D-SafeMPC Diffusion-Driven Safe Model Predictive Control with Discrete-Time Control Barrier Functions

Jul 16, 2026

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Diffusion models used for robotic planning often fail to inherently enforce safety or dynamical constraints, producing trajectories that can violate physical feasibility or safety margins. Hybrid diffusion–MPC methods improve constraint handling but may become unstable when the diffusion model provides poor initial trajectories that stop MPC from converging. D-SafeMPC guides reverse diffusion with control barrier functions (CBFs) and control Lyapunov functions (CLFs) and uses an iterative-projection MPC refinement at each denoising step. Experiments on a Franka manipulator, including sim-to-real, improve safety, task success, and planning efficiency while improving MPC warm starts.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages8

Reading Time20 min

Introduction

Diffusion models for robotic trajectory planning

Limitations: constraint and safety enforcement

Hybrid diffusion–MPC approaches and instability

D-SafeMPC method overview

D-SafeMPC: Diffusion-Driven Safe Model Predictive Control with Discrete-Time Control Barrier Functions Erdi Sayar1 , Ersin Da¸s2 , Joel W. Burdick3 , Alois Knoll4 , and Erdal Kayacan 1 arXiv :2607 . 10842v1 [ cs .RO] 12 Jul 2026 Abstract—A key limitation on the use of diffusion models in robotic planning is their inability to inherently enforce safety or dynamical constraints, which often results in physically infeasible or unsafe outputs. Hybrid approaches that employ model predictive control (MPC) to address this problem can be unstable, as poor trajectory initializations from the diffusion model prevent the MPC from converging to a safe and feasible solution. To overcome these challenges, we propose D-SafeMPC, which enhances the interaction between diffusion and control. Our method guides the reverse diffusion process with control barrier functions (CBFs) and control Lyapunov functions (CLFs) and employs an iterative-projection scheme where an MPC refines the trajectory at each denoising step. This steers sampling toward safe, goal-directed regions and provides reliable MPC warm starts. In simulations on a Franka manipulator across four scenarios (one static-obstacle and three dynamic-obstacle settings) and in a sim-to-real experiment on a physical Franka robot, D-SafeMPC improves safety, task success rates, and planning efficiency over state-of-the-art baselines. To facilitate reproducibility, our source code and experimental configurations are available in a repository at [https://github.com/erdiphd/D-SafeMPC](https://github.com/erdiphd/D-SafeMPC) I. INTRODUCTION Diffusion models [1] have established state-of-the-art performance in generative tasks such as image and video synthesis. In robotics, they demonstrate impressive capabilities in trajectory planning, where they learn complex policies from demonstrations [2]–[5] . These models excel at capturing multimodal behaviors and generating high-dimensional trajectories holistically, which mitigates the compounding errors common in sequential methods and improves longterm performance. However, despite their success with large datasets, diffusion models lack an intrinsic mechanism to enforce explicit constraints, such as system dynamics, obstacle avoidance, and safety margins [6] . As a result, the trajectories produced via their iterative stochastic denoising process frequently violate the physical constraints of the system [7] . To address this limitation,[8] combines a diffusion model with control barrier functions (CBFs) [9] and control Lyapunov functions (CLFs) [10] to avoid obstacles while reaching a target set during the reverse diffusion process. Although *This work was partially supported by the Horizon Europe Grant Agreement No. 101136056. 1 E. Sayar and E. Kayacan are with the Department of Electrical Engineering and Information Technology, Paderborn University, 33098 Paderborn, Germany, {erdi .sayar, erdal .kayacan}@uni-paderborn .de. 2 E. Da¸s is with the Department of Mechanical, Materials, and Aerospace Engineering, Illinois Institute of Technology, Chicago, IL 60616, USA, [edas2@illinoistech.edu](edas2@illinoistech.edu). 3 J. W. Burdick is with the Mechanical and Civil Engineering, California Institute of Technology, Pasadena, CA 91125, USA, [jburdick@caltech.edu](jburdick@caltech.edu). 4 A. Knoll is with the School of Computation, Information, and Technology, Technical University of Munich, 80333 Munich, Germany, [k@tum.de](k@tum.de). this approach guides the planner, it only acts as a form of guidance, pushing generated trajectories toward safe and goaldirected regions. In other words, CBFs and CLFs improve the probabilistic safety of the planned trajectories, but no hard safety constraints are enforced on the final trajectory, which may still violate safety or dynamic constraints. To enforce such hard constraints, an alternative strategy is to leverage model predictive control (MPC) [11], an optimization-based control framework that

FAQs

Why do diffusion models struggle with safety in robotic planning?

Diffusion models do not intrinsically enforce explicit constraints like system dynamics, obstacle avoidance, or safety margins during their stochastic denoising process, so generated trajectories can violate feasibility and safety requirements.

What problem can occur in hybrid diffusion–MPC frameworks?

When the diffusion model produces a poor initial trajectory, the MPC refinement may fail to converge to a feasible solution, causing instability or failure in complex environments.

How does D-SafeMPC improve safety and convergence during planning?

D-SafeMPC steers reverse diffusion using control barrier functions (CBFs) and control Lyapunov functions (CLFs), then applies an iterative-projection MPC refinement with explicit safety and dynamic constraints at each denoising step to provide reliable MPC warm starts.

Jul 16, 2026

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