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

arXiv: https://arxiv.org/abs/2607.10842 · HTML: https://mlsanity.com/paper/2607.10842/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion and flow policies for robotics, one of 14 directions in Diffusion models.
- Builds on 19 of its 24 references that are in the map.
- First posted on arXiv 12 Jul 2026.

## Placed in

- Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/)

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

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [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)
- [Motion Planning Diffusion: Learning and Planning of Robot Motions with Diffusion Models](https://mlsanity.com/paper/2308.01557/) (2023)
- [SafeDiffuser: Safe Planning with Diffusion Probabilistic Models](https://mlsanity.com/paper/2306.00148/) (2023)
- [Towards Diverse Behaviors: A Benchmark for Imitation Learning with Human Demonstrations](https://mlsanity.com/paper/2402.14606/) (2024)
- [Aligning Optimization Trajectories with Diffusion Models for Constrained Design Generation](https://mlsanity.com/paper/2305.18470/) (2023)
- [Diffusion Model Predictive Control](https://mlsanity.com/paper/2410.05364/) (2024)
- [CoBL-Diffusion: Diffusion-Based Conditional Robot Planning in Dynamic Environments Using Control Barrier and Lyapunov Functions](https://mlsanity.com/paper/2406.05309/) (2024)
- [Diffusion Predictive Control with Constraints](https://mlsanity.com/paper/2412.09342/) (2024)
- [Motion Planning Diffusion: Learning and Adapting Robot Motion Planning with Diffusion Models](https://mlsanity.com/paper/2412.19948/) (2024)
- [Safe Policy Synthesis in Multi-Agent POMDPs via Discrete-Time Barrier Functions](https://mlsanity.com/paper/1903.07823/) (2019)
- [Equality Constrained Diffusion for Direct Trajectory Optimization](https://mlsanity.com/paper/2410.01939/) (2024)
- [Visual Tracking Nonlinear Model Predictive Control Method for Autonomous Wind Turbine Inspection](https://mlsanity.com/paper/2310.14030/) (2023)

## Abstract (arXiv)

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