# Quantum Normalizing Flows for Anomaly Detection

arXiv: https://arxiv.org/abs/2402.02866 · HTML: https://mlsanity.com/paper/2402.02866/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 68 references that are in the map.
- First posted on arXiv 5 Feb 2024.

## Builds on (most cited first, 15 of 15)

- [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)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [Deep Semi-Supervised Anomaly Detection](https://mlsanity.com/paper/1906.02694/) (2019)
- [SNAS: Stochastic Neural Architecture Search](https://mlsanity.com/paper/1812.09926/) (2018)
- [Same Same But DifferNet: Semi-Supervised Defect Detection with Normalizing Flows](https://mlsanity.com/paper/2008.12577/) (2020)
- [Probabilistic Monocular 3D Human Pose Estimation with Normalizing Flows](https://mlsanity.com/paper/2107.13788/) (2021)
- [Quantum-Inspired Support Vector Machine](https://mlsanity.com/paper/1906.08902/) (2019)
- [Anomaly Detection in High Dimensional Data](https://mlsanity.com/paper/1908.04000/) (2019)
- [Quantum Circuit Evolution on NISQ Devices](https://mlsanity.com/paper/2012.13453/) (2020)
- [The voraus-AD Dataset for Anomaly Detection in Robot Applications](https://mlsanity.com/paper/2311.04765/) (2023)
- [Exact Identification of a Quantum Change Point](https://mlsanity.com/paper/1707.07769/) (2017)

## Built on by (most cited first, 5 of 5)

- [SplatPose & Detect: Pose-Agnostic 3D Anomaly Detection](https://mlsanity.com/paper/2404.06832/) (2024)
- [Anomaly Detection in Dynamic Graphs: A Comprehensive Survey](https://mlsanity.com/paper/2406.00134/) (2024)
- [Robust Fitting on a Gate Quantum Computer](https://mlsanity.com/paper/2409.02006/) (2024)
- [Multi-Flow: Multi-View-Enriched Normalizing Flows for Industrial Anomaly Detection](https://mlsanity.com/paper/2504.03306/) (2025)
- [Complex normalizing flows can almost be information K"ahler-Ricci flows](https://mlsanity.com/paper/2604.17954/) (2026)

## Abstract (arXiv)

A Normalizing Flow computes a bijective mapping from an arbitrary distribution to a predefined (e.g. normal) distribution. Such a flow can be used to address different tasks, e.g. anomaly detection, once such a mapping has been learned. In this work we introduce Normalizing Flows for Quantum architectures, describe how to model and optimize such a flow and evaluate our method on example datasets. Our proposed models show competitive performance for anomaly detection compared to classical methods, esp. those ones where there are already quantum inspired algorithms available. In the experiments we compare our performance to isolation forests (IF), the local outlier factor (LOF) or single-class SVMs.