mlsanityData to 7 Oct 2026

Building Expressive and Tractable Probabilistic Generative Models: A Review

arXiv 2402.00759 ↗First posted 1 Feb 2024cs.LG cs.AIcited by 12

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Abstract (arXiv)

We present a comprehensive survey of the advancements and techniques in the field of tractable probabilistic generative modeling, primarily focusing on Probabilistic Circuits (PCs). We provide a unified perspective on the inherent trade-offs between expressivity and tractability, highlighting the design principles and algorithmic extensions that have enabled building expressive and efficient PCs, and provide a taxonomy of the field. We also discuss recent efforts to build deep and hybrid PCs by fusing notions from deep neural models, and outline the challenges and open questions that can guide future research in this evolving field.

Key facts. Cited by 12 papers in the map (data through 7 Oct 2026). Builds on 37 of its 78 references that are in the map. First posted on arXiv 1 Feb 2024.

Builds on

37 of 78 references.

References · 37

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2021Masked Autoencoders Are Scalable Vision Learnerscited by 7,339
  3. 2018Recurrent World Models Facilitate Policy Evolutioncited by 761
  4. 2021Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Modelscited by 251
  5. 2013Learning Bayesian Networks: The Combination of Knowledge and Statistical Datacited by 185
  6. 2022Semantic Probabilistic Layers for Neuro-Symbolic Learningcited by 103
  7. 2020Einsum Networks: Fast and Scalable Learning of Tractable Probabilistic Circuitscited by 102
  8. 2013A Differential Approach to Inference in Bayesian Networkscited by 93
  9. 2023Tractable Control for Autoregressive Language Generationcited by 65
  10. 2020Active Feature Acquisition with Generative Surrogate Modelscited by 53
  11. 2016On the Latent Variable Interpretation in Sum-Product Networkscited by 40
  12. 2023Subtractive Mixture Models via Squaring: Representation and Learningcited by 39
25 more
  1. 2022Scaling Up Probabilistic Circuits by Latent Variable Distillationcited by 35
  2. 2013The Bayesian Structural EM Algorithmcited by 26
  3. 2016A Unified Approach for Learning the Parameters of Sum-Product Networkscited by 24
  4. 2019Bayesian Learning of Sum-Product Networkscited by 24
  5. 2020Strudel: Learning Structured-Decomposable Probabilistic Circuitscited by 24
  6. 2023Image Inpainting via Tractable Steering of Diffusion Modelscited by 22
  7. 2020Probabilistic Circuits for Variational Inference in Discrete Graphical Modelscited by 20
  8. 2021Lossless Compression with Probabilistic Circuitscited by 20
  9. 2019On Tractable Computation of Expected Predictionscited by 19
  10. 2022Continuous Mixtures of Tractable Probabilistic Modelscited by 19
  11. 2023Understanding the Distillation Process from Deep Generative Models to Tractable Probabilistic Circuitscited by 19
  12. 2016Visualizing and Understanding Sum-Product Networkscited by 18
  13. 2022Sparse Probabilistic Circuits via Pruning and Growingcited by 17
  14. 2019Deep Structured Mixtures of Gaussian Processescited by 16
  15. 2020Sum-product networks: A surveycited by 15
  16. 2021HyperSPNs: Compact and Expressive Probabilistic Circuitscited by 14
  17. 2021Solving Marginal MAP Exactly by Probabilistic Circuit Transformationscited by 11
  18. 2023Compositional Probabilistic and Causal Inference using Tractable Circuit Modelscited by 10
  19. 2021Leveraging Probabilistic Circuits for Nonparametric Multi-Output Regressioncited by 8
  20. 2023Characteristic Circuitscited by 8
  21. 2023Probabilistic Circuits That Know What They Don't Knowcited by 7
  22. 2023Bayesian Structure Scores for Probabilistic Circuitscited by 7
  23. 2017Sum-Product-Quotient Networkscited by 5
  24. 2020Sum-Product-Transform Networks: Exploiting Symmetries using Invertible Transformationscited by 3
  25. 2022Certifying Fairness of Probabilistic Circuitscited by 3

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 4; 2025: 1; 2026: 7.

12 papers.

  1. 2024What is the Relationship between Tensor Factorizations and Circuits (and How Can We Exploit it)?cited by 22
  2. 2024On the Relationship Between Monotone and Squared Probabilistic Circuitscited by 14
  3. 2024Restructuring Tractable Probabilistic Circuitscited by 7
  4. 2024Credibility-Aware Multi-Modal Fusion Using Probabilistic Circuitscited by 5
  5. 2025Tractable Sharpness-Aware Learning of Probabilistic Circuitscited by 3
  6. 2026Context-specific Credibility-aware Multimodal Fusion with Conditional Probabilistic Circuitscited by 2
  7. 2026Geometry-Aware Probabilistic Circuits via Voronoi Tessellationscited by 1
  8. 2026ExplainFuzz: Explainable and Constraint-Conditioned Test Generation with Probabilistic Circuitscited by 1
  9. 2026CircuitSynth: Reliable Synthetic Data Generationcited by 1
  10. 2026A Compositional Theory of Curvature in Probabilistic Circuitscited by 0
  11. 2026On Probabilistic Inference Through Parametric Tensor Decomposition in Base Tensor Networkscited by 0
  12. 2026Reliable Fusion of Conflicting Expertscited by 0