# Out-of-distribution detection using normalizing flows on the data manifold

arXiv: https://arxiv.org/abs/2308.13792 · HTML: https://mlsanity.com/paper/2308.13792/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 34 of its 49 references that are in the map.
- First posted on arXiv 26 Aug 2023.

## Builds on (most cited first, 30 of 34)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [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)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks](https://mlsanity.com/paper/1706.02690/) (2017)
- [Deep Anomaly Detection with Outlier Exposure](https://mlsanity.com/paper/1812.04606/) (2018)
- [Generalized Out-of-Distribution Detection: A Survey](https://mlsanity.com/paper/2110.11334/) (2021)
- [Likelihood Ratios for Out-of-Distribution Detection](https://mlsanity.com/paper/1906.02845/) (2019)
- [Do Deep Generative Models Know What They Don't Know?](https://mlsanity.com/paper/1810.09136/) (2018)
- [Training Confidence-calibrated Classifiers for Detecting Out-of-Distribution Samples](https://mlsanity.com/paper/1711.09325/) (2017)
- [The Intrinsic Dimension of Images and Its Impact on Learning](https://mlsanity.com/paper/2104.08894/) (2021)
- [A note on the evaluation of generative models](https://mlsanity.com/paper/1511.01844/) (2015)
- [Learning Confidence for Out-of-Distribution Detection in Neural Networks](https://mlsanity.com/paper/1802.04865/) (2018)
- [Why Normalizing Flows Fail to Detect Out-of-Distribution Data](https://mlsanity.com/paper/2006.08545/) (2020)
- [Input complexity and out-of-distribution detection with likelihood-based generative models](https://mlsanity.com/paper/1909.11480/) (2019)
- [Understanding the Failure Modes of Out-of-Distribution Generalization](https://mlsanity.com/paper/2010.15775/) (2020)
- [Likelihood Regret: An Out-of-Distribution Detection Score For Variational Auto-encoder](https://mlsanity.com/paper/2003.02977/) (2020)
- [Flows for simultaneous manifold learning and density estimation](https://mlsanity.com/paper/2003.13913/) (2020)
- [SoftFlow: Probabilistic Framework for Normalizing Flow on Manifolds](https://mlsanity.com/paper/2006.04604/) (2020)
- [Understanding Failures in Out-of-Distribution Detection with Deep Generative Models](https://mlsanity.com/paper/2107.06908/) (2021)
- [Rectangular Flows for Manifold Learning](https://mlsanity.com/paper/2106.01413/) (2021)
- [Densely connected normalizing flows](https://mlsanity.com/paper/2106.04627/) (2021)
- [Trumpets: Injective Flows for Inference and Inverse Problems](https://mlsanity.com/paper/2102.10461/) (2021)
- [Tractable Density Estimation on Learned Manifolds with Conformal Embedding Flows](https://mlsanity.com/paper/2106.05275/) (2021)

## Abstract (arXiv)

Using the intuition that out-of-distribution data have lower likelihoods, a common approach for out-of-distribution detection involves estimating the underlying data distribution. Normalizing flows are likelihood-based generative models providing a tractable density estimation via dimension-preserving invertible transformations. Conventional normalizing flows are prone to fail in out-of-distribution detection, because of the well-known curse of dimensionality problem of the likelihood-based models. To solve the problem of likelihood-based models, some works try to modify likelihood for example by incorporating a data complexity measure. We observed that these modifications are still insufficient. According to the manifold hypothesis, real-world data often lie on a low-dimensional manifold. Therefore, we proceed by estimating the density on a low-dimensional manifold and calculating a distance from the manifold as a measure for out-of-distribution detection. We propose a powerful criterion that combines this measure with the modified likelihood measure based on data complexity. Extensive experimental results show that incorporating manifold learning while accounting for the estimation of data complexity improves the out-of-distribution detection ability of normalizing flows. This improvement is achieved without modifying the model structure or using auxiliary out-of-distribution data during training.