Contextual anomaly detection in tabular data aims to identify objects whose behavior is unexpected under their contextual conditions. In data-engineering pipelines, this task screens table rows whose measurements violate context-dependent integrity relationships. Most existing approaches rely on either shallow conditional models with limited distributional expressiveness or localized estimators that require per-context modeling, making it difficult to capture complex conditional relationships and scale to high-dimensional settings. We propose Flow-CAD, a new framework for contextual anomaly detection based on Flow Matching. Flow-CAD learns a single global and amortized conditional generative model that flexibly represents behavioral distributions conditioned on context, without assuming simple parametric forms or retraining local models. To enable robust and interpretable anomaly scoring, we introduce a scale-normalized and truncated residual energy derived from the learned conditional flow, which stabilizes anomaly scores, mitigates domination by extreme deviations, and supports feature-wise attribution. We further provide theoretical insights showing that the proposed residual-based anomaly score is stable under velocity estimation error, and that its Monte Carlo estimator satisfies concentration bounds. Experiments on 20 benchmark datasets with 13 competitors demonstrate that Flow-CAD has the best average rank for PR AUC, ROC AUC, and P@n, highlighting its effectiveness and practicality for contextual anomaly detection in tabular data. We provide the source code at https://github.com/ZhongLIFR/FlowCAD.

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