TCT-diff: A physics-informed topology-conditioned diffusion framework for trajectory anomaly detection

Vehicle trajectory anomaly detection is a fundamental task within intelligent transportation systems, as it supports urban safety through the identification of reckless driving behaviors and traffic violations. Recently, generative models have emerged as promising solutions, as they alleviate reliance on costly manual annotations. However, existing approaches suffer from an inherent trade-off between noise suppression and behavioral fidelity. Standard diffusion-based baselines typically adopt rigid map-matching preprocessing to mitigate sensor noise, which inevitably smooths out safety-critical micro-kinematic anomalies such as serpentine driving. In contrast, methods that ignore topological constraints tend to generate physically implausible ghost trajectories that violate physical feasibility. To address this challenge, we propose a novel framework referred to as Topology-conditioned Trajectory Diffusion (TCT-Diff). This physics-informed model operates directly in continuous trajectory space without destructive geometric transformations. Specifically, we introduce a topology-aware geometric conditioning mechanism that injects discrete road attributes and continuous geometric features into a global Transformer encoder as probabilistic guidance, enabling the reconstruction of valid traffic behaviors while explicitly respecting road structures. In addition, a gradient-level physics-informed loss is incorporated to penalize kinematic violations, such as unrealistically large acceleration, during the denoising process. Experiments on a large-scale taxi trajectory dataset, conducted under a synthetic anomaly injection protocol, demonstrate that TCT-Diff achieves competitive detection performance, attaining a peak F1 score of 0.941 and an AUC of 0.959. Notably, the proposed method reduces the physical violation rate to a remarkably low 0.32%, representing a 93% reduction compared to the unconstrained diffusion baseline without physics guidance. These results demonstrate the effectiveness of TCT-Diff in capturing fine-grained behavioral anomalies while maintaining rigorous physical and topological consistency.