Selective Denoising Diffusion Model for Time Series Anomaly Detection

Diffusion models have recently shown strong potential for multivariate time-series anomaly detection by learning the distribution of normal data through iterative denoising. Existing diffusion-based approaches, however, typically perform anomaly detection after completing the reverse diffusion process, relying primarily on the final reconstructed signal and overlooking informative representations produced during denoising. This design incurs substantial computational cost and limits the use of intermediate diffusion information for anomaly detection. In this paper, we propose FirstDiff, a diffusion-based anomaly detection framework based on the observation that the predicted diffusion noise at the initial reverse-diffusion evaluation already contains sufficient information for accurate anomaly detection. FirstDiff models the statistical distribution of predicted diffusion noise under normal behavior using validation data, enabling anomaly inference from a single denoising-network evaluation rather than completing the reverse diffusion trajectory. To model complex temporal and inter-sensor dependencies, FirstDiff employs a Diffusion Transformer as the denoising backbone. Extensive experiments on five public benchmark datasets demonstrate that FirstDiff achieves state-of-the-art performance while reducing diffusion inference from the full reverse trajectory to a single denoising-network evaluation.

Reconstruction-based methods are a dominant paradigm in time series anomaly detection (TSAD), however, their near-universal reliance on Mean Squared Error (MSE) loss results in statistically flawed reconstruction residuals. This fundamental weakness leads to noisy, unstable anomaly scores, hindering reliable detection. To address this, we propose Constrained Gaussian-Noise Optimization and Smoothing (COGNOS), a universal, model-agnostic enhancement framework that tackles this issue at its source. COGNOS introduces a novel Gaussian-White Noise Regularization strategy during training, which directly constrains the model's output residuals to conform to a Gaussian white noise distribution. This engineered statistical property creates the ideal precondition for our second contribution: Adaptive Residual Kalman Smoother that operates as a statistically robust estimator to denoise the raw anomaly scores. Extensive experiments on multiple benchmarks demonstrate that COGNOS consistently enhances the performance of state-of-the-art backbones significantly, validating the efficacy of coupling statistical regularization with adaptive filtering.

We propose NV-Tesseract-AD, a curriculum learning-enhanced conditional diffusion framework for multivariate time-series anomaly detection. Our central hypothesis is that reconstruction difficulty can be explicitly structured along two complementary axes, masking severity and diffusion noise level, and that training from easier to harder tasks along both axes simultaneously stabilizes optimization and improves residual discriminability. We integrate a Transformer-based diffusion backbone with a three-stage dual curriculum over masking ratios and diffusion timesteps, retaining anomalous samples throughout training and relying on structured corruption to drive self-supervised representation learning. We evaluate NV-Tesseract-AD under two regimes: in-distribution training on the TSB-UAD-M corpus and strict zero-shot transfer to ten EasyTSAD benchmark families without per-dataset tuning. The dual-axis curriculum produces masking-invariant reconstruction, confirmed by a near-zero loss gap between complementary masking strategies within the first training stage, and yields an approximately 3.7-fold improvement in F1 and a 56 percent reduction in MSE relative to a non-curriculum baseline. Zero-shot performance reaches F1 = 0.984 on NAB and F1 = 0.948 on NormA. Weaker results on heterogeneous families are traced to unsupervised threshold calibration rather than reconstruction quality, identifying calibration as the dominant remaining detection bottleneck. Accelerated inference via DPM-Solver++ reduces sampling cost by a factor of 3.5 to 5.7 at the dataset level but couples to thresholding behavior, establishing that the sampler and threshold must be validated jointly. Together, these findings demonstrate that aligning diffusion denoising difficulty with curriculum learning principles provides a principled and practical approach for robust anomaly detection in complex multivariate time series.