# Motion Planning with Model-Based Diffusion via Constraint Optimization and Adaptive Scheduling

arXiv: https://arxiv.org/abs/2607.14455 · HTML: https://mlsanity.com/paper/2607.14455/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion and flow policies for robotics, one of 14 directions in Diffusion models.
- Builds on 25 of its 36 references that are in the map.
- First posted on arXiv 16 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, 25 of 25)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [Reinforcement Learning and Control as Probabilistic Inference: Tutorial and Review](https://mlsanity.com/paper/1805.00909/) (2018)
- [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)
- [Information Theoretic Model Predictive Control: Theory and Applications to Autonomous Driving](https://mlsanity.com/paper/1707.02342/) (2017)
- [Constrained Synthesis with Projected Diffusion Models](https://mlsanity.com/paper/2402.03559/) (2024)
- [SafeDiffuser: Safe Planning with Diffusion Probabilistic Models](https://mlsanity.com/paper/2306.00148/) (2023)
- [Diffusion Models for Constrained Domains](https://mlsanity.com/paper/2304.05364/) (2023)
- [Towards Diverse Behaviors: A Benchmark for Imitation Learning with Human Demonstrations](https://mlsanity.com/paper/2402.14606/) (2024)
- [Simultaneous Multi-Robot Motion Planning with Projected Diffusion Models](https://mlsanity.com/paper/2502.03607/) (2025)
- [Diffusion Predictive Control with Constraints](https://mlsanity.com/paper/2412.09342/) (2024)
- [Model-Based Diffusion for Trajectory Optimization](https://mlsanity.com/paper/2407.01573/) (2024)
- [An Inexact Augmented Lagrangian Framework for Nonconvex Optimization with Nonlinear Constraints](https://mlsanity.com/paper/1906.11357/) (2019)
- [Safe and Stable Control via Lyapunov-Guided Diffusion Models](https://mlsanity.com/paper/2509.25375/) (2025)
- [The Convex Feasible Set Algorithm for Real Time Optimization in Motion Planning](https://mlsanity.com/paper/1709.00627/) (2017)
- [Probabilistic completeness of RRT for geometric and kinodynamic planning with forward propagation](https://mlsanity.com/paper/1809.07051/) (2018)
- [GuSTO: Guaranteed Sequential Trajectory Optimization via Sequential Convex Programming](https://mlsanity.com/paper/1903.00155/) (2019)
- [ADMM Penalty Parameter Selection by Residual Balancing](https://mlsanity.com/paper/1704.06209/) (2017)
- [Multi-Agent Path Finding in Continuous Spaces with Projected Diffusion Models](https://mlsanity.com/paper/2412.17993/) (2024)
- [Constrained Differential Dynamic Programming: A primal-dual augmented Lagrangian approach](https://mlsanity.com/paper/2210.15409/) (2022)
- [EB-MBD: Emerging-Barrier Model-Based Diffusion for Safe Trajectory Optimization in Highly Constrained Environments](https://mlsanity.com/paper/2510.07700/) (2025)
- [Model-Based Diffusion Optimal Control for Multi-Robot Motion Planning](https://mlsanity.com/paper/2607.12423/) (2026)
- [Distributed Motion Coordination Using Convex Feasible Set Based Model Predictive Control](https://mlsanity.com/paper/2101.07994/) (2021)

## Built on by (most cited first, 1 of 1)

- [FedGuide: Diffusion Prior Alignment and Value Baseline Guidance for Heterogeneous Federated Reinforcement Learning](https://mlsanity.com/paper/2609.18964/) (2026)

## Abstract (arXiv)

Single-Robot Motion Planning (SRMP) in highly non-convex constrained environments, where robots must satisfy collision-free guarantees, dynamic feasibility, and task-related constraints, is challenging under complex constraints and computational limits. Recent Model-Based Diffusion (MBD) approaches recast the SRMP as trajectory optimization that samples from a posterior over trajectories, using known dynamics, and analytically estimates the score function from rollout samples to guide diffusion denoising toward a low-cost, clean trajectory without demonstration learning. While existing works further adapt MBD to constrained environments and showcase promising performance, they are still limited by (1) enforcing safety either via soft feasibility diffusion priors or hard projection operators, but lack a unified framework to integrate both, and (2) fixing safety enforcement to neglect the changing of diffusion scheduling. Therefore, we introduce Model-Based Diffusion via Constraint Optimization and Adaptive Scheduling (MD-COAS) for SRMP that unifies the inexact Augmented Lagrangian Method (iALM) soft diffusion prior with a Convex Feasible Set (CFS)-based hard projection operator, and adaptively schedules and co-optimizes safety enforcement, along with diffusion scheduling. Experiments demonstrate that our method achieves higher safety & success rates, faster convergence, and lower final costs than baseline planners on randomly generated highly non-convex 2D benchmarks and a 7-DoF robot arm avoidance task.