# Kurtosis-Guided Denoising Score Matching for Tabular Anomaly Detection

arXiv: https://arxiv.org/abs/2605.06955 · HTML: https://mlsanity.com/paper/2605.06955/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 54 references that are in the map.
- First posted on arXiv 7 May 2026.

## Builds on (most cited first, 23 of 23)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Temporal Ensembling for Semi-Supervised Learning](https://mlsanity.com/paper/1610.02242/) (2016)
- [Revisiting Deep Learning Models for Tabular Data](https://mlsanity.com/paper/2106.11959/) (2021)
- [SPot-the-Difference Self-Supervised Pre-training for Anomaly Detection and Segmentation](https://mlsanity.com/paper/2207.14315/) (2022)
- [ADBench: Anomaly Detection Benchmark](https://mlsanity.com/paper/2206.09426/) (2022)
- [Classification-Based Anomaly Detection for General Data](https://mlsanity.com/paper/2005.02359/) (2020)
- [ECOD: Unsupervised Outlier Detection Using Empirical Cumulative Distribution Functions](https://mlsanity.com/paper/2201.00382/) (2022)
- [COPOD: Copula-Based Outlier Detection](https://mlsanity.com/paper/2009.09463/) (2020)
- [Neural Transformation Learning for Deep Anomaly Detection Beyond Images](https://mlsanity.com/paper/2103.16440/) (2021)
- [On Diffusion Modeling for Anomaly Detection](https://mlsanity.com/paper/2305.18593/) (2023)
- [A Closer Look at AUROC and AUPRC under Class Imbalance](https://mlsanity.com/paper/2401.06091/) (2024)
- [A Survey on Explainable Anomaly Detection](https://mlsanity.com/paper/2210.06959/) (2022)
- [Multiscale Score Matching for Out-of-Distribution Detection](https://mlsanity.com/paper/2010.13132/) (2020)
- [Fascinating Supervisory Signals and Where to Find Them: Deep Anomaly Detection with Scale Learning](https://mlsanity.com/paper/2305.16114/) (2023)
- [Minimum Covariance Determinant and Extensions](https://mlsanity.com/paper/1709.07045/) (2017)
- [AutoAudit: Mining Accounting and Time-Evolving Graphs](https://mlsanity.com/paper/2011.00447/) (2020)
- [Semi-supervised Rare Disease Detection Using Generative Adversarial Network](https://mlsanity.com/paper/1812.00547/) (2018)
- [Diffusion-Scheduled Denoising Autoencoders for Anomaly Detection in Tabular Data](https://mlsanity.com/paper/2508.00758/) (2025)
- [Fault Detection of Broken Rotor Bar in LS-PMSM Using Random Forests](https://mlsanity.com/paper/1711.02510/) (2017)

## Abstract (arXiv)

Denoising score matching (DSM) provides a way to learn data distributions by training a neural network to recover the score function, defined as the gradient of the log density, from noise-corrupted samples. Once trained, the score magnitude at a test point reflects how consistent that point is with the learned distribution, making it a natural anomaly signal. The key practical challenge is selecting the perturbation scale: too little noise yields unstable score estimates in sparse regions, while too much erases local structure and weakens anomaly sensitivity. This is compounded by the difficulty of hyperparameter tuning when anomalies are unknown and no validation set is available. We introduce kurtosis-based noise scaling (K-DSM), a per-feature scheme that sets noise levels from the shape of each marginal distribution, improving coverage of low-density regions and precision in high-density regions without extra model complexity. Contrary to prior claims that multi-scale or noise-conditioned training is necessary, we find that a carefully trained single-scale model is already a strong anomaly detector. On standard tabular anomaly detection benchmarks, K-DSM achieves state-of-the-art performance in the semi-supervised setting. When combined with a lightweight EMA-teacher filtering rule that removes low-density training points before each gradient step, it also achieves strong performance in the fully unsupervised (contaminated) setting, suggesting that simple, data-adaptive noise scaling enables robust anomaly detection while reducing reliance on hyperparameter tuning.