Anomaly-Related Residual Fields for Cross-domain Anomaly Detection

Label-free image anomaly detection is difficult because anomalies must be separated from intra-normal variability. Diffusion models learn a manifold for normal data, and, under the common assumption that off-manifold anomalies are harder to generate and yield larger prediction errors, many methods build detectors from prediction residuals; yet reverse-process stochasticity and complex but normal structure also produce large residuals, so magnitude alone is non-diagnostic. To clarify what is recoverable from such noisy residuals, the theory examines how residual signals propagate through later reverse steps, showing that variability consistent with normal statistics is gradually absorbed toward stationarity, whereas anomalous regions retain an additional non-stationary signal that persists. Building on this insight, the Residual-Evolution Field (REF) isolates this persistent signal, with labeled source data calibrating the extractor and Cross-domain Field Alignment (CFA) transferring it to unlabeled targets. A theoretical framework with formal analysis is established, and experiments across multiple benchmarks under substantial domain shifts demonstrate state-of-the-art performance, improving over strong baselines by 2.01-14 percentage points (pp).