# Joint Bayesian Inference of Graphical Structure and Parameters with a Single Generative Flow Network

arXiv: https://arxiv.org/abs/2305.19366 · HTML: https://mlsanity.com/paper/2305.19366/

## Key facts

- Cited by 50 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 56 references that are in the map.
- First posted on arXiv 30 May 2023.

## Builds on (most cited first, 30 of 31)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [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)
- [Learning Bayesian Networks: The Combination of Knowledge and Statistical Data](https://mlsanity.com/paper/1302.6815/) (2013)
- [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)
- [DiBS: Differentiable Bayesian Structure Learning](https://mlsanity.com/paper/2105.11839/) (2021)
- [GFlowNets and variational inference](https://mlsanity.com/paper/2210.00580/) (2022)
- [A theory of continuous generative flow networks](https://mlsanity.com/paper/2301.12594/) (2023)
- [Amortized Inference for Causal Structure Learning](https://mlsanity.com/paper/2205.12934/) (2022)
- [Better Training of GFlowNets with Local Credit and Incomplete Trajectories](https://mlsanity.com/paper/2302.01687/) (2023)
- [Robust Scheduling with GFlowNets](https://mlsanity.com/paper/2302.05446/) (2023)
- [BCD Nets: Scalable Variational Approaches for Bayesian Causal Discovery](https://mlsanity.com/paper/2112.02761/) (2021)
- [GFlowNets for AI-Driven Scientific Discovery](https://mlsanity.com/paper/2302.00615/) (2023)
- [Learning Gaussian Networks](https://mlsanity.com/paper/1302.6808/) (2013)
- [Differentiable DAG Sampling](https://mlsanity.com/paper/2203.08509/) (2022)
- [Variational Causal Networks: Approximate Bayesian Inference over Causal Structures](https://mlsanity.com/paper/2106.07635/) (2021)
- [GFlowNet-EM for learning compositional latent variable models](https://mlsanity.com/paper/2302.06576/) (2023)
- [A Variational Perspective on Generative Flow Networks](https://mlsanity.com/paper/2210.07992/) (2022)
- [Towards Scalable Bayesian Learning of Causal DAGs](https://mlsanity.com/paper/2010.00684/) (2020)
- [Data Analysis with Bayesian Networks: A Bootstrap Approach](https://mlsanity.com/paper/1301.6695/) (2013)
- [Bayesian learning of Causal Structure and Mechanisms with GFlowNets and Variational Bayes](https://mlsanity.com/paper/2211.02763/) (2022)
- [NODAGS-Flow: Nonlinear Cyclic Causal Structure Learning](https://mlsanity.com/paper/2301.01849/) (2023)
- [CFlowNets: Continuous Control with Generative Flow Networks](https://mlsanity.com/paper/2303.02430/) (2023)
- [Optimal experimental design via Bayesian optimization: active causal structure learning for Gaussian process networks](https://mlsanity.com/paper/1910.03962/) (2019)

## Built on by (most cited first, 30 of 50)

- [Amortizing intractable inference in large language models](https://mlsanity.com/paper/2310.04363/) (2023)
- [Towards Guaranteed Safe AI: A Framework for Ensuring Robust and Reliable AI Systems](https://mlsanity.com/paper/2405.06624/) (2024)
- [Diffusion Generative Flow Samplers: Improving learning signals through partial trajectory optimization](https://mlsanity.com/paper/2310.02679/) (2023)
- [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)
- [Learning to Scale Logits for Temperature-Conditional GFlowNets](https://mlsanity.com/paper/2310.02823/) (2023)
- [Adaptive teachers for amortized samplers](https://mlsanity.com/paper/2410.01432/) (2024)
- [PhyloGFN: Phylogenetic inference with generative flow networks](https://mlsanity.com/paper/2310.08774/) (2023)
- [Graph Neural Flows for Unveiling Systemic Interactions Among Irregularly Sampled Time Series](https://mlsanity.com/paper/2410.14030/) (2024)
- [Generative Flow Networks: a Markov Chain Perspective](https://mlsanity.com/paper/2307.01422/) (2023)
- [Can a Bayesian Oracle Prevent Harm from an Agent?](https://mlsanity.com/paper/2408.05284/) (2024)
- [Beyond Squared Error: Exploring Loss Design for Enhanced Training of Generative Flow Networks](https://mlsanity.com/paper/2410.02596/) (2024)
- [Amortized Active Causal Induction with Deep Reinforcement Learning](https://mlsanity.com/paper/2405.16718/) (2024)
- [Expert-Aided Causal Discovery of Ancestral Graphs](https://mlsanity.com/paper/2309.12032/) (2023)
- [Looking Backward: Retrospective Backward Synthesis for Goal-Conditioned GFlowNets](https://mlsanity.com/paper/2406.01150/) (2024)
- [Can Knowledge-Graph-based Retrieval Augmented Generation Really Retrieve What You Need?](https://mlsanity.com/paper/2510.16582/) (2025)
- [Delta-AI: Local objectives for amortized inference in sparse graphical models](https://mlsanity.com/paper/2310.02423/) (2023)
- [Expected flow networks in stochastic environments and two-player zero-sum games](https://mlsanity.com/paper/2310.02779/) (2023)
- [Baking Symmetry into GFlowNets](https://mlsanity.com/paper/2406.05426/) (2024)
- [Investigating Generalization Behaviours of Generative Flow Networks](https://mlsanity.com/paper/2402.05309/) (2024)
- [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)
- [Challenges and Considerations in the Evaluation of Bayesian Causal Discovery](https://mlsanity.com/paper/2406.03209/) (2024)
- [Permutation-based Inference for Variational Learning of Directed Acyclic Graphs](https://mlsanity.com/paper/2402.02644/) (2024)
- [CausalPlayground: Addressing Data-Generation Requirements in Cutting-Edge Causality Research](https://mlsanity.com/paper/2405.13092/) (2024)
- [ProDAG: Projected Variational Inference for Directed Acyclic Graphs](https://mlsanity.com/paper/2405.15167/) (2024)
- [Streaming Bayes GFlowNets](https://mlsanity.com/paper/2411.05899/) (2024)
- [Avoid What You Know: Divergent Trajectory Balance for GFlowNets](https://mlsanity.com/paper/2602.17827/) (2026)
- [Differentiable Bayesian Structure Learning with Acyclicity Assurance](https://mlsanity.com/paper/2309.01392/) (2023)
- [Embarrassingly Parallel GFlowNets](https://mlsanity.com/paper/2406.03288/) (2024)

## Abstract (arXiv)

Generative Flow Networks (GFlowNets), a class of generative models over discrete and structured sample spaces, have been previously applied to the problem of inferring the marginal posterior distribution over the directed acyclic graph (DAG) of a Bayesian Network, given a dataset of observations. Based on recent advances extending this framework to non-discrete sample spaces, we propose in this paper to approximate the joint posterior over not only the structure of a Bayesian Network, but also the parameters of its conditional probability distributions. We use a single GFlowNet whose sampling policy follows a two-phase process: the DAG is first generated sequentially one edge at a time, and then the corresponding parameters are picked once the full structure is known. Since the parameters are included in the posterior distribution, this leaves more flexibility for the local probability models of the Bayesian Network, making our approach applicable even to non-linear models parametrized by neural networks. We show that our method, called JSP-GFN, offers an accurate approximation of the joint posterior, while comparing favorably against existing methods on both simulated and real data.