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

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.

Figures (6)

• Figure 1: IMLE-based planning. (1) Noise is sampled from a Gaussian distribution. (2) Our model generates a set of candidate trajectories from the sampled noise. (3) Sampling-based model predictive control is used to select and refine the top trajectory.
• Figure 2: Illustration of IMLE's nearest neighbor matching. The method enforces that, for every data point, there exists a generated sample in its neighborhood, ensuring that the generator covers the full data distribution.
• Figure 3: FiLM-conditioned block used throughout the U-Net. Two small MLPs conditioning $c$ to scale $\gamma(c)$ and shift $\beta(c)$, which modulate the two blocks via FiLM ($x \mapsto \gamma(c)\odot x + \beta(c)$).
• Figure 4: IMLE vs Diffusion. Median per-plan latency (ms) split into generator and guidance on CPU/GPU, averaged over Walker/Hopper/HalfCheetah (Batch Size 64)
• Figure 5: Using IMLE-generated plans at 50 Hz, the robot reaches the goal while avoiding collisions. The top row shows the conditioning variables (robot and pedestrian past and current states). We also plot the generated plan and the waypoint tracked by the low-level controller.