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Scalable, Explainable and Provably Robust Anomaly Detection with One-Step Flow Matching
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Proposes TCCM, a flow-matching-inspired semi-supervised tabular anomaly detector that learns a time-conditioned contraction velocity field toward the origin and scores anomalies with a single forward pass.
Problem
Semi-supervised anomaly detection in tabular data needs accurate, scalable, and explainable detectors, but existing deep methods (diffusion-based DTE, GANs, graph-based LUNAR) are slow, unstable, or opaque.
Approach
Instead of integrating a flow trajectory, directly regress a time-conditioned contraction vector pointing from each normal sample to the origin with a least-squares loss; score test points by the residual norm at a fixed time (default t=1) in one forward pass, making per-feature residuals directly attributable.
Key results
- TCCM ranks first on average (average rank 5.8 for AUPRC, 5.7 for AUROC) across 47 ADBench datasets versus 44 baselines, with DTE-NonParametric second and LUNAR third.
- TCCM inference is reported as 1,573.39x faster than DTE-NonParametric and 85.91x faster than LUNAR on average.
- On the census dataset (299,285 x 500), TCCM takes 1.50 s of inference versus 48,942 s for DTE-NonParametric.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use TCCM instead of DTE-NonParametric | ADBench · ADBench, average across datasets | inference speed: 1,573.39× faster | Helped |
| use TCCM instead of KDE | ADBench · ADBench, average across datasets | inference speed: 4,864.76× faster | Helped |
| use TCCM instead of LUNAR | ADBench · ADBench, average across datasets | inference speed: 85.91× faster | Helped |
| use TCCM instead of DTE-NonParametric, KDE, or LUNAR | ADBench · ADBench, average across datasets | total runtime: 79.49×, 311.95×, and 50.89× | Helped |
| vary the time embedding or inference time (ablation) | TCCM · ADBench | anomaly detection accuracy | No clear effect |
| add noise injection during training (ablation) | TCCM · ADBench | anomaly detection accuracy | Hurt |
| increase the anomaly ratio in training data (ablation) | TCCM · ADBench | anomaly detection accuracy | Hurt |
| add z-score feature normalization (ablation) | TCCM · ADBench | anomaly detection accuracy | Helped |
| use time-interpolated inputs (ablation) | TCCM · ADBench | anomaly detection accuracy | No clear effect |
| replace the time-conditioned velocity field with an autoencoder plus time embedding (ablation) | TCCM · ADBench | anomaly detection accuracy | Mixed |
Surprising findings
- DTE-NonParametric trains about 16x faster than TCCM (training time 0.06x of TCCM), so TCCM is not fastest in training.
Limitations
- Training is slower than DTE-NonParametric (0.06x its training speed).
- Lipschitz guarantee depends on an assumed bound L on the network, which is not enforced by default and is only stated as controllable via spectral normalization.
- Theoretical discriminative result relies on idealized Gaussian mixture assumptions that real tabular data may not satisfy.
Experimental setup
Datasets: ADBench (47 datasets, normal-only training split) MNIST (explainability case study)
Benchmarks: ADBench
Metrics: AUROC AUPRC training time inference time
Baselines: DTE-NonParametric LUNAR KDE DeepSVDD AnoGAN GANomaly DAGMM OneFlow Anomaly-DDPM OCSVM
Builds on: flow matching rectified flow DTE Deep SVDD
Closest papers by meaning
- On Diffusion Modeling for Anomaly Detection (ICLR 2024 · similarity 0.86)
- One-for-More: Continual Diffusion Model for Anomaly Detection (CVPR 2025 · similarity 0.86)
- The Elephant in the Room: Towards A Reliable Time-Series Anomaly Detection Benchmark (NeurIPS 2024 · similarity 0.85)
- OmiAD: One-Step Adaptive Masked Diffusion Model for Multi-class Anomaly Detection via Adversarial Distillation (ICML 2025 · similarity 0.85)
- Fortifying Time Series: DTW-Certified Robust Anomaly Detection (NeurIPS 2025 · similarity 0.85)
- SDFlow: Similarity-Driven Flow Matching for Time Series Generation (NeurIPS 2026 · similarity 0.85)
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