KRAFT: Koopman-Referenced Adaptive Flow for Time-Series Anomaly Detection under Latent Domain Shifts

Time-series anomaly detection (TSAD) in real-world systems is challenged by evolving normal behavior, where distribution shifts can be misidentified as anomalies. Existing drift-aware, domain adaptation, and test-time adaptation methods often require explicit domain information or risk anomaly contamination during adaptation. We study TSAD under latent domain shifts, where anomaly labels, domain labels, and shift boundaries are unavailable during deployment. We propose KRAFT, a Koopman-Referenced Adaptive Flow framework that models predictable normal evolution through Koopman latent propagation and constructs a dynamics-conditioned normal reference via conditional flow matching. A Koopman-pushed maximum mean discrepancy (KP-MMD) identifies residual mismatch beyond modeled evolution, while validation-guided restricted adapter updates accommodate latent shifts without absorbing anomalies. Theoretical analysis establishes conditions for residual shift detection and preservation of anomaly separability during adaptation. Experiments on diverse TSAD benchmarks, drift datasets, and multi-domain scenarios demonstrate that KRAFT effectively adapts to evolving normal behavior while maintaining anomaly detection capability.