# Perfect density models cannot guarantee anomaly detection

arXiv: https://arxiv.org/abs/2012.03808 · HTML: https://mlsanity.com/paper/2012.03808/

## Key facts

- Cited by 39 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Dec 2020.

## Built on by (most cited first, 30 of 39)

- [Asymmetric Student-Teacher Networks for Industrial Anomaly Detection](https://mlsanity.com/paper/2210.07829/) (2022)
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- [Diagnosing and Fixing Manifold Overfitting in Deep Generative Models](https://mlsanity.com/paper/2204.07172/) (2022)
- [Autoencoding Under Normalization Constraints](https://mlsanity.com/paper/2105.05735/) (2021)
- [Feature Likelihood Divergence: Evaluating the Generalization of Generative Models Using Samples](https://mlsanity.com/paper/2302.04440/) (2023)
- [A Geometric Explanation of the Likelihood OOD Detection Paradox](https://mlsanity.com/paper/2403.18910/) (2024)
- [Do We Really Need to Learn Representations from In-domain Data for Outlier Detection?](https://mlsanity.com/paper/2105.09270/) (2021)
- [Entropic Issues in Likelihood-Based OOD Detection](https://mlsanity.com/paper/2109.10794/) (2021)
- [Natural Posterior Network: Deep Bayesian Uncertainty for Exponential Family Distributions](https://mlsanity.com/paper/2105.04471/) (2021)
- [A Survey on Diffusion Models for Anomaly Detection](https://mlsanity.com/paper/2501.11430/) (2025)
- [What makes an image realistic?](https://mlsanity.com/paper/2403.04493/) (2024)
- [Anomaly Detection with Variance Stabilized Density Estimation](https://mlsanity.com/paper/2306.00582/) (2023)
- [PQMass: Probabilistic Assessment of the Quality of Generative Models using Probability Mass Estimation](https://mlsanity.com/paper/2402.04355/) (2024)
- [Innovations Autoencoder and its Application in One-class Anomalous Sequence Detection](https://mlsanity.com/paper/2106.12382/) (2021)
- [Understanding Out-of-distribution: A Perspective of Data Dynamics](https://mlsanity.com/paper/2111.14730/) (2021)
- [ODIM: Outlier Detection via Likelihood of Under-Fitted Generative Models](https://mlsanity.com/paper/2301.04257/) (2023)
- [New Methods and Datasets for Group Anomaly Detection From Fundamental Physics](https://mlsanity.com/paper/2107.02821/) (2021)
- [Inference and Sampling for Archimax Copulas](https://mlsanity.com/paper/2205.14025/) (2022)
- [Invariant Representation Driven Neural Classifier for Anti-QCD Jet Tagging](https://mlsanity.com/paper/2201.07199/) (2022)
- [Generative Artificial Intelligence for Internet of Things Computing: A Systematic Survey](https://mlsanity.com/paper/2504.07635/) (2025)
- [Approximations to the Fisher Information Metric of Deep Generative Models for Out-Of-Distribution Detection](https://mlsanity.com/paper/2403.01485/) (2024)
- [Repairing Systematic Outliers by Learning Clean Subspaces in VAEs](https://mlsanity.com/paper/2207.08050/) (2022)
- [Evaluating Out-of-Distribution Detectors Through Adversarial Generation of Outliers](https://mlsanity.com/paper/2208.10940/) (2022)
- [Master's Thesis: Out-of-distribution Detection with Energy-based Models](https://mlsanity.com/paper/2302.12002/) (2023)
- [Vacant Holes for Unsupervised Detection of the Outliers in Compact Latent Representation](https://mlsanity.com/paper/2306.09646/) (2023)
- [ALTBI: Constructing Improved Outlier Detection Models via Optimization of Inlier-Memorization Effect](https://mlsanity.com/paper/2408.09791/) (2024)
- [Channel Matters: Estimating Channel Influence for Multivariate Time Series](https://mlsanity.com/paper/2408.14763/) (2024)
- [Why CNN Features Are not Gaussian: A Statistical Anatomy of Deep Representations](https://mlsanity.com/paper/2411.05183/) (2024)
- [Time-reversed Flow Matching with Worst Transport in High-dimensional Latent Space for Image Anomaly Detection](https://mlsanity.com/paper/2508.05461/) (2025)

## Abstract (arXiv)

Thanks to the tractability of their likelihood, several deep generative models show promise for seemingly straightforward but important applications like anomaly detection, uncertainty estimation, and active learning. However, the likelihood values empirically attributed to anomalies conflict with the expectations these proposed applications suggest. In this paper, we take a closer look at the behavior of distribution densities through the lens of reparametrization and show that these quantities carry less meaningful information than previously thought, beyond estimation issues or the curse of dimensionality. We conclude that the use of these likelihoods for anomaly detection relies on strong and implicit hypotheses, and highlight the necessity of explicitly formulating these assumptions for reliable anomaly detection.