Implicit Maximum Likelihood Estimation for Real-time Generative Model Predictive Control

TL;DR

This paper introduces IMLE, a fast and effective generative modeling approach for real-time trajectory planning in model predictive control, outperforming diffusion models in speed while maintaining competitive accuracy.

Contribution

The paper proposes Implicit Maximum Likelihood Estimation (IMLE) as a novel, faster alternative to diffusion models for trajectory planning in real-time MPC applications.

Findings

IMLE achieves two orders of magnitude faster inference than diffusion models.

IMLE maintains competitive performance on offline reinforcement learning benchmarks.

IMLE enables real-time, adaptive planning in dynamic environments like human navigation.

Abstract

Diffusion-based models have recently shown strong performance in trajectory planning, as they are capable of capturing diverse, multimodal distributions of complex behaviors. A key limitation of these models is their slow inference speed, which results from the iterative denoising process. This makes them less suitable for real-time applications such as closed-loop model predictive control (MPC), where plans must be generated quickly and adapted continuously to a changing environment. In this paper, we investigate Implicit Maximum Likelihood Estimation (IMLE) as an alternative generative modeling approach for planning. IMLE offers strong mode coverage while enabling inference that is two orders of magnitude faster, making it particularly well suited for real-time MPC tasks. Our results demonstrate that IMLE achieves competitive performance on standard offline reinforcement learning benchmarks compared to the standard diffusion-based planner, while substantially improving planning speed in both open-loop and closed-loop settings. We further validate IMLE in a closed-loop human navigation scenario, operating in real-time, demonstrating how it enables rapid and adaptive plan generation in dynamic environments. Real-world videos and code are available at https://gmpc-imle.github.io/.