mlsanityData to 14 Oct 2026

Advances in Variational Inference

arXiv 1711.05597 ↗First posted 15 Nov 2017cs.LG stat.MLcited by 236

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Abstract (arXiv)

Many modern unsupervised or semi-supervised machine learning algorithms rely on Bayesian probabilistic models. These models are usually intractable and thus require approximate inference. Variational inference (VI) lets us approximate a high-dimensional Bayesian posterior with a simpler variational distribution by solving an optimization problem. This approach has been successfully used in various models and large-scale applications. In this review, we give an overview of recent trends in variational inference. We first introduce standard mean field variational inference, then review recent advances focusing on the following aspects: (a) scalable VI, which includes stochastic approximations, (b) generic VI, which extends the applicability of VI to a large class of otherwise intractable models, such as non-conjugate models, (c) accurate VI, which includes variational models beyond the mean field approximation or with atypical divergences, and (d) amortized VI, which implements the inference over local latent variables with inference networks. Finally, we provide a summary of promising future research directions.

Key facts. Cited by 236 papers in the map (data through 14 Oct 2026). First posted on arXiv 15 Nov 2017.

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 54; 2022: 41; 2023: 56; 2024: 39; 2025: 30; 2026: 16.

236 papers.

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  1. 2022Diffusion Probabilistic Modeling for Video Generationcited by 238
  2. 2022GFlowNets and variational inferencecited by 106
  3. 2021The Bayesian Learning Rulecited by 99
  4. 2022Deep End-to-end Causal Inferencecited by 95
  5. 2021Towards a Science of Human-AI Decision Making: A Survey of Empirical Studiescited by 86
  6. 2022An Introduction to Neural Data Compressioncited by 79
  7. 2021Large-Scale Wasserstein Gradient Flowscited by 77
  8. 2025InverseBench: Benchmarking Plug-and-Play Diffusion Priors for Inverse Problems in Physical Sciencescited by 68
  9. 2021Bayesian Learning via Neural Schr"odinger-F"ollmer Flowscited by 56
  10. 2024Estimating Epistemic and Aleatoric Uncertainty with a Single Modelcited by 54
  11. 2021Integrating Expert ODEs into Neural ODEs: Pharmacology and Disease Progressioncited by 48
  12. 2022Probability flow solution of the Fokker-Planck equationcited by 47
38 more
  1. 2021MCMC Variational Inference via Uncorrected Hamiltonian Annealingcited by 39
  2. 2024Neural Methods for Amortized Inferencecited by 39
  3. 2021Is MC Dropout Bayesian?cited by 35
  4. 2023BayesDAG: Gradient-Based Posterior Inference for Causal Discoverycited by 33
  5. 2025Simulation-Based Inference: A Practical Guidecited by 32
  6. 2021Identifiable Generative Models for Missing Not at Random Data Imputationcited by 30
  7. 2022Rhino: Deep Causal Temporal Relationship Learning With History-dependent Noisecited by 30
  8. 2023Provable convergence guarantees for black-box variational inferencecited by 29
  9. 2021Data Augmentation in High Dimensional Low Sample Size Setting Using a Geometry-Based Variational Autoencodercited by 27
  10. 2023Uncertainty Quantification in Machine Learning for Engineering Design and Health Prognostics: A Tutorialcited by 27
  11. 2022Active Surrogate Estimators: An Active Learning Approach to Label-Efficient Model Evaluationcited by 26
  12. 2022Hybrid Predictive Coding: Inferring, Fast and Slowcited by 26
  13. 2022Pythae: Unifying Generative Autoencoders in Python -- A Benchmarking Use Casecited by 26
  14. 2023Conditional Optimal Transport on Function Spacescited by 26
  15. 2022Variational Deep Image Restorationcited by 24
  16. 2022A Geometric Perspective on Variational Autoencoderscited by 24
  17. 2021The Internet of Federated Things (IoFT): A Vision for the Future and In-depth Survey of Data-driven Approaches for Federated Learningcited by 23
  18. 2025Generative Uncertainty in Diffusion Modelscited by 23
  19. 2023On the Convergence of Black-Box Variational Inferencecited by 22
  20. 2025Variational Control for Guidance in Diffusion Modelscited by 22
  21. 2022Missing Data Imputation and Acquisition with Deep Hierarchical Models and Hamiltonian Monte Carlocited by 19
  22. 2023Learning to Jump: Thinning and Thickening Latent Counts for Generative Modelingcited by 18
  23. 2021Model-based Meta Reinforcement Learning using Graph Structured Surrogate Modelscited by 17
  24. 2023Counterfactual (Non-)identifiability of Learned Structural Causal Modelscited by 17
  25. 2023Federated Learning as Variational Inference: A Scalable Expectation Propagation Approachcited by 17
  26. 2021Sparse Uncertainty Representation in Deep Learning with Inducing Weightscited by 16
  27. 2021Reactive Message Passing for Scalable Bayesian Inferencecited by 16
  28. 2022Amortized Variational Inference: A Systematic Reviewcited by 16
  29. 2024Sparse Inducing Points in Deep Gaussian Processes: Enhancing Modeling with Denoising Diffusion Variational Inferencecited by 16
  30. 2021Stein Variational Gradient Descent: many-particle and long-time asymptoticscited by 15
  31. 2023Causal Reasoning in the Presence of Latent Confounders via Neural ADMG Learningcited by 15
  32. 2023A Transformer-based Diffusion Probabilistic Model for Heart Rate and Blood Pressure Forecasting in Intensive Care Unitcited by 14
  33. 2023Boosting Offline Reinforcement Learning for Autonomous Driving with Hierarchical Latent Skillscited by 14
  34. 2023Neural Structure Learning with Stochastic Differential Equationscited by 14
  35. 2021Natural Posterior Network: Deep Bayesian Uncertainty for Exponential Family Distributionscited by 13
  36. 2022Partitioned Variational Inference: A Framework for Probabilistic Federated Learningcited by 13
  37. 2021Structured Stochastic Gradient MCMCcited by 12
  38. 2021An Introduction to Variational Inferencecited by 12

50 most cited of 236 All 236 (JSON)