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

arXiv: https://arxiv.org/abs/2603.13733 · HTML: https://mlsanity.com/paper/2603.13733/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 44 references that are in the map.
- First posted on arXiv 14 Mar 2026.

## Builds on (most cited first, 30 of 34)

- [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)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Decision Transformer: Reinforcement Learning via Sequence Modeling](https://mlsanity.com/paper/2106.01345/) (2021)
- [D4RL: Datasets for Deep Data-Driven Reinforcement Learning](https://mlsanity.com/paper/2004.07219/) (2020)
- [Offline Reinforcement Learning with Implicit Q-Learning](https://mlsanity.com/paper/2110.06169/) (2021)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [Advantage-Weighted Regression: Simple and Scalable Off-Policy Reinforcement Learning](https://mlsanity.com/paper/1910.00177/) (2019)
- [Offline Reinforcement Learning as One Big Sequence Modeling Problem](https://mlsanity.com/paper/2106.02039/) (2021)
- [MOPO: Model-based Offline Policy Optimization](https://mlsanity.com/paper/2005.13239/) (2020)
- [MOReL : Model-Based Offline Reinforcement Learning](https://mlsanity.com/paper/2005.05951/) (2020)
- [Is Conditional Generative Modeling all you need for Decision-Making?](https://mlsanity.com/paper/2211.15657/) (2022)
- [Reinforcement Learning and Control as Probabilistic Inference: Tutorial and Review](https://mlsanity.com/paper/1805.00909/) (2018)
- [Control Barrier Functions: Theory and Applications](https://mlsanity.com/paper/1903.11199/) (2019)
- [RvS: What is Essential for Offline RL via Supervised Learning?](https://mlsanity.com/paper/2112.10751/) (2021)
- [AdaptDiffuser: Diffusion Models as Adaptive Self-evolving Planners](https://mlsanity.com/paper/2302.01877/) (2023)
- [Contrastive Energy Prediction for Exact Energy-Guided Diffusion Sampling in Offline Reinforcement Learning](https://mlsanity.com/paper/2304.12824/) (2023)
- [Model-Based Offline Planning](https://mlsanity.com/paper/2008.05556/) (2020)
- [Reinforcement Learning Upside Down: Don't Predict Rewards -- Just Map Them to Actions](https://mlsanity.com/paper/1912.02875/) (2019)
- [SafeDiffuser: Safe Planning with Diffusion Probabilistic Models](https://mlsanity.com/paper/2306.00148/) (2023)
- [Implicit Maximum Likelihood Estimation](https://mlsanity.com/paper/1809.09087/) (2018)
- [On the Guidance of Flow Matching](https://mlsanity.com/paper/2502.02150/) (2025)
- [DiffuserLite: Towards Real-time Diffusion Planning](https://mlsanity.com/paper/2401.15443/) (2024)
- [What Makes a Good Diffusion Planner for Decision Making?](https://mlsanity.com/paper/2503.00535/) (2025)
- [CoBL-Diffusion: Diffusion-Based Conditional Robot Planning in Dynamic Environments Using Control Barrier and Lyapunov Functions](https://mlsanity.com/paper/2406.05309/) (2024)
- [trajdata: A Unified Interface to Multiple Human Trajectory Datasets](https://mlsanity.com/paper/2307.13924/) (2023)
- [Multimodal Image Synthesis with Conditional Implicit Maximum Likelihood Estimation](https://mlsanity.com/paper/2004.03590/) (2020)
- [IMLE Policy: Fast and Sample Efficient Visuomotor Policy Learning via Implicit Maximum Likelihood Estimation](https://mlsanity.com/paper/2502.12371/) (2025)

## Built on by (most cited first, 3 of 3)

- [SalsaAgent: A multimodal embodied language model for interactive dance generation](https://mlsanity.com/paper/2605.29219/) (2026)
- [ROMS-IMLE: A Minimalist Approach to Competitive Single-Step Generative Modelling](https://mlsanity.com/paper/2607.19332/) (2026)
- [IMLE-VLA: Fast Single-Step Action Generation for Vision-Language-Action Policies](https://mlsanity.com/paper/2609.10915/) (2026)

## Abstract (arXiv)

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/.