mlsanityData to 7 Oct 2026

GFlowNets and variational inference

arXiv 2210.00580 ↗First posted 2 Oct 2022cs.LG stat.MLcited by 103

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Abstract (arXiv)

This paper builds bridges between two families of probabilistic algorithms: (hierarchical) variational inference (VI), which is typically used to model distributions over continuous spaces, and generative flow networks (GFlowNets), which have been used for distributions over discrete structures such as graphs. We demonstrate that, in certain cases, VI algorithms are equivalent to special cases of GFlowNets in the sense of equality of expected gradients of their learning objectives. We then point out the differences between the two families and show how these differences emerge experimentally. Notably, GFlowNets, which borrow ideas from reinforcement learning, are more amenable than VI to off-policy training without the cost of high gradient variance induced by importance sampling. We argue that this property of GFlowNets can provide advantages for capturing diversity in multimodal target distributions.

Key facts. Cited by 103 papers in the map (data through 7 Oct 2026). Builds on 47 of its 65 references that are in the map. First posted on arXiv 2 Oct 2022.

Builds on

47 of 65 references.

References · 47

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2016SGDR: Stochastic Gradient Descent with Warm Restartscited by 4,993
  3. 2013Auto-Encoding Variational Bayescited by 3,980
  4. 2018Relational inductive biases, deep learning, and graph networkscited by 1,341
  5. 2018Junction Tree Variational Autoencoder for Molecular Graph Generationcited by 647
  6. 2020NVAE: A Deep Hierarchical Variational Autoencodercited by 635
  7. 2016Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithmcited by 498
  8. 2015Importance Weighted Autoencoderscited by 454
  9. 2021Flow Network based Generative Models for Non-Iterative Diverse Candidate Generationcited by 384
  10. 2013Black Box Variational Inferencecited by 317
  11. 2016Ladder Variational Autoencoderscited by 315
  12. 2021GFlowNet Foundationscited by 286
35 more
  1. 2020Very Deep VAEs Generalize Autoregressive Models and Can Outperform Them on Imagescited by 261
  2. 2022Trajectory balance: Improved credit assignment in GFlowNetscited by 244
  3. 2017Advances in Variational Inferencecited by 236
  4. 2013Expectation Propagation for approximate Bayesian inferencecited by 172
  5. 2022Biological Sequence Design with GFlowNetscited by 172
  6. 2022Bayesian Structure Learning with Generative Flow Networkscited by 153
  7. 2022Learning GFlowNets from partial episodes for improved convergence and stabilitycited by 129
  8. 2014Neural Variational Inference and Learning in Belief Networkscited by 116
  9. 2022Generative Flow Networks for Discrete Probabilistic Modelingcited by 113
  10. 2019BIVA: A Very Deep Hierarchy of Latent Variables for Generative Modelingcited by 109
  11. 2017Backpropagation through the Void: Optimizing control variates for black-box gradient estimationcited by 104
  12. 2015Hierarchical Variational Modelscited by 89
  13. 2013The Optimal Reward Baseline for Gradient-Based Reinforcement Learningcited by 84
  14. 2016Variational inference for Monte Carlo objectivescited by 83
  15. 2017REBAR: Low-variance, unbiased gradient estimates for discrete latent variable modelscited by 78
  16. 2018Tighter Variational Bounds are Not Necessarily Bettercited by 76
  17. 2020VarGrad: A Low-Variance Gradient Estimator for Variational Inferencecited by 73
  18. 2014Reweighted Wake-Sleepcited by 66
  19. 2018Variance Reduction for Policy Gradient with Action-Dependent Factorized Baselinescited by 65
  20. 2013Learning Gaussian Networkscited by 62
  21. 2018Semi-Implicit Variational Inferencecited by 55
  22. 2018Importance Weighting and Variational Inferencecited by 55
  23. 2015Black-box α-divergence Minimizationcited by 37
  24. 2014Addendum on the scoring of Gaussian directed acyclic graphical modelscited by 32
  25. 2020f-Divergence Variational Inferencecited by 28
  26. 2019The Thermodynamic Variational Objectivecited by 26
  27. 2018Variational Inference with Tail-adaptive f-Divergencecited by 25
  28. 2022Unifying Generative Models with GFlowNets and Beyondcited by 24
  29. 2015Stochastic Expectation Propagationcited by 22
  30. 2019Importance Weighted Hierarchical Variational Inferencecited by 20
  31. 2016Operator Variational Inferencecited by 16
  32. 2019Variational f-divergence Minimizationcited by 16
  33. 2020Learning to learn generative programs with Memoised Wake-Sleepcited by 15
  34. 2021Nested Variational Inferencecited by 14
  35. 2021Hybrid Memoised Wake-Sleep: Approximate Inference at the Discrete-Continuous Interfacecited by 3

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 4; 2023: 25; 2024: 32; 2025: 27; 2026: 15.

103 papers.

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  1. 2024Iterated Denoising Energy Matching for Sampling from Boltzmann Densitiescited by 113
  2. 2023Improved sampling via learned diffusionscited by 103
  3. 2023A theory of continuous generative flow networkscited by 98
  4. 2023Amortizing intractable inference in large language modelscited by 94
  5. 2023Better Training of GFlowNets with Local Credit and Incomplete Trajectoriescited by 83
  6. 2024Amortizing intractable inference in diffusion models for vision, language, and controlcited by 70
  7. 2023GFlowNets for AI-Driven Scientific Discoverycited by 63
  8. 2023Generative Flow Networks as Entropy-Regularized RLcited by 60
  9. 2023Diffusion Generative Flow Samplers: Improving learning signals through partial trajectory optimizationcited by 57
  10. 2024Beyond ELBOs: A Large-Scale Evaluation of Variational Methods for Samplingcited by 55
  11. 2024Ant Colony Sampling with GFlowNets for Combinatorial Optimizationcited by 53
  12. 2022A-NeSI: A Scalable Approximate Method for Probabilistic Neurosymbolic Inferencecited by 50
38 more
  1. 2023Joint Bayesian Inference of Graphical Structure and Parameters with a Single Generative Flow Networkcited by 50
  2. 2024Improved off-policy training of diffusion samplerscited by 47
  3. 2023Local Search GFlowNetscited by 45
  4. 2024DEFT: Efficient Fine-Tuning of Diffusion Models by Learning the Generalised h-transformcited by 44
  5. 2023GFlowNet-EM for learning compositional latent variable modelscited by 40
  6. 2023Let the Flows Tell: Solving Graph Combinatorial Optimization Problems with GFlowNetscited by 40
  7. 2024Discrete Probabilistic Inference as Control in Multi-path Environmentscited by 40
  8. 2022A Variational Perspective on Generative Flow Networkscited by 39
  9. 2025FlowRL: Matching Reward Distributions for LLM Reasoningcited by 38
  10. 2024Genetic-guided GFlowNets for Sample Efficient Molecular Optimizationcited by 36
  11. 2023Stochastic Generative Flow Networkscited by 32
  12. 2023Thompson sampling for improved exploration in GFlowNetscited by 31
  13. 2024Efficient Diversity-Preserving Diffusion Alignment via Gradient-Informed GFlowNetscited by 30
  14. 2024Flow of Reasoning: Training LLMs for Divergent Reasoning with Minimal Examplescited by 29
  15. 2023Distributional GFlowNets with Quantile Flowscited by 28
  16. 2024Improving GFlowNets for Text-to-Image Diffusion Alignmentcited by 27
  17. 2023Learning to Scale Logits for Temperature-Conditional GFlowNetscited by 26
  18. 2023Conformal Contextual Robust Optimizationcited by 25
  19. 2023Learning Energy Decompositions for Partial Inference of GFlowNetscited by 24
  20. 2024Adaptive teachers for amortized samplerscited by 23
  21. 2022GFlowOut: Dropout with Generative Flow Networkscited by 22
  22. 2023PhyloGFN: Phylogenetic inference with generative flow networkscited by 20
  23. 2024QGFN: Controllable Greediness with Action Valuescited by 18
  24. 2023Goal-conditioned GFlowNets for Controllable Multi-Objective Molecular Designcited by 17
  25. 2025From discrete-time policies to continuous-time diffusion samplers: Asymptotic equivalences and faster trainingcited by 17
  26. 2023Pre-Training and Fine-Tuning Generative Flow Networkscited by 16
  27. 2025Outsourced diffusion sampling: Efficient posterior inference in latent spaces of generative modelscited by 16
  28. 2025GFlowVLM: Enhancing Multi-step Reasoning in Vision-Language Models with Generative Flow Networkscited by 15
  29. 2023Improving Gradient-guided Nested Sampling for Posterior Inferencecited by 14
  30. 2025Offline Model-Based Optimization: Comprehensive Reviewcited by 14
  31. 2022Latent State Marginalization as a Low-cost Approach for Improving Explorationcited by 13
  32. 2024Pessimistic Backward Policy for GFlowNetscited by 13
  33. 2024Optimizing Backward Policies in GFlowNets via Trajectory Likelihood Maximizationcited by 12
  34. 2024RetroGFN: Diverse and Feasible Retrosynthesis using GFlowNetscited by 10
  35. 2025On scalable and efficient training of diffusion samplerscited by 10
  36. 2024Beyond Squared Error: Exploring Loss Design for Enhanced Training of Generative Flow Networkscited by 9
  37. 2025Revisiting Non-Acyclic GFlowNets in Discrete Environmentscited by 8
  38. 2023Delta-AI: Local objectives for amortized inference in sparse graphical modelscited by 7

50 most cited of 103 All 103 (JSON)