Conditional Flow Matching for Continuous Anomaly Detection in Autonomous Driving on a Manifold-Aware Spectral Space

Antonio Guillen-Perez

cs.ROFeb 19, 2026

Conditional Flow Matching for Continuous Anomaly Detection in Autonomous Driving on a Manifold-Aware Spectral Space

Authors: Antonio Guillen-Perez

Organizations: Independent Researcher

Abstract

Safety validation for Level 4 autonomous vehicles (AVs) is currently bottlenecked by the inability to scale the detection of rare, high-risk long-tail scenarios using traditional rule-based heuristics. We present Deep-Flow, an unsupervised framework for safety-critical anomaly detection that utilizes Optimal Transport Conditional Flow Matching (OT-CFM) to characterize the continuous probability density of expert human driving behavior. Unlike standard generative approaches that operate in unstable, high-dimensional coordinate spaces, Deep-Flow constrains the generative process to a low-rank spectral manifold via a Principal Component Analysis (PCA) bottleneck. This ensures kinematic smoothness by design and enables the computation of the exact Jacobian trace for numerically stable, deterministic log-likelihood estimation. To resolve multi-modal ambiguity at complex junctions, we utilize an Early Fusion Transformer encoder with lane-aware goal conditioning, featuring a direct skip-connection to the flow head to maintain intent-integrity throughout the network. We introduce a kinematic complexity weighting scheme that prioritizes high-energy maneuvers (quantified via path tortuosity and jerk) during the simulation-free training process. Evaluated on the Waymo Open Motion Dataset (WOMD), our framework achieves an AUC-ROC of 0.766 against a heuristic golden set of safety-critical events. More significantly, our analysis reveals a fundamental distinction between kinematic danger and semantic non-compliance. Deep-Flow identifies a critical predictability gap by surfacing out-of-distribution behaviors, such as lane-boundary violations and non-normative junction maneuvers, that traditional safety filters overlook. This work provides a mathematically rigorous foundation for defining statistical safety gates, enabling objective, data-driven validation for the safe deployment of autonomous fleets.

Figures & tables

Figure 1: Overview of the Deep-Flow Framework. (Left) We observe an agent’s trajectory within a goal-conditioned context. While both safe (Blue) and anomalous (Orange) maneuvers may reach the same goal, they represent different densities on the driving manifold. (Center) Trajectories are projected into a low-rank spectral manifold where backward ODE integration (

t=1\to 0

) maps maneuvers to a Gaussian prior. (Right) Deep-Flow identifies safety-critical anomalies by mapping non-normative behaviors to the low-probability tails of the expert distribution, providing a continuous and mathematically rigorous safety score.

Figure 2: Deep-Flow Encoder Architecture. Heterogeneous modalities are tokenized and fused via a Hierarchical Transformer. The Goal signal is injected twice: once in the global context and once as a direct skip-connection to the Flow Head to preserve intent-integrity.

Method	Modality	AUC-ROC
Random Guessing	N/A	0.500
Kinematic Heuristic (Hard Brake)	Discriminative	0.682
Deep-Flow (Ours)	Generative (Holistic)	0.766

Table 1: Anomaly Detection Performance on WOMD Validation Set.

Panel of Figure 5 — Figure 5: Latent Flow Dynamics and Physical Grounding. (a) In the spectral latent space, nominal trajectories align with the vector field to reach high-density regions, while anomalies “fight” the flow. (b) Deep-Flow identifies semantic violations: the anomalous scenario shows the actual path (Red) deviating from the learned expert manifold (Cyan), signifying an OOD event.

Panel of Figure 6 — Figure 6: Deep-Flow Discovery Engine: Top-5 Semantic Anomalies. A gallery of scenarios with the lowest log-likelihood scores in the validation set. These events highlight systematic deviations from the learned expert manifold, including sharp lane-line violations, corner-cutting at complex junctions, and OOD maneuvers that do not trigger standard kinematic safety rules.

Appendix figures & tables5 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 7: Manifold Traversal of the 12 Principal Components. Each panel illustrates the geometric influence of a specific spectral coefficient on the 8-second trajectory. Colors represent standard deviations from the mean expert maneuver. PC1 and PC2 define the vehicle’s reachability set , while PC3 and PC4 modulate lateral/phase transitions. Higher-order components (PC5–PC12) represent residual harmonics required for geometric fine-tuning in non-linear topologies.

Integration Steps ( $N$ )	Mean Log-Likelihood	Variance in $\mathcal{A}$	Latency (ms/sample)
5	42.15	4.21	12
10	53.82	1.15	22
20	55.41	0.08	41
50	55.45	0.02	98

Appendix

Table 2: Likelihood Stability vs. ODE Integration Steps.

Figure 8: Generative Robustness Gallery (1/3). A random selection of validation scenarios. The model (Cyan bundles) demonstrates consistent lane adherence and goal convergence across various driving contexts, verifying that the learned vector field generalizes well beyond the training distribution.

Figure 9: Generative Robustness Gallery (2/3). Additional randomly sampled validation scenarios highlighting stable trajectory generation under diverse road geometries and motion patterns.

Figure 10: Generative Robustness Gallery (3/3). Further examples illustrating consistent goal convergence and smooth trajectory manifolds across complex dynamic scenes.

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