# Flexible Locomotion Learning with Diffusion Model Predictive Control

arXiv: https://arxiv.org/abs/2510.04234 · HTML: https://mlsanity.com/paper/2510.04234/

## 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 41 of its 52 references that are in the map.
- First posted on arXiv 5 Oct 2025.

## 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, 30 of 41)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [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)
- [Isaac Gym: High Performance GPU-Based Physics Simulation For Robot Learning](https://mlsanity.com/paper/2108.10470/) (2021)
- [Training Diffusion Models with Reinforcement Learning](https://mlsanity.com/paper/2305.13301/) (2023)
- [Advantage-Weighted Regression: Simple and Scalable Off-Policy Reinforcement Learning](https://mlsanity.com/paper/1910.00177/) (2019)
- [Diffusion Forcing: Next-token Prediction Meets Full-Sequence Diffusion](https://mlsanity.com/paper/2407.01392/) (2024)
- [Learning Quadrupedal Locomotion over Challenging Terrain](https://mlsanity.com/paper/2010.11251/) (2020)
- [Is Conditional Generative Modeling all you need for Decision-Making?](https://mlsanity.com/paper/2211.15657/) (2022)
- [Universal Guidance for Diffusion Models](https://mlsanity.com/paper/2302.07121/) (2023)
- [ManiSkill2: A Unified Benchmark for Generalizable Manipulation Skills](https://mlsanity.com/paper/2302.04659/) (2023)
- [Diffusion Policy Policy Optimization](https://mlsanity.com/paper/2409.00588/) (2024)
- [ManiSkill3: GPU Parallelized Robotics Simulation and Rendering for Generalizable Embodied AI](https://mlsanity.com/paper/2410.00425/) (2024)
- [Guided Motion Diffusion for Controllable Human Motion Synthesis](https://mlsanity.com/paper/2305.12577/) (2023)
- [Extreme Parkour with Legged Robots](https://mlsanity.com/paper/2309.14341/) (2023)
- [Efficient Diffusion Policies for Offline Reinforcement Learning](https://mlsanity.com/paper/2305.20081/) (2023)
- [ANYmal Parkour: Learning Agile Navigation for Quadrupedal Robots](https://mlsanity.com/paper/2306.14874/) (2023)
- [Robot Parkour Learning](https://mlsanity.com/paper/2309.05665/) (2023)
- [Agile But Safe: Learning Collision-Free High-Speed Legged Locomotion](https://mlsanity.com/paper/2401.17583/) (2024)
- [DiffuseLoco: Real-Time Legged Locomotion Control with Diffusion from Offline Datasets](https://mlsanity.com/paper/2404.19264/) (2024)
- [Potential Based Diffusion Motion Planning](https://mlsanity.com/paper/2407.06169/) (2024)
- [Generative Trajectory Stitching through Diffusion Composition](https://mlsanity.com/paper/2503.05153/) (2025)
- [Diffusion Model Predictive Control](https://mlsanity.com/paper/2410.05364/) (2024)
- [SPIN: Simultaneous Perception, Interaction and Navigation](https://mlsanity.com/paper/2405.07991/) (2024)
- [Diffuse-CLoC: Guided Diffusion for Physics-based Character Look-ahead Control](https://mlsanity.com/paper/2503.11801/) (2025)
- [HuB: Learning Extreme Humanoid Balance](https://mlsanity.com/paper/2505.07294/) (2025)

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

- [TTT-Parkour: Rapid Test-Time Training for Perceptive Robot Parkour](https://mlsanity.com/paper/2602.02331/) (2026)

## Abstract (arXiv)

Legged locomotion demands controllers that are both robust and adaptable, while remaining compatible with task and safety considerations. However, model-free reinforcement learning (RL) methods often yield a fixed policy that can be difficult to adapt to new behaviors at test time. In contrast, Model Predictive Control (MPC) provides a natural approach to flexible behavior synthesis by incorporating different objectives and constraints directly into its optimization process. However, classical MPC relies on accurate dynamics models, which are often difficult to obtain in complex environments and typically require simplifying assumptions. We present Diffusion-MPC, which leverages a learned generative diffusion model as an approximate dynamics prior for planning, enabling flexible test-time adaptation through reward and constraint based optimization. Diffusion-MPC jointly predicts future states and actions; at each reverse step, we incorporate reward planning and impose constraint projection, yielding trajectories that satisfy task objectives while remaining within physical limits. To obtain a planning model that adapts beyond imitation pretraining, we introduce an interactive training algorithm for diffusion based planner: we execute our reward-and-constraint planner in environment, then filter and reweight the collected trajectories by their realized returns before updating the denoiser. Our design enables strong test-time adaptability, allowing the planner to adjust to new reward specifications without retraining. We validate Diffusion-MPC on real world, demonstrating strong locomotion and flexible adaptation.