# GFlowCausal: Generative Flow Networks for Causal Discovery

arXiv: https://arxiv.org/abs/2210.08185 · HTML: https://mlsanity.com/paper/2210.08185/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 52 references that are in the map.
- First posted on arXiv 15 Oct 2022.

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

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [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)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Flow Network based Generative Models for Non-Iterative Diverse Candidate Generation](https://mlsanity.com/paper/2106.04399/) (2021)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [Trajectory balance: Improved credit assignment in GFlowNets](https://mlsanity.com/paper/2201.13259/) (2022)
- [Gradient-Based Neural DAG Learning](https://mlsanity.com/paper/1906.02226/) (2019)
- [On the Role of Sparsity and DAG Constraints for Learning Linear DAGs](https://mlsanity.com/paper/2006.10201/) (2020)
- [Learning Bayesian Networks: The Combination of Knowledge and Statistical Data](https://mlsanity.com/paper/1302.6815/) (2013)
- [CAM: Causal additive models, high-dimensional order search and penalized regression](https://mlsanity.com/paper/1310.1533/) (2013)
- [Biological Sequence Design with GFlowNets](https://mlsanity.com/paper/2203.04115/) (2022)
- [Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Game](https://mlsanity.com/paper/2102.13647/) (2021)
- [Bayesian Structure Learning with Generative Flow Networks](https://mlsanity.com/paper/2202.13903/) (2022)
- [Causal Discovery with Reinforcement Learning](https://mlsanity.com/paper/1906.04477/) (2019)
- [Generative Flow Networks for Discrete Probabilistic Modeling](https://mlsanity.com/paper/2202.01361/) (2022)
- [DAGs with No Fears: A Closer Look at Continuous Optimization for Learning Bayesian Networks](https://mlsanity.com/paper/2010.09133/) (2020)
- [Learning Gaussian Networks](https://mlsanity.com/paper/1302.6808/) (2013)
- [Ordering-Based Causal Discovery with Reinforcement Learning](https://mlsanity.com/paper/2105.06631/) (2021)
- [Structural Agnostic Modeling: Adversarial Learning of Causal Graphs](https://mlsanity.com/paper/1803.04929/) (2018)
- [CASTLE: Regularization via Auxiliary Causal Graph Discovery](https://mlsanity.com/paper/2009.13180/) (2020)
- [A Constraint-Based Algorithm For Causal Discovery with Cycles, Latent Variables and Selection Bias](https://mlsanity.com/paper/1805.02087/) (2018)
- [Causal Adversarial Network for Learning Conditional and Interventional Distributions](https://mlsanity.com/paper/2008.11376/) (2020)

## Built on by (most cited first, 11 of 11)

- [DAG Matters! GFlowNets Enhanced Explainer For Graph Neural Networks](https://mlsanity.com/paper/2303.02448/) (2023)
- [Causal Deep Learning](https://mlsanity.com/paper/2303.02186/) (2023)
- [CFlowNets: Continuous Control with Generative Flow Networks](https://mlsanity.com/paper/2303.02430/) (2023)
- [Generalized Universal Domain Adaptation with Generative Flow Networks](https://mlsanity.com/paper/2305.04466/) (2023)
- [Hybrid-Balance GFlowNet for Solving Vehicle Routing Problems](https://mlsanity.com/paper/2510.04792/) (2025)
- [CORE: Towards Scalable and Efficient Causal Discovery with Reinforcement Learning](https://mlsanity.com/paper/2401.16974/) (2024)
- [Ada-HGNN: Adaptive Sampling for Scalable Hypergraph Neural Networks](https://mlsanity.com/paper/2405.13372/) (2024)
- [Generative Flow Networks for Precise Reward-Oriented Active Learning on Graphs](https://mlsanity.com/paper/2304.11989/) (2023)
- [GFlowNets with Human Feedback](https://mlsanity.com/paper/2305.07036/) (2023)
- [Test-Time Learning of Causal Structure from Interventional Data](https://mlsanity.com/paper/2602.19131/) (2026)
- [Enhancing Solution Efficiency in Reinforcement Learning: Leveraging Sub-GFlowNet and Entropy Integration](https://mlsanity.com/paper/2410.00461/) (2024)

## Abstract (arXiv)

Causal discovery aims to uncover causal structure among a set of variables. Score-based approaches mainly focus on searching for the best Directed Acyclic Graph (DAG) based on a predefined score function. However, most of them are not applicable on a large scale due to the limited searchability. Inspired by the active learning in generative flow networks, we propose a novel approach to learning a DAG from observational data called GFlowCausal. It converts the graph search problem to a generation problem, in which direct edges are added gradually. GFlowCausal aims to learn the best policy to generate high-reward DAGs by sequential actions with probabilities proportional to predefined rewards. We propose a plug-and-play module based on transitive closure to ensure efficient sampling. Theoretical analysis shows that this module could guarantee acyclicity properties effectively and the consistency between final states and fully-connected graphs. We conduct extensive experiments on both synthetic and real datasets, and results show the proposed approach to be superior and also performs well in a large-scale setting.