# Feature Density Estimation for Out-of-Distribution Detection via Normalizing Flows

arXiv: https://arxiv.org/abs/2402.06537 · HTML: https://mlsanity.com/paper/2402.06537/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 39 references that are in the map.
- First posted on arXiv 9 Feb 2024.

## Builds on (most cited first, 28 of 28)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Describing Textures in the Wild](https://mlsanity.com/paper/1311.3618/) (2013)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks](https://mlsanity.com/paper/1706.02690/) (2017)
- [Energy-based Out-of-distribution Detection](https://mlsanity.com/paper/2010.03759/) (2020)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [Generalized Out-of-Distribution Detection: A Survey](https://mlsanity.com/paper/2110.11334/) (2021)
- [ReAct: Out-of-distribution Detection With Rectified Activations](https://mlsanity.com/paper/2111.12797/) (2021)
- [Do Deep Generative Models Know What They Don't Know?](https://mlsanity.com/paper/1810.09136/) (2018)
- [Understanding the Behaviour of Contrastive Loss](https://mlsanity.com/paper/2012.09740/) (2020)
- [CFLOW-AD: Real-Time Unsupervised Anomaly Detection with Localization via Conditional Normalizing Flows](https://mlsanity.com/paper/2107.12571/) (2021)
- [Flow++: Improving Flow-Based Generative Models with Variational Dequantization and Architecture Design](https://mlsanity.com/paper/1902.00275/) (2019)
- [Residual Flows for Invertible Generative Modeling](https://mlsanity.com/paper/1906.02735/) (2019)
- [Why Normalizing Flows Fail to Detect Out-of-Distribution Data](https://mlsanity.com/paper/2006.08545/) (2020)
- [Same Same But DifferNet: Semi-Supervised Defect Detection with Normalizing Flows](https://mlsanity.com/paper/2008.12577/) (2020)
- [Extremely Simple Activation Shaping for Out-of-Distribution Detection](https://mlsanity.com/paper/2209.09858/) (2022)
- [A Unified Survey on Anomaly, Novelty, Open-Set, and Out-of-Distribution Detection: Solutions and Future Challenges](https://mlsanity.com/paper/2110.14051/) (2021)
- [Fully Convolutional Cross-Scale-Flows for Image-based Defect Detection](https://mlsanity.com/paper/2110.02855/) (2021)
- [Hybrid Models for Open Set Recognition](https://mlsanity.com/paper/2003.12506/) (2020)
- [Denoising diffusion models for out-of-distribution detection](https://mlsanity.com/paper/2211.07740/) (2022)
- [Unsupervised Out-of-Distribution Detection with Diffusion Inpainting](https://mlsanity.com/paper/2302.10326/) (2023)
- [Hierarchical VAEs Know What They Don't Know](https://mlsanity.com/paper/2102.08248/) (2021)
- [Unsupervised Video Anomaly Detection via Normalizing Flows with Implicit Latent Features](https://mlsanity.com/paper/2010.07524/) (2020)
- [Improving the Intra-class Long-tail in 3D Detection via Rare Example Mining](https://mlsanity.com/paper/2210.08375/) (2022)

## Built on by (most cited first, 4 of 4)

- [Probability Density from Latent Diffusion Models for Out-of-Distribution Detection](https://mlsanity.com/paper/2508.15737/) (2025)
- [Breaking the Adversarial Robustness-Performance Trade-off in Text Classification via Manifold Purification](https://mlsanity.com/paper/2511.07888/) (2025)
- [Image Quality Dependent Degradation for AI Systems](https://mlsanity.com/paper/2607.25736/) (2026)
- [Vmem-varphi: Low-Compute Out-of-Distribution Detection in Spiking Neural Networks from Membrane-Potential Statistics](https://mlsanity.com/paper/2610.00350/) (2026)

## Abstract (arXiv)

Out-of-distribution (OOD) detection is a critical task for safe deployment of learning systems in the open world setting. In this work, we investigate the use of feature density estimation via normalizing flows for OOD detection and present a fully unsupervised approach which requires no exposure to OOD data, avoiding researcher bias in OOD sample selection. This is a post-hoc method which can be applied to any pretrained model, and involves training a lightweight auxiliary normalizing flow model to perform the out-of-distribution detection via density thresholding. Experiments on OOD detection in image classification show strong results for far-OOD data detection with only a single epoch of flow training, including 98.2% AUROC for ImageNet-1k vs. Textures, which exceeds the state of the art by 7.8%. We additionally explore the connection between the feature space distribution of the pretrained model and the performance of our method. Finally, we provide insights into training pitfalls that have plagued normalizing flows for use in OOD detection.