# Improving Generative Flow Networks with Path Regularization

arXiv: https://arxiv.org/abs/2209.15092 · HTML: https://mlsanity.com/paper/2209.15092/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 45 references that are in the map.
- First posted on arXiv 29 Sep 2022.

## Builds on (most cited first, 24 of 24)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Flow Network based Generative Models for Non-Iterative Diverse Candidate Generation](https://mlsanity.com/paper/2106.04399/) (2021)
- [Learning Generative Models with Sinkhorn Divergences](https://mlsanity.com/paper/1706.00292/) (2017)
- [Trajectory balance: Improved credit assignment in GFlowNets](https://mlsanity.com/paper/2201.13259/) (2022)
- [Evaluating Protein Transfer Learning with TAPE](https://mlsanity.com/paper/1906.08230/) (2019)
- [Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration](https://mlsanity.com/paper/1705.09634/) (2017)
- [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)
- [Improved Contrastive Divergence Training of Energy Based Models](https://mlsanity.com/paper/2012.01316/) (2020)
- [Generative Flow Networks for Discrete Probabilistic Modeling](https://mlsanity.com/paper/2202.01361/) (2022)
- [Oops I Took A Gradient: Scalable Sampling for Discrete Distributions](https://mlsanity.com/paper/2102.04509/) (2021)
- [Conservative Objective Models for Effective Offline Model-Based Optimization](https://mlsanity.com/paper/2107.06882/) (2021)
- [Generalized Energy Based Models](https://mlsanity.com/paper/2003.05033/) (2020)
- [AdaLead: A simple and robust adaptive greedy search algorithm for sequence design](https://mlsanity.com/paper/2010.02141/) (2020)
- [On Efficient Optimal Transport: An Analysis of Greedy and Accelerated Mirror Descent Algorithms](https://mlsanity.com/paper/1901.06482/) (2019)
- [Learning Generative Models across Incomparable Spaces](https://mlsanity.com/paper/1905.05461/) (2019)
- [Multilevel Clustering via Wasserstein Means](https://mlsanity.com/paper/1706.03883/) (2017)
- [Point-set Distances for Learning Representations of 3D Point Clouds](https://mlsanity.com/paper/2102.04014/) (2021)
- [On the Efficiency of Entropic Regularized Algorithms for Optimal Transport](https://mlsanity.com/paper/1906.01437/) (2019)
- [Exponential Family Estimation via Adversarial Dynamics Embedding](https://mlsanity.com/paper/1904.12083/) (2019)
- [Learning Discrete Energy-based Models via Auxiliary-variable Local Exploration](https://mlsanity.com/paper/2011.05363/) (2020)
- [Revisiting Sliced Wasserstein on Images: From Vectorization to Convolution](https://mlsanity.com/paper/2204.01188/) (2022)
- [Hierarchical Sliced Wasserstein Distance](https://mlsanity.com/paper/2209.13570/) (2022)

## Built on by (most cited first, 3 of 3)

- [Towards Understanding and Improving GFlowNet Training](https://mlsanity.com/paper/2305.07170/) (2023)
- [A Variational Perspective on Generative Flow Networks](https://mlsanity.com/paper/2210.07992/) (2022)
- [Bayesian Decision Trees via Tractable Priors and Probabilistic Context-Free Grammars](https://mlsanity.com/paper/2302.07407/) (2023)

## Abstract (arXiv)

Generative Flow Networks (GFlowNets) are recently proposed models for learning stochastic policies that generate compositional objects by sequences of actions with the probability proportional to a given reward function. The central problem of GFlowNets is to improve their exploration and generalization. In this work, we propose a novel path regularization method based on optimal transport theory that places prior constraints on the underlying structure of the GFlowNets. The prior is designed to help the GFlowNets better discover the latent structure of the target distribution or enhance its ability to explore the environment in the context of active learning. The path regularization controls the flow in GFlowNets to generate more diverse and novel candidates via maximizing the optimal transport distances between two forward policies or to improve the generalization via minimizing the optimal transport distances. In addition, we derive an efficient implementation of the regularization by finding its closed form solutions in specific cases and a meaningful upper bound that can be used as an approximation to minimize the regularization term. We empirically demonstrate the advantage of our path regularization on a wide range of tasks, including synthetic hypergrid environment modeling, discrete probabilistic modeling, and biological sequence design.