GE-Div: A Gaussian Entropy-Based Metric for Trajectory Prediction Diversity Assessment

The safety and robustness of autonomous driving systems critically depend on diverse scenario coverage, especially for rare but safety-critical corner cases that are difficult to capture with finite real-world data. Trajectory prediction models provide a means to augment test scenarios, however, conventional evaluation primarily focuses on accuracy while overlooking whether the generated results sufficiently cover diverse behaviors. This paper proposes Gaussian Entropy-based Diversity(GE-Div), a novel metric that quantifies the structural diversity of predicted trajectories from an information-theoretic perspective, based on Gaussian entropy. GE-Div vectorizes trajectories, applies Principal Component Analysis(PCA) to extract dominant variation modes, and computes the differential entropy of the fitted Gaussian distribution, yielding an interpretable measure of how broadly a model explores plausible futures. Experiments demonstrate that GE-Div complements accuracy metrics by revealing structural variations and helping identify local mode collapse, ultimately supporting scenario generation that better captures long-tail behaviors and corner cases critical for safe autonomous driving.