# Temporal-Conditioned Normalizing Flows for Multivariate Time Series Anomaly Detection

arXiv: https://arxiv.org/abs/2603.09490 · HTML: https://mlsanity.com/paper/2603.09490/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 41 references that are in the map.
- First posted on arXiv 10 Mar 2026.

## Builds on (most cited first, 14 of 14)

- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [WaveGlow: A Flow-based Generative Network for Speech Synthesis](https://mlsanity.com/paper/1811.00002/) (2018)
- [Graph Neural Network-Based Anomaly Detection in Multivariate Time Series](https://mlsanity.com/paper/2106.06947/) (2021)
- [Multivariate Probabilistic Time Series Forecasting via Conditioned Normalizing Flows](https://mlsanity.com/paper/2002.06103/) (2020)
- [Deep Learning for Time Series Anomaly Detection: A Survey](https://mlsanity.com/paper/2211.05244/) (2022)
- [Lag-Llama: Towards Foundation Models for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2310.08278/) (2023)
- [Graph-Augmented Normalizing Flows for Anomaly Detection of Multiple Time Series](https://mlsanity.com/paper/2202.07857/) (2022)
- [Multivariate Industrial Time Series with Cyber-Attack Simulation: Fault Detection Using an LSTM-based Predictive Data Model](https://mlsanity.com/paper/1612.06676/) (2016)
- [Navigating the Metric Maze: A Taxonomy of Evaluation Metrics for Anomaly Detection in Time Series](https://mlsanity.com/paper/2303.01272/) (2023)
- [Neural Density Estimation and Likelihood-free Inference](https://mlsanity.com/paper/1910.13233/) (2019)
- [Label-Free Multivariate Time Series Anomaly Detection](https://mlsanity.com/paper/2312.11549/) (2023)
- [The voraus-AD Dataset for Anomaly Detection in Robot Applications](https://mlsanity.com/paper/2311.04765/) (2023)
- [Adaptive Anomaly Detection in Chaotic Time Series with a Spatially Aware Echo State Network](https://mlsanity.com/paper/1909.01709/) (2019)

## Abstract (arXiv)

This paper introduces temporal-conditioned normalizing flows (tcNF), a novel framework that addresses anomaly detection in time series data with accurate modeling of temporal dependencies and uncertainty. By conditioning normalizing flows on previous observations, tcNF effectively captures complex temporal dynamics and generates accurate probability distributions of expected behavior. This autoregressive approach enables robust anomaly detection by identifying low-probability events within the learned distribution. We evaluate tcNF on diverse datasets, demonstrating good accuracy and robustness compared to existing methods. A comprehensive analysis of strengths and limitations and open-source code is provided to facilitate reproducibility and future research.