# Better Training of GFlowNets with Local Credit and Incomplete Trajectories

arXiv: https://arxiv.org/abs/2302.01687 · HTML: https://mlsanity.com/paper/2302.01687/

## Key facts

- Cited by 85 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 51 references that are in the map.
- First posted on arXiv 3 Feb 2023.

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [Reinforcement Learning with Deep Energy-Based Policies](https://mlsanity.com/paper/1702.08165/) (2017)
- [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)
- [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)
- [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)
- [A theory of continuous generative flow networks](https://mlsanity.com/paper/2301.12594/) (2023)
- [Generative Augmented Flow Networks](https://mlsanity.com/paper/2210.03308/) (2022)
- [A Variational Perspective on Generative Flow Networks](https://mlsanity.com/paper/2210.07992/) (2022)
- [Learning Long-Term Reward Redistribution via Randomized Return Decomposition](https://mlsanity.com/paper/2111.13485/) (2021)
- [Softmax Deep Double Deterministic Policy Gradients](https://mlsanity.com/paper/2010.09177/) (2020)
- [Bayesian learning of Causal Structure and Mechanisms with GFlowNets and Variational Bayes](https://mlsanity.com/paper/2211.02763/) (2022)
- [Unifying Generative Models with GFlowNets and Beyond](https://mlsanity.com/paper/2209.02606/) (2022)
- [Latent State Marginalization as a Low-cost Approach for Improving Exploration](https://mlsanity.com/paper/2210.00999/) (2022)

## Built on by (most cited first, 30 of 85)

- [A Review of Modern Recommender Systems Using Generative Models (Gen-RecSys)](https://mlsanity.com/paper/2404.00579/) (2024)
- [Diffusion Generative Flow Samplers: Improving learning signals through partial trajectory optimization](https://mlsanity.com/paper/2310.02679/) (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)
- [Local Search GFlowNets](https://mlsanity.com/paper/2310.02710/) (2023)
- [Improved off-policy training of diffusion samplers](https://mlsanity.com/paper/2402.05098/) (2024)
- [Discrete Probabilistic Inference as Control in Multi-path Environments](https://mlsanity.com/paper/2402.10309/) (2024)
- [GFlowNet-EM for learning compositional latent variable models](https://mlsanity.com/paper/2302.06576/) (2023)
- [Let the Flows Tell: Solving Graph Combinatorial Optimization Problems with GFlowNets](https://mlsanity.com/paper/2305.17010/) (2023)
- [FlowRL: Matching Reward Distributions for LLM Reasoning](https://mlsanity.com/paper/2509.15207/) (2025)
- [Genetic-guided GFlowNets for Sample Efficient Molecular Optimization](https://mlsanity.com/paper/2402.05961/) (2024)
- [Stochastic Generative Flow Networks](https://mlsanity.com/paper/2302.09465/) (2023)
- [Thompson sampling for improved exploration in GFlowNets](https://mlsanity.com/paper/2306.17693/) (2023)
- [Efficient Diversity-Preserving Diffusion Alignment via Gradient-Informed GFlowNets](https://mlsanity.com/paper/2412.07775/) (2024)
- [Distributional GFlowNets with Quantile Flows](https://mlsanity.com/paper/2302.05793/) (2023)
- [Learning to Scale Logits for Temperature-Conditional GFlowNets](https://mlsanity.com/paper/2310.02823/) (2023)
- [Improving GFlowNets for Text-to-Image Diffusion Alignment](https://mlsanity.com/paper/2406.00633/) (2024)
- [Learning Energy Decompositions for Partial Inference of GFlowNets](https://mlsanity.com/paper/2310.03301/) (2023)
- [Adaptive teachers for amortized samplers](https://mlsanity.com/paper/2410.01432/) (2024)
- [From discrete-time policies to continuous-time diffusion samplers: Asymptotic equivalences and faster training](https://mlsanity.com/paper/2501.06148/) (2025)
- [QGFN: Controllable Greediness with Action Values](https://mlsanity.com/paper/2402.05234/) (2024)
- [Goal-conditioned GFlowNets for Controllable Multi-Objective Molecular Design](https://mlsanity.com/paper/2306.04620/) (2023)
- [Pre-Training and Fine-Tuning Generative Flow Networks](https://mlsanity.com/paper/2310.03419/) (2023)
- [Learning to Sample Effective and Diverse Prompts for Text-to-Image Generation](https://mlsanity.com/paper/2502.11477/) (2025)
- [Generative Models in Decision Making: A Survey](https://mlsanity.com/paper/2502.17100/) (2025)
- [Pessimistic Backward Policy for GFlowNets](https://mlsanity.com/paper/2405.16012/) (2024)
- [Order-Preserving GFlowNets](https://mlsanity.com/paper/2310.00386/) (2023)
- [Improved Off-policy Reinforcement Learning in Biological Sequence Design](https://mlsanity.com/paper/2410.04461/) (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)

## Abstract (arXiv)

Generative Flow Networks or GFlowNets are related to Monte-Carlo Markov chain methods (as they sample from a distribution specified by an energy function), reinforcement learning (as they learn a policy to sample composed objects through a sequence of steps), generative models (as they learn to represent and sample from a distribution) and amortized variational methods (as they can be used to learn to approximate and sample from an otherwise intractable posterior, given a prior and a likelihood). They are trained to generate an object x through a sequence of steps with probability proportional to some reward function R(x) (or exp(-E(x)) with E(x) denoting the energy function), given at the end of the generative trajectory. Like for other RL settings where the reward is only given at the end, the efficiency of training and credit assignment may suffer when those trajectories are longer. With previous GFlowNet work, no learning was possible from incomplete trajectories (lacking a terminal state and the computation of the associated reward). In this paper, we consider the case where the energy function can be applied not just to terminal states but also to intermediate states. This is for example achieved when the energy function is additive, with terms available along the trajectory. We show how to reparameterize the GFlowNet state flow function to take advantage of the partial reward already accrued at each state. This enables a training objective that can be applied to update parameters even with incomplete trajectories. Even when complete trajectories are available, being able to obtain more localized credit and gradients is found to speed up training convergence, as demonstrated across many simulations.