Anomaly Detection for Sparse and Irregular Multivariate Time Series with Latent SDEs

Existing Multivariate Time Series Anomaly Detection (MTSAD) frameworks increasingly rely on integrating Graph Neural Networks (GNNs) with sequence models to capture complex spatio-temporal dependencies. However, less attention is paid to the spatial over-generalization problem, where unconstrained structural modeling indiscriminately reconstructs anomalies, inevitably degrading detection recall. To tackle this problem, we propose a novel framework that unifies spatio-temporal modeling through a joint prior-observation adversarial learning paradigm. In the spatial dimension, the model alternately learns adjacency matrices as structural prior and models the association discrepancy between prior and data-driven observation in a minimax manner during training. Such adversarial optimization not only improves the model sensitivity for time-wise detection, but also enables the model to localize anomalies to specific channels. To systematically evaluate this anomaly localization capability, we further construct a synthetic benchmark equipped with precise channel-wise annotations. Extensive experiments across public datasets and our dedicated benchmark demonstrate that the proposed framework establishes a new state-of-the-art in both time-wise detection and spatial localization tasks. Our code, pre-trained models, and benchmark are publicly available at https://github.com/anocodetest1/POST.

Anomaly detection in multivariate time series (MTS) is hindered by dynamic inter-variable dependencies and feature entanglement under spectral noise, and in practice, is further complicated by the absence of anomaly labels. Existing reconstruction-based detectors tend to recover anomalies as faithfully as normal patterns, while prevailing graph contrastive methods enforce invariance across views and thus assume a stationary relational structure, an assumption that breaks under structural drift in real systems. We propose ContrastAD, an unsupervised framework that turns structural evolution itself into a learning signal rather than suppressing it. A Multi-Perspective Embedder encodes inputs from temporal, attribute, and structural perspectives. A Frequency-Aware Attention Mixer then performs spectral top-K filtering before attention, preventing noise from leaking into query-key similarities. The core component, a Dynamic Graph Contrastive Learner, builds power-law-inspired sparse graph snapshots from batch-level DTW distances and contrasts the most divergent pair against a stable anchor, regularizing the latent space without imposing rigid invariance. Across five real-world benchmarks, ContrastAD attains the highest mean F1 on all five datasets and the highest AUC on three (SWaT 93.60, SMD 98.66, PSM 97.79), with statistically significant F1 and AUC margins over the strongest baseline on SWaT and PSM. On MSL and SMAP, it trails the AUC leader by under 0.7 points while still leading on F1. Ablation and sensitivity studies further confirm that the contrastive objective works best as a soft regularizer, supporting our claim that strict invariance is suboptimal under non-stationary dynamics.

The core challenge in unsupervised anomaly detection is identifying abnormal patterns without prior knowledge of their characteristics. While existing methods have addressed aspects of this problem, they often struggle to learn a robust representation of the normal data distribution that is distinct from anomalous patterns. In this paper, we present a novel framework, Unified Unsupervised Anomaly Detection ($\text{U}^2\text{AD}$), that comprehensively addresses anomaly detection in multivariate time series. Our approach learns the underlying data distribution of normal samples by utilizing score-based generative modeling. We introduce a novel time-dependent score network and a unified training objective that together delineate the manifold of normal data while considering both local and global temporal contexts. Reconstruction is then performed via a deterministic sampling process using an ordinary differential equation solver. Our extensive experimental evaluations demonstrate that $\text{U}^2\text{AD}$ not only outperforms current state-of-the-art methods in detection accuracy but also identifies anomalies at significantly earlier stages of their occurrence.