Kurtosis-Guided Denoising Score Matching for Tabular Anomaly Detection

Denoising models provide a way to learn data distributions from noise-corrupted samples. We show that at a fixed default noise scale, denoising score matching (DSM) provides strong tabular anomaly detection by evaluating the score norm on clean inputs in one forward pass. However, its performance depends on the noise scale: insufficient noise leaves sparse regions poorly represented, while excessive noise blurs local structure. A shared scale also overlooks differences in marginal shape, and tuning this trade-off is difficult without anomaly labels. We introduce kurtosis-guided denoising score matching (K-DSM), which allocates feature-specific noise scales from rearranged marginal histograms of the training data. Rearrangement separates marginal concentration from the locations of modes, while a local coverage analysis motivates assigning larger noise scales to profiles with higher kurtosis. The network trains on the original joint observations and scores clean inputs by the norm of its predicted correction in noise units. On 57 ADBench datasets with normal-only training, K-DSM raises mean AUC-PR from 0.585 to 0.627 and outperforms single-scale DSM at every tested base noise scale. It achieves the highest mean AUC-PR among evaluated baselines, with competitive AUC-ROC, while requiring one forward pass per input compared with fifteen for the strongest AUC-PR baseline. For contaminated training data, an exponential moving average teacher excludes likely anomalies from training updates, raising K-DSM’s mean AUC-PR from 0.189 to 0.343 while preserving one-pass inference.