mlsanityData to 13 Oct 2026

Importance Weighted Autoencoders

arXiv 1509.00519 ↗First posted 1 Sep 2015cs.LG stat.MLcited by 454

Not on the map. Why?

Cited by 27 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

The variational autoencoder (VAE; Kingma, Welling (2014)) is a recently proposed generative model pairing a top-down generative network with a bottom-up recognition network which approximates posterior inference. It typically makes strong assumptions about posterior inference, for instance that the posterior distribution is approximately factorial, and that its parameters can be approximated with nonlinear regression from the observations. As we show empirically, the VAE objective can lead to overly simplified representations which fail to use the network's entire modeling capacity. We present the importance weighted autoencoder (IWAE), a generative model with the same architecture as the VAE, but which uses a strictly tighter log-likelihood lower bound derived from importance weighting. In the IWAE, the recognition network uses multiple samples to approximate the posterior, giving it increased flexibility to model complex posteriors which do not fit the VAE modeling assumptions. We show empirically that IWAEs learn richer latent space representations than VAEs, leading to improved test log-likelihood on density estimation benchmarks.

Key facts. Cited by 454 papers in the map (data through 13 Oct 2026). First posted on arXiv 1 Sep 2015.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 13 Oct)

Citing papers per year: 2019: 3; 2020: 0; 2021: 103; 2022: 109; 2023: 91; 2024: 49; 2025: 55; 2026: 44.

454 papers.

Sort:

By area:

  1. 2021Score-based Generative Modeling in Latent Spacecited by 635
  2. 2021Argmax Flows and Multinomial Diffusion: Learning Categorical Distributionscited by 570
  3. 2022Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Modelscited by 333
  4. 2025LLaDA 1.5: Variance-Reduced Preference Optimization for Large Language Diffusion Modelscited by 275
  5. 2021Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Modelscited by 252
  6. 2021Score-Based Generative Modeling with Critically-Damped Langevin Diffusioncited by 231
  7. 2021Offline-to-Online Reinforcement Learning via Balanced Replay and Pessimistic Q-Ensemblecited by 211
  8. 2019Variational Mixture-of-Experts Autoencoders for Multi-Modal Deep Generative Modelscited by 177
  9. 2022Weakly supervised causal representation learningcited by 140
  10. 2023Modern Bayesian Experimental Designcited by 123
  11. 2022Riemannian Diffusion Modelscited by 121
  12. 2022GFlowNets and variational inferencecited by 104
38 more
  1. 2022DiffuseVAE: Efficient, Controllable and High-Fidelity Generation from Low-Dimensional Latentscited by 103
  2. 2022Let us Build Bridges: Understanding and Extending Diffusion Generative Modelscited by 103
  3. 2024Probabilistic Inference in Language Models via Twisted Sequential Monte Carlocited by 89
  4. 2021Generalized Multimodal ELBOcited by 86
  5. 2022HyperImpute: Generalized Iterative Imputation with Automatic Model Selectioncited by 81
  6. 2022An Introduction to Neural Data Compressioncited by 79
  7. 2022Supported Policy Optimization for Offline Reinforcement Learningcited by 73
  8. 2022Latent Diffusion Energy-Based Model for Interpretable Text Modelingcited by 67
  9. 2021What Do We Mean by Generalization in Federated Learning?cited by 62
  10. 2021On Memorization in Probabilistic Deep Generative Modelscited by 60
  11. 2021Differentiable Particle Filtering via Entropy-Regularized Optimal Transportcited by 59
  12. 2021Hierarchical VAEs Know What They Don't Knowcited by 58
  13. 2023Posterior Collapse and Latent Variable Non-identifiabilitycited by 57
  14. 2023Diffusion Generative Flow Samplers: Improving learning signals through partial trajectory optimizationcited by 57
  15. 2023Improved Techniques for Maximum Likelihood Estimation for Diffusion ODEscited by 54
  16. 2023High Fidelity Image Counterfactuals with Probabilistic Causal Modelscited by 53
  17. 2021Consistency Regularization for Variational Auto-Encoderscited by 51
  18. 2022Score-Based Diffusion meets Annealed Importance Samplingcited by 51
  19. 2025Optimizing Language Models for Inference Time Objectives using Reinforcement Learningcited by 51
  20. 2022A survey of multimodal deep generative modelscited by 47
  21. 2024Improved off-policy training of diffusion samplerscited by 47
  22. 2023Training Chain-of-Thought via Latent-Variable Inferencecited by 46
  23. 2023Stable Target Field for Reduced Variance Score Estimation in Diffusion Modelscited by 44
  24. 2022Variational methods for simulation-based inferencecited by 43
  25. 2025Reasoning to Learn from Latent Thoughtscited by 43
  26. 2022Maximum Likelihood Training of Implicit Nonlinear Diffusion Modelscited by 42
  27. 2021Class-Incremental Learning with Generative Classifierscited by 39
  28. 2021MCMC Variational Inference via Uncorrected Hamiltonian Annealingcited by 39
  29. 2022Recent Advances for Quantum Neural Networks in Generative Learningcited by 39
  30. 2022Deep Latent State Space Models for Time-Series Generationcited by 37
  31. 2023Multimodal Variational Auto-encoder based Audio-Visual Segmentationcited by 37
  32. 2021Data augmentation in Bayesian neural networks and the cold posterior effectcited by 36
  33. 2021Monte Carlo Variational Auto-Encoderscited by 36
  34. 2021Differentiable Annealed Importance Sampling and the Perils of Gradient Noisecited by 36
  35. 2023Modelling Cellular Perturbations with the Sparse Additive Mechanism Shift Variational Autoencodercited by 36
  36. 2022A Study on the Evaluation of Generative Modelscited by 35
  37. 2022Learning Causal Representations of Single Cells via Sparse Mechanism Shift Modelingcited by 34
  38. 2025Esoteric Language Models: A Family of Any-Order Diffusion LLMscited by 34

50 most cited of 454 All 454 (JSON)