Ldm-Phys: a Lightweight Physics-Constrained Diffusion Model for Anomaly Detection in Safety-Critical Cyber-Physical Systems

The reliable operation of Cyber-Physical Systems depends on efficient and interpretable time series anomaly detection techniques. Although existing methods based on diffusion models can capture complex time series patterns, their multi-step iterative denoising mechanism leads to insufficient real-time performance. Moreover, the generated data often violates physical laws, which restricts their application in safety-critical scenarios. To address this issue, we propose the LDM-Phys model, an anomaly detection method that integrates a lightweight single-step diffusion architecture with physical constraints to achieve efficient and interpretable anomaly detection. Experiments on crossdomain datasets demonstrate that LDM-Phys excels in multiple aspects. In detection performance, its average F1 score is <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$91.7 \%, 3.7 \%$</tex> higher than the latest baseline model, and the average false positive rate is only 1.7 %, a 51.1 % drop compared to it. Regarding real-time performance, LDMPhys's inference speed is 5.2 times faster than the latest baseline, fulfilling CPS's millisecond-level response needs. In physical rationality, the residuals between LDM-Physgenerated data and physical equations are, on average, 72.0 % lower than similar models, offering interpretability for anomaly localization.