SPDD: Guided Progressive Distillation for Fast and Safe Diffusion-Based Planning

Diffusion models have shown strong performance in trajectory planning, but their iterative denoising process introduces considerable inference latency, which limits their deployment in real-time and resource-constrained settings. In this work, we propose safe progressive diffusion distillation (SPDD), a framework for accelerating diffusion-based planning while preserving teacher consistency and trajectory safety. SPDD introduces a quadratic program-based guidance mechanism that integrates prescribed-time control Lyapunov function (CLF) and control barrier function (CBF) into the denoising process. The CLF guides the student denoising process toward the teacher output, whereas the CBF is prioritized to enforce the desired safety constraints. We theoretically characterize the consistency and safety properties of the guided denoising process. To mitigate discretization errors caused by aggressive step reduction, SPDD progressively reduces the sampling horizon during distillation. Experiments on multiple trajectory planning tasks demonstrate that SPDD achieves competitive inference efficiency while maintaining low teacher–student discrepancy and improved safety compared with existing diffusion-based planning baselines.