# Toward Near-Globally Optimal Nonlinear Model Predictive Control via Diffusion Models

arXiv: https://arxiv.org/abs/2412.08278 · HTML: https://mlsanity.com/paper/2412.08278/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Dec 2024.

## Built on by (most cited first, 8 of 8)

- [Diffusion-Based Approximate MPC: Fast and Consistent Imitation of Multi-Modal Action Distributions](https://mlsanity.com/paper/2504.04603/) (2025)
- [Generative Models From and For Sampling-Based MPC: A Bootstrapped Approach For Adaptive Contact-Rich Manipulation](https://mlsanity.com/paper/2510.14643/) (2025)
- [SAD-Flower: Flow Matching for Safe, Admissible, and Dynamically Consistent Planning](https://mlsanity.com/paper/2511.05355/) (2025)
- [Model-Based Diffusion Sampling for Predictive Control in Offline Decision Making](https://mlsanity.com/paper/2512.08280/) (2025)
- [Warm-Starting Collision-Free Model Predictive Control With Object-Centric Diffusion](https://mlsanity.com/paper/2601.02873/) (2026)
- [Dynamic Neural Koopman Distillation for Real-Time Robot Control Using Diffusion Models](https://mlsanity.com/paper/2605.24924/) (2026)
- [Training-Free Imitation Learning with Closed-Form Diffusion Policies](https://mlsanity.com/paper/2606.01238/) (2026)
- [D-IMPL: A Diffusion-based Solver for Parameterized BBOs](https://mlsanity.com/paper/2609.22752/) (2026)

## Abstract (arXiv)

Achieving global optimality in nonlinear model predictive control (NMPC) is challenging due to the non-convex nature of the underlying optimization problem. Since commonly employed local optimization techniques depend on carefully chosen initial guesses, this non-convexity often leads to suboptimal performance resulting from local optima. To overcome this limitation, we propose a novel diffusion model-based approach for near-globally optimal NMPC consisting of an offline and an online phase. The offline phase employs a local optimizer to sample from the distribution of optimal NMPC control sequences along generated system trajectories through random initial guesses. Subsequently, the generated diverse dataset is used to train a diffusion model to reflect the multi-modal distribution of optima. In the online phase, the trained model is leveraged to efficiently perform a variant of random shooting optimization to obtain near-globally optimal control sequences without relying on any initial guesses or online NMPC solving. The effectiveness of our approach is illustrated in a numerical simulation indicating high performance benefits compared to direct neural network approximations of NMPC and significantly lower computation times than online solving NMPC using global optimizers.