EC-IGM: Explicit Expectation Compensation through Infinitesimal Generator Matching for Drift-Free Trajectory Generation

We propose EC-IGM, a trajectory generation approach via matching the infinitesimal generator of a latent stochastic process with a deterministic kinematic vector field, aiming to address kinematic drift during long-term prediction. Conventional generation methods focus on matching the distribution of generated samples to real data. However, these methods overlook the expectation bias induced by stochastic noise during nonlinear mapping, which causes the generated trajectories to progressively deviate from actual vehicle kinematics over extended prediction horizons. In contrast, our EC-IGM leverages the infinitesimal generator to explicitly compensate for the expectation bias induced by stochastic noise in nonlinear mapping, thereby aligning the expected evolution of the latent stochastic process with the deterministic kinematic vector field. This alignment ensures consistency between the generated trajectories and actual vehicle kinematics during long-term prediction. Furthermore, to circumvent the extreme local curvature introduced by modeling non-linear mappings, we decouple kinematic uncertainty from multimodal behavioral intentions by transforming the complex joint distribution into an independent modeling of stochastic kinematic noise, achieving sampling-free stochastic kinematic evolution with $\mathcal{O}(K{L}^3)$ computational complexity. Compared with state-of-the-art approaches, the EC-IGM achieves a kinematic compliance score of 98.9 during long-term prediction, representing a 12% improvement. Extensive experiments on the NAVSIM and Bench2Drive benchmarks demonstrate that our approach achieves state-of-the-art performance, setting new records with 93.2 PDMS and 92.28 DrivingScore, while significantly outperforming existing methods in maintaining kinematic consistency during long-term prediction.