mlsanityData to 7 Oct 2026

Hierarchical VAEs Know What They Don't Know

arXiv 2102.08248 ↗First posted 16 Feb 2021cs.LG cs.AI cs.CVcited by 58

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Abstract (arXiv)

Deep generative models have been demonstrated as state-of-the-art density estimators. Yet, recent work has found that they often assign a higher likelihood to data from outside the training distribution. This seemingly paradoxical behavior has caused concerns over the quality of the attained density estimates. In the context of hierarchical variational autoencoders, we provide evidence to explain this behavior by out-of-distribution data having in-distribution low-level features. We argue that this is both expected and desirable behavior. With this insight in hand, we develop a fast, scalable and fully unsupervised likelihood-ratio score for OOD detection that requires data to be in-distribution across all feature-levels. We benchmark the method on a vast set of data and model combinations and achieve state-of-the-art results on out-of-distribution detection.

Key facts. Cited by 58 papers in the map (data through 7 Oct 2026). Builds on 42 of its 64 references that are in the map. First posted on arXiv 16 Feb 2021.

Builds on

42 of 64 references.

References · 42

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
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  3. 2015Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shiftcited by 6,979
  4. 2017Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithmscited by 4,283
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  11. 2018A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attackscited by 1,472
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30 more
  1. 2017Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networkscited by 1,325
  2. 2018Deep Anomaly Detection with Outlier Exposurecited by 939
  3. 2016Conditional Image Generation with PixelCNN Decoderscited by 859
  4. 2016Pixel Recurrent Neural Networkscited by 814
  5. 2014Deep Neural Networks are Easily Fooled: High Confidence Predictions for Unrecognizable Imagescited by 774
  6. 2016Improving Variational Inference with Inverse Autoregressive Flowcited by 636
  7. 2020NVAE: A Deep Hierarchical Variational Autoencodercited by 635
  8. 2016Weight Normalization: A Simple Reparameterization to Accelerate Training of Deep Neural Networkscited by 541
  9. 2014Semi-Supervised Learning with Deep Generative Modelscited by 494
  10. 2015Importance Weighted Autoencoderscited by 454
  11. 2019Likelihood Ratios for Out-of-Distribution Detectioncited by 451
  12. 2018Do Deep Generative Models Know What They Don't Know?cited by 443
  13. 2017PixelCNN++: Improving the PixelCNN with Discretized Logistic Mixture Likelihood and Other Modificationscited by 415
  14. 2018Deep Learning for Classical Japanese Literaturecited by 415
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  17. 2020Very Deep VAEs Generalize Autoregressive Models and Can Outperform Them on Imagescited by 261
  18. 2019Flow++: Improving Flow-Based Generative Models with Variational Dequantization and Architecture Designcited by 258
  19. 2018Learning Confidence for Out-of-Distribution Detection in Neural Networkscited by 245
  20. 2019Input complexity and out-of-distribution detection with likelihood-based generative modelscited by 186
  21. 2020Likelihood Regret: An Out-of-Distribution Detection Score For Variational Auto-encodercited by 145
  22. 2018Inference Suboptimality in Variational Autoencoderscited by 131
  23. 2019BIVA: A Very Deep Hierarchy of Latent Variables for Generative Modelingcited by 109
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  25. 2016Auxiliary Deep Generative Modelscited by 72
  26. 2020Understanding Anomaly Detection with Deep Invertible Networks through Hierarchies of Distributions and Featurescited by 64
  27. 2018Avoiding Latent Variable Collapse With Generative Skip Modelscited by 47
  28. 2018Uncertainty in the Variational Information Bottleneckcited by 39
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 8; 2022: 12; 2023: 15; 2024: 11; 2025: 8; 2026: 4.

58 papers.

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  1. 2022Denoising diffusion models for out-of-distribution detectioncited by 102
  2. 2021Prior and Posterior Networks: A Survey on Evidential Deep Learning Methods For Uncertainty Estimationcited by 71
  3. 2021Conditional Image Generation by Conditioning Variational Auto-Encoderscited by 25
  4. 2023Unsupervised 3D out-of-distribution detection with latent diffusion modelscited by 22
  5. 2024A Geometric Explanation of the Likelihood OOD Detection Paradoxcited by 22
  6. 2022Adaptive Multi-stage Density Ratio Estimation for Learning Latent Space Energy-based Modelcited by 18
  7. 2023t3-Variational Autoencoder: Learning Heavy-tailed Data with Student's t and Power Divergencecited by 17
  8. 2021Do We Really Need to Learn Representations from In-domain Data for Outlier Detection?cited by 16
  9. 2022Model-agnostic out-of-distribution detection using combined statistical testscited by 14
  10. 2023NPCL: Neural Processes for Uncertainty-Aware Continual Learningcited by 14
  11. 2021Bounds all around: training energy-based models with bidirectional boundscited by 10
  12. 2023Likelihood-based Out-of-Distribution Detection with Denoising Diffusion Probabilistic Modelscited by 10
38 more
  1. 2025Autoencoders for Anomaly Detection are Unreliablecited by 9
  2. 2023Learning Joint Latent Space EBM Prior Model for Multi-layer Generatorcited by 8
  3. 2021How to Sense the World: Leveraging Hierarchy in Multimodal Perception for Robust Reinforcement Learning Agentscited by 6
  4. 2023eVAE: Evolutionary Variational Autoencodercited by 6
  5. 2023Inverse problem regularization with hierarchical variational autoencoderscited by 6
  6. 2023Learning Hierarchical Features with Joint Latent Space Energy-Based Priorcited by 6
  7. 2024Learning Latent Space Hierarchical EBM Diffusion Modelscited by 6
  8. 2021Data Invariants to Understand Unsupervised Out-of-Distribution Detectioncited by 5
  9. 2023Learning Unnormalized Statistical Models via Compositional Optimizationcited by 5
  10. 2022Parallel Neural Local Lossless Compressioncited by 4
  11. 2022When less is more: Simplifying inputs aids neural network understandingcited by 4
  12. 2022Out-of-Distribution Detection with Class Ratio Estimationcited by 4
  13. 2024Feature Density Estimation for Out-of-Distribution Detection via Normalizing Flowscited by 4
  14. 2024A Non-negative VAE:the Generalized Gamma Belief Networkcited by 4
  15. 2022Robust uncertainty estimates with out-of-distribution pseudo-inputs trainingcited by 3
  16. 2023How to train your VAEcited by 3
  17. 2021Robust Out-of-Distribution Detection on Deep Probabilistic Generative Modelscited by 2
  18. 2022Top-down inference in an early visual cortex inspired hierarchical Variational Autoencodercited by 2
  19. 2023Look At Me, No Replay! SurpriseNet: Anomaly Detection Inspired Class Incremental Learningcited by 2
  20. 2024Approximations to the Fisher Information Metric of Deep Generative Models for Out-Of-Distribution Detectioncited by 2
  21. 2024Deep Positive-Unlabeled Anomaly Detection for Contaminated Unlabeled Datacited by 2
  22. 2022Geometric instability of out of distribution data across autoencoder architecturecited by 1
  23. 2022Benchmarking Generative Latent Variable Models for Speechcited by 1
  24. 2022The Transitive Information Theory and its Application to Deep Generative Modelscited by 1
  25. 2023Variational Autoencoding of Dental Point Cloudscited by 1
  26. 2024Low-Quality Image Detection by Hierarchical VAEcited by 1
  27. 2025DisCoPatch: Taming Adversarially-driven Batch Statistics for Improved Out-of-Distribution Detectioncited by 1
  28. 2025Clotho: Measuring Task-Specific Pre-Generation Test Adequacy for LLM Inputscited by 1
  29. 2026The Signal in the Noise: OOD Detection Through Goodness-of-Fit Testing in Factorised Latent Spacescited by 1
  30. 2021The Exponentially Tilted Gaussian Prior for Variational Autoencoderscited by 0
  31. 2022Diverse super-resolution with pretrained deep hiererarchical VAEscited by 0
  32. 2023A Semi-supervised Object Detection Algorithm for Underwater Imagerycited by 0
  33. 2023Unsupervised Out-of-Distribution Detection by Restoring Lossy Inputs with Variational Autoencodercited by 0
  34. 2023Learning Nonparametric High-Dimensional Generative Models: The Empirical-Beta-Copula Autoencodercited by 0
  35. 2024Rethinking Test-time Likelihood: The Likelihood Path Principle and Its Application to OOD Detectioncited by 0
  36. 2024Image-based Novel Fault Detection with Deep Learning Classifiers using Hierarchical Labelscited by 0
  37. 2024Resultant: Incremental Effectiveness on Likelihood for Unsupervised Out-of-Distribution Detectioncited by 0
  38. 2024Hallucination Detection in Virtually-Stained Histology: A Latent Space Baselinecited by 0

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