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PC-Diffuser: Path-Consistent Capsule CBF Safety Filtering for Diffusion-Based Trajectory Planner

Eugene Ku, Yiwei Lyu

TL;DR

PC-Diffuser is presented, a safety augmentation framework that embeds a certifiable, path-consistent barrier-function structure directly into the denoising loop of diffusion planning, and enables iterative, context-aware safeguarding instead of post-hoc repair.

Abstract

Autonomous driving in complex traffic requires planners that generalize beyond hand-crafted rules, motivating data-driven approaches that learn behavior from expert demonstrations. Diffusion-based trajectory planners have recently shown strong closed-loop performance by iteratively denoising a full-horizon plan, but they remain difficult to certify and can fail catastrophically in rare or out-of-distribution scenarios. To address this challenge, we present PC-Diffuser, a safety augmentation framework that embeds a certifiable, path-consistent barrier-function structure directly into the denoising loop of diffusion planning. The key idea is to make safety an intrinsic part of trajectory generation rather than a post-hoc fix: we enforce forward invariance along the rollout while preserving the diffusion model's intended path geometry. Specifically, PC-Diffuser (i) evaluates collision risk using a capsule-distance barrier function that better reflects vehicle geometry and reduces unnecessary conservativeness, (ii) converts denoised waypoints into dynamically feasible motion under a kinematic bicycle model, and (iii) applies a path-consistent safety filter that eliminates residual constraint violations without geometric distortion, so the corrected plan remains close to the learned distribution. By injecting these safety-consistent corrections at every denoising step and feeding the refined trajectory back into the diffusion process, PC-Diffuser enables iterative, context-aware safeguarding instead of post-hoc repair...

PC-Diffuser: Path-Consistent Capsule CBF Safety Filtering for Diffusion-Based Trajectory Planner

TL;DR

PC-Diffuser is presented, a safety augmentation framework that embeds a certifiable, path-consistent barrier-function structure directly into the denoising loop of diffusion planning, and enables iterative, context-aware safeguarding instead of post-hoc repair.

Abstract

Autonomous driving in complex traffic requires planners that generalize beyond hand-crafted rules, motivating data-driven approaches that learn behavior from expert demonstrations. Diffusion-based trajectory planners have recently shown strong closed-loop performance by iteratively denoising a full-horizon plan, but they remain difficult to certify and can fail catastrophically in rare or out-of-distribution scenarios. To address this challenge, we present PC-Diffuser, a safety augmentation framework that embeds a certifiable, path-consistent barrier-function structure directly into the denoising loop of diffusion planning. The key idea is to make safety an intrinsic part of trajectory generation rather than a post-hoc fix: we enforce forward invariance along the rollout while preserving the diffusion model's intended path geometry. Specifically, PC-Diffuser (i) evaluates collision risk using a capsule-distance barrier function that better reflects vehicle geometry and reduces unnecessary conservativeness, (ii) converts denoised waypoints into dynamically feasible motion under a kinematic bicycle model, and (iii) applies a path-consistent safety filter that eliminates residual constraint violations without geometric distortion, so the corrected plan remains close to the learned distribution. By injecting these safety-consistent corrections at every denoising step and feeding the refined trajectory back into the diffusion process, PC-Diffuser enables iterative, context-aware safeguarding instead of post-hoc repair...
Paper Structure (19 sections, 3 theorems, 18 equations, 4 figures, 2 tables, 2 algorithms)

This paper contains 19 sections, 3 theorems, 18 equations, 4 figures, 2 tables, 2 algorithms.

Table of Contents

  1. INTRODUCTION
  2. Related Works
  3. Preliminaries
  4. Vehicle Dynamics
  5. Control Barrier Functions
  6. Diffusion-Based Planning
  7. Methodology
  8. Safety: Capsule Distance Barrier Function
  9. Dynamic Feasibility: Certifying the Executed Rollout
  10. Minimal Distributional Deviation: Path-Consistent Corrections
  11. Path-Consistent Capsule CBF (PC-CBF) Safety Filter
  12. Integrating Certifiable Structure into Diffusion Planning
  13. PC-Diffuser and Practical Considerations
  14. Evaluation
  15. Dataset and Metrics
  16. ...and 4 more sections

Key Result

Proposition 1

For any ego state $\mathbf{x}=(x,y,\theta,\delta,v)$ and neighbor state $\mathbf{x}^j$ with $d_{\mathrm{cap}}(S_{\mathrm{ego}}(\mathbf{x}), S_j(\mathbf{x}^j))>0$, the capsule barrier $h^j(\mathbf{x}) = d_{\mathrm{cap}}(S_{\mathrm{ego}}(\mathbf{x}), S_j(\mathbf{x}^j)) - d_{\mathrm{safe}}$ is continuo

Figures (4)

  • Figure 1: Overview of the proposed PC-Diffuser safety augmentation framework.
  • Figure 2: Capsule distance diagram. Each vehicle is represented by its longitudinal axis (line segment). Then the capsule distance is the minimum distance between the two segments minus $r_n + r_e$, the sum of half widths of the two vehicles.
  • Figure 3: Qualitative comparison on a collision critical intersection scenario. The ego vehicle (orange box) approaches from the left. Planned trajectory for ego is depicted in bright gradient while neighbors' is depicted in blue-green gradient. The first Collision in the future timeframe is marked with a red x. The vanilla Diffuser (a) and Classifier Guidance (b) collide with an oncoming traffic. SafeDiffuser (c) produces a safe but dynamically infeasible trajectory. MPC-CBF (d) produces safe and feasible trajectory but deviates into the on-coming lane. PC-Diffuser (e) yields to the on-coming traffics before safely making a left turn while preserving a lane-consistent trajectory. More qualitative comparisons are available in the accompanying video.
  • Figure 4: Average slack activation rate (%) in the CBF-QP across denoising steps. Iterative PC-CBF shows monotonically decreasing corrections as denoising progresses, indicating convergence to a safe trajectory. Single-step PC-CBF (dashed line) applies a larger correction at the final step with higher slack activation rate due to the absence of iterative refinement.

Theorems & Definitions (6)

  • Proposition 1: Smoothness of the Capsule Barrier
  • proof
  • Definition 1: Fixed-Steering CBF
  • Theorem 1: Feasibility of Velocity-Level Capsule CBF
  • proof
  • Corollary 1: Forward Invariance