# Anomaly Detection via Gumbel Noise Score Matching

arXiv: https://arxiv.org/abs/2304.03220 · HTML: https://mlsanity.com/paper/2304.03220/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 47 references that are in the map.
- First posted on arXiv 6 Apr 2023.

## Builds on (most cited first, 24 of 24)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Rethinking Atrous Convolution for Semantic Image Segmentation](https://mlsanity.com/paper/1706.05587/) (2017)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [EfficientNetV2: Smaller Models and Faster Training](https://mlsanity.com/paper/2104.00298/) (2021)
- [Revisiting Deep Learning Models for Tabular Data](https://mlsanity.com/paper/2106.11959/) (2021)
- [PaDiM: a Patch Distribution Modeling Framework for Anomaly Detection and Localization](https://mlsanity.com/paper/2011.08785/) (2020)
- [Argmax Flows and Multinomial Diffusion: Learning Categorical Distributions](https://mlsanity.com/paper/2102.05379/) (2021)
- [A Unifying Review of Deep and Shallow Anomaly Detection](https://mlsanity.com/paper/2009.11732/) (2020)
- [Uninformed Students: Student-Teacher Anomaly Detection with Discriminative Latent Embeddings](https://mlsanity.com/paper/1911.02357/) (2019)
- [Sliced Score Matching: A Scalable Approach to Density and Score Estimation](https://mlsanity.com/paper/1905.07088/) (2019)
- [ADBench: Anomaly Detection Benchmark](https://mlsanity.com/paper/2206.09426/) (2022)
- [PyOD: A Python Toolbox for Scalable Outlier Detection](https://mlsanity.com/paper/1901.01588/) (2019)
- [Score-based Continuous-time Discrete Diffusion Models](https://mlsanity.com/paper/2211.16750/) (2022)
- [Deep Learning for Anomaly Detection: A Review](https://mlsanity.com/paper/2007.02500/) (2020)
- [ECOD: Unsupervised Outlier Detection Using Empirical Cumulative Distribution Functions](https://mlsanity.com/paper/2201.00382/) (2022)
- [A* Sampling](https://mlsanity.com/paper/1411.0030/) (2014)
- [Multiscale Score Matching for Out-of-Distribution Detection](https://mlsanity.com/paper/2010.13132/) (2020)
- [Homophily Outlier Detection in Non-IID Categorical Data](https://mlsanity.com/paper/2103.11516/) (2021)

## Built on by (most cited first, 1 of 1)

- [Gumbel-Softmax Flow Matching with Straight-Through Guidance for Controllable Biological Sequence Generation](https://mlsanity.com/paper/2503.17361/) (2025)

## Abstract (arXiv)

We propose Gumbel Noise Score Matching (GNSM), a novel unsupervised method to detect anomalies in categorical data. GNSM accomplishes this by estimating the scores, i.e. the gradients of log likelihoods w.r.t.~inputs, of continuously relaxed categorical distributions. We test our method on a suite of anomaly detection tabular datasets. GNSM achieves a consistently high performance across all experiments. We further demonstrate the flexibility of GNSM by applying it to image data where the model is tasked to detect poor segmentation predictions. Images ranked anomalous by GNSM show clear segmentation failures, with the outputs of GNSM strongly correlating with segmentation metrics computed on ground-truth. We outline the score matching training objective utilized by GNSM and provide an open-source implementation of our work.