# On Uniformly Scaling Flows: A Density-Aligned Approach to Deep One-Class Classification

arXiv: https://arxiv.org/abs/2510.09452 · HTML: https://mlsanity.com/paper/2510.09452/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 34 of its 40 references that are in the map.
- First posted on arXiv 10 Oct 2025.

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

- [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)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [A Unifying Review of Deep and Shallow Anomaly Detection](https://mlsanity.com/paper/2009.11732/) (2020)
- [SPot-the-Difference Self-Supervised Pre-training for Anomaly Detection and Segmentation](https://mlsanity.com/paper/2207.14315/) (2022)
- [CFLOW-AD: Real-Time Unsupervised Anomaly Detection with Localization via Conditional Normalizing Flows](https://mlsanity.com/paper/2107.12571/) (2021)
- [Deep Semi-Supervised Anomaly Detection](https://mlsanity.com/paper/1906.02694/) (2019)
- [VAE with a VampPrior](https://mlsanity.com/paper/1705.07120/) (2017)
- [FastFlow: Unsupervised Anomaly Detection and Localization via 2D Normalizing Flows](https://mlsanity.com/paper/2111.07677/) (2021)
- [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)
- [Deep Industrial Image Anomaly Detection: A Survey](https://mlsanity.com/paper/2301.11514/) (2023)
- [Deep Learning for Medical Anomaly Detection -- A Survey](https://mlsanity.com/paper/2012.02364/) (2020)
- [DROCC: Deep Robust One-Class Classification](https://mlsanity.com/paper/2002.12718/) (2020)
- [Fully Convolutional Cross-Scale-Flows for Image-based Defect Detection](https://mlsanity.com/paper/2110.02855/) (2021)
- [Anomalib: A Deep Learning Library for Anomaly Detection](https://mlsanity.com/paper/2202.08341/) (2022)
- [Understanding and Mitigating Exploding Inverses in Invertible Neural Networks](https://mlsanity.com/paper/2006.09347/) (2020)
- [Improving Variational Auto-Encoders using Householder Flow](https://mlsanity.com/paper/1611.09630/) (2016)
- [SE(3) Equivariant Augmented Coupling Flows](https://mlsanity.com/paper/2308.10364/) (2023)
- [MaCow: Masked Convolutional Generative Flow](https://mlsanity.com/paper/1902.04208/) (2019)
- [Emerging Convolutions for Generative Normalizing Flows](https://mlsanity.com/paper/1901.11137/) (2019)
- [DASVDD: Deep Autoencoding Support Vector Data Descriptor for Anomaly Detection](https://mlsanity.com/paper/2106.05410/) (2021)
- [Efficient Out-of-Distribution Detection Using Latent Space of β-VAE for Cyber-Physical Systems](https://mlsanity.com/paper/2108.11800/) (2021)
- [On the Universality of Volume-Preserving and Coupling-Based Normalizing Flows](https://mlsanity.com/paper/2402.06578/) (2024)
- [Simple and Effective Prevention of Mode Collapse in Deep One-Class Classification](https://mlsanity.com/paper/2001.08873/) (2020)
- [U-Flow: A U-shaped Normalizing Flow for Anomaly Detection with Unsupervised Threshold](https://mlsanity.com/paper/2211.12353/) (2022)
- [OneFlow: One-class flow for anomaly detection based on a minimal volume region](https://mlsanity.com/paper/2010.03002/) (2020)
- [Jacobian Determinant of Normalizing Flows](https://mlsanity.com/paper/2102.06539/) (2021)
- [LU-Net: Invertible Neural Networks Based on Matrix Factorization](https://mlsanity.com/paper/2302.10524/) (2023)

## Abstract (arXiv)

Unsupervised anomaly detection is often framed around two widely studied paradigms. Deep one-class classification, exemplified by Deep SVDD, learns compact latent representations of normality, while density estimators realized by normalizing flows directly model the likelihood of nominal data. In this work, we show that uniformly scaling flows (USFs), normalizing flows with a constant Jacobian determinant, precisely connect these approaches. Specifically, we prove how training a USF via maximum-likelihood reduces to a Deep SVDD objective with a unique regularization that inherently prevents representational collapse. This theoretical bridge implies that USFs inherit both the density faithfulness of flows and the distance-based reasoning of one-class methods. We further demonstrate that USFs induce a tighter alignment between negative log-likelihood and latent norm than either Deep SVDD or non-USFs, and how recent hybrid approaches combining one-class objectives with VAEs can be naturally extended to USFs. Consequently, we advocate using USFs as a drop-in replacement for non-USFs in modern anomaly detection architectures. Empirically, this substitution yields consistent performance gains and substantially improved training stability across multiple benchmarks and model backbones for both image-level and pixel-level detection. These results unify two major anomaly detection paradigms, advancing both theoretical understanding and practical performance.