com/paper/2406.05673/) (2024)
- [Adaptive teachers for amortized samplers](https://mlsanity.com/paper/2410.01432/) (2024)
- [Learning to Sample Effective and Diverse Prompts for Text-to-Image Generation](https://mlsanity.com/paper/2502.11477/) (2025)
- [Pessimistic Backward Policy for GFlowNets](https://mlsanity.com/paper/2405.16012/) (2024)
- [Improved Off-policy Reinforcement Learning in Biological Sequence Design](https://mlsanity.com/paper/2410.04461/) (2024)
- [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)
- [On Divergence Measures for Training GFlowNets](https://mlsanity.com/paper/2410.09355/) (2024)
- [Adaptive Destruction Processes for Diffusion Samplers](https://mlsanity.com/paper/2506.01541/) (2025)
- [Random Policy Evaluation Uncovers Policies of Generative Flow Networks](https://mlsanity.com/paper/2406.02213/) (2024)
- [GFlowNet Training by Policy Gradients](https://mlsanity.com/paper/2408.05885/) (2024)
- [Learning to Learn Weight Generation via Local Consistency Diffusion](https://mlsanity.com/paper/2502.01117/) (2025)
- [Avoid What You Know: Divergent Trajectory Balance for GFlowNets](https://mlsanity.com/paper/2602.17827/) (2026)
- [Evaluating GFlowNet from partial episodes for stable and flexible policy-based training](https://mlsanity.com/paper/2603.01047/) (2026)
- [Information-Geometric Forward Policy Training in GFlowNets](https://mlsanity.com/paper/2608.03967/) (2026)
- [Beyond the Proxy: Trajectory-Distilled Guidance for Offline GFlowNet Training](https://mlsanity.com/paper/2505.20110/) (2025)
- [Signal from Structure: Exploiting Submodular Upper Bounds in Generative Flow Networks](https://mlsanity.com/paper/2601.21061/) (2026)
- [Controlling Exploration-Exploitation in GFlowNets via Markov Chain Perspectives](https://mlsanity.com/paper/2602.01749/) (2026)
- [A Systematic Evaluation of Co-folding Model Representations for Small-Molecule Learning](https://mlsanity.com/paper/2602.13249/) (2026)
- [Path-dependent Discrete Amortized Inference](https://mlsanity.com/paper/2608.08644/) (2026)
- [Particle GFlowNets: Rethinking Generative Marginalization Models](https://mlsanity.com/paper/2609.11538/) (2026)

## Abstract (arXiv)

This paper studies generative flow networks (GFlowNets) to sample objects from the Boltzmann energy distribution via a sequence of actions. In particular, we focus on improving GFlowNet with partial inference: training flow functions with the evaluation of the intermediate states or transitions. To this end, the recently developed forward-looking GFlowNet reparameterizes the flow functions based on evaluating the energy of intermediate states. However, such an evaluation of intermediate energies may (i) be too expensive or impossible to evaluate and (ii) even provide misleading training signals under large energy fluctuations along the sequence of actions. To resolve this issue, we propose learning energy decompositions for GFlowNets (LED-GFN). Our main idea is to (i) decompose the energy of an object into learnable potential functions defined on state transitions and (ii) reparameterize the flow functions using the potential functions. In particular, to produce informative local credits, we propose to regularize the potential to change smoothly over the sequence of actions. It is also noteworthy that training GFlowNet with our learned potential can preserve the optimal policy. We empirically verify the superiority of LED-GFN in five problems including the generation of unstructured and maximum independent sets, molecular graphs, and RNA sequences.