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

arXiv: https://arxiv.org/abs/2603.10330 · HTML: https://mlsanity.com/paper/2603.10330/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 23 references that are in the map.
- First posted on arXiv 11 Mar 2026.

## Builds on (most cited first, 19 of 19)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [NuPlan: A closed-loop ML-based planning benchmark for autonomous vehicles](https://mlsanity.com/paper/2106.11810/) (2021)
- [Control Barrier Functions: Theory and Applications](https://mlsanity.com/paper/1903.11199/) (2019)
- [Control Barrier Function Based Quadratic Programs for Safety Critical Systems](https://mlsanity.com/paper/1609.06408/) (2016)
- [Alpamayo-R1: Bridging Reasoning and Action Prediction for Generalizable Autonomous Driving in the Long Tail](https://mlsanity.com/paper/2511.00088/) (2025)
- [Diffusion-Based Planning for Autonomous Driving with Flexible Guidance](https://mlsanity.com/paper/2501.15564/) (2025)
- [SafeDiffuser: Safe Planning with Diffusion Probabilistic Models](https://mlsanity.com/paper/2306.00148/) (2023)
- [Safety-Critical Model Predictive Control with Discrete-Time Control Barrier Function](https://mlsanity.com/paper/2007.11718/) (2020)
- [CoBL-Diffusion: Diffusion-Based Conditional Robot Planning in Dynamic Environments Using Control Barrier and Lyapunov Functions](https://mlsanity.com/paper/2406.05309/) (2024)
- [Flow Matching-Based Autonomous Driving Planning with Advanced Interactive Behavior Modeling](https://mlsanity.com/paper/2510.11083/) (2025)
- [SafeFlow: Safe Robot Motion Planning with Flow Matching via Control Barrier Functions](https://mlsanity.com/paper/2504.08661/) (2025)
- [Probabilistic Safety-Assured Adaptive Merging Control for Autonomous Vehicles](https://mlsanity.com/paper/2104.14159/) (2021)
- [RAIL: Reachability-Aided Imitation Learning for Safe Policy Execution](https://mlsanity.com/paper/2409.19190/) (2024)
- [From Demonstrations to Safe Deployment: Path-Consistent Safety Filtering for Diffusion Policies](https://mlsanity.com/paper/2511.06385/) (2025)
- [SAD-Flower: Flow Matching for Safe, Admissible, and Dynamically Consistent Planning](https://mlsanity.com/paper/2511.05355/) (2025)
- [Active Probing and Influencing Human Behaviors Via Autonomous Agents](https://mlsanity.com/paper/2304.11817/) (2023)
- [Risk-aware Safe Control for Decentralized Multi-agent Systems via Dynamic Responsibility Allocation](https://mlsanity.com/paper/2305.13467/) (2023)
- [Multimodal Belief-Space Covariance Steering with Active Probing and Influence for Interactive Driving](https://mlsanity.com/paper/2602.14540/) (2026)

## Abstract (arXiv)

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...