Analytic Bayesian Uncertainty for LiDAR Segmentation: A Single-pass Generative Approach

Accurate predictions with well-calibrated uncertainties are vital for safety-critical LiDAR scene understanding in autonomous driving and robotics. While Bayesian Neural Networks and deep ensembles are effective, they are computationally expensive, requiring multiple forward passes or independently trained models. We propose GMM-NIG, a Bayesian generative classification head that extends the GMMSeg framework by placing conjugate Normal-Inverse-Gamma (NIG) priors over class-conditional GMM parameters to obtain posterior-predictive uncertainty. While the backbone remains deterministic, GMM-NIG enables analytic closed-form posterior updates in a single training run. In inference, GMM-NIG yields a mixture of Student-t distributions, providing wellcalibrated predictive uncertainty without extra computational overhead. On SemanticKITTI and nuScenes, GMM-NIG achieves state-of-the-art calibration with an Adaptive Calibration Error of 2.01%, outperforming deep ensembles, Monte Carlo Dropout, evidential models and post-hoc calibration methods. Beyond calibration, it increases segmentation mIoU by nearly 6% and yields the strongest failure detection performance.