# Flow-based Self-supervised Density Estimation for Anomalous Sound Detection

arXiv: https://arxiv.org/abs/2103.08801 · HTML: https://mlsanity.com/paper/2103.08801/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 23 references that are in the map.
- First posted on arXiv 16 Mar 2021.

## Builds on (most cited first, 16 of 16)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Deep Anomaly Detection with Outlier Exposure](https://mlsanity.com/paper/1812.04606/) (2018)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [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)
- [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 and Mitigating Exploding Inverses in Invertible Neural Networks](https://mlsanity.com/paper/2006.09347/) (2020)
- [Description and Discussion on DCASE2020 Challenge Task2: Unsupervised Anomalous Sound Detection for Machine Condition Monitoring](https://mlsanity.com/paper/2006.05822/) (2020)
- [Anomalous sound detection based on interpolation deep neural network](https://mlsanity.com/paper/2005.09234/) (2020)
- [Anomaly Detection in Trajectory Data with Normalizing Flows](https://mlsanity.com/paper/2004.05958/) (2020)
- [AdaFlow: Domain-Adaptive Density Estimator with Application to Anomaly Detection and Unpaired Cross-Domain Translation](https://mlsanity.com/paper/1812.05796/) (2018)
- [Normalizing flows for novelty detection in industrial time series data](https://mlsanity.com/paper/1906.06904/) (2019)

## Built on by (most cited first, 15 of 15)

- [MIMII DG: Sound Dataset for Malfunctioning Industrial Machine Investigation and Inspection for Domain Generalization Task](https://mlsanity.com/paper/2205.13879/) (2022)
- [Description and Discussion on DCASE 2021 Challenge Task 2: Unsupervised Anomalous Sound Detection for Machine Condition Monitoring under Domain Shifted Conditions](https://mlsanity.com/paper/2106.04492/) (2021)
- [Self-Supervised Learning for Anomalous Sound Detection](https://mlsanity.com/paper/2312.09578/) (2023)
- [Anomalous Sound Detection using Audio Representation with Machine ID based Contrastive Learning Pretraining](https://mlsanity.com/paper/2304.03588/) (2023)
- [Why do Angular Margin Losses work well for Semi-Supervised Anomalous Sound Detection?](https://mlsanity.com/paper/2309.15643/) (2023)
- [Noisy-ArcMix: Additive Noisy Angular Margin Loss Combined With Mixup Anomalous Sound Detection](https://mlsanity.com/paper/2310.06364/) (2023)
- [Image-based Freeform Handwriting Authentication with Energy-oriented Self-Supervised Learning](https://mlsanity.com/paper/2408.09676/) (2024)
- [ASD-Diffusion: Anomalous Sound Detection with Diffusion Models](https://mlsanity.com/paper/2409.15957/) (2024)
- [Anomalous Sound Detection Based on Machine Activity Detection](https://mlsanity.com/paper/2204.07353/) (2022)
- [CSSL-RHA: Contrastive Self-Supervised Learning for Robust Handwriting Authentication](https://mlsanity.com/paper/2307.11100/) (2023)
- [CoopASD: Cooperative Machine Anomalous Sound Detection with Privacy Concerns](https://mlsanity.com/paper/2408.14753/) (2024)
- [Distributed collaborative anomalous sound detection by embedding sharing](https://mlsanity.com/paper/2403.16610/) (2024)
- [ESTM: An Enhanced Dual-Branch Spectral-Temporal Mamba for Anomalous Sound Detection](https://mlsanity.com/paper/2509.02471/) (2025)
- [Noise Supervised Contrastive Learning and Feature-Perturbed for Anomalous Sound Detection](https://mlsanity.com/paper/2509.13853/) (2025)
- [Sub-Band Spectral Matching with Localized Score Aggregation for Robust Anomalous Sound Detection](https://mlsanity.com/paper/2603.13749/) (2026)

## Abstract (arXiv)

To develop a machine sound monitoring system, a method for detecting anomalous sound is proposed. Exact likelihood estimation using Normalizing Flows is a promising technique for unsupervised anomaly detection, but it can fail at out-of-distribution detection since the likelihood is affected by the smoothness of the data. To improve the detection performance, we train the model to assign higher likelihood to target machine sounds and lower likelihood to sounds from other machines of the same machine type. We demonstrate that this enables the model to incorporate a self-supervised classification-based approach. Experiments conducted using the DCASE 2020 Challenge Task2 dataset showed that the proposed method improves the AUC by 4.6% on average when using Masked Autoregressive Flow (MAF) and by 5.8% when using Glow, which is a significant improvement over the previous method.