# Dynamics-aware Diffusion Models for Planning and Control

arXiv: https://arxiv.org/abs/2504.00236 · HTML: https://mlsanity.com/paper/2504.00236/

## Key facts

- Cited by 4 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 17 of its 22 references that are in the map.
- First posted on arXiv 31 Mar 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, 17 of 17)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [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)
- [A Physics-informed Diffusion Model for High-fidelity Flow Field Reconstruction](https://mlsanity.com/paper/2211.14680/) (2022)
- [Diffusion Model is an Effective Planner and Data Synthesizer for Multi-Task Reinforcement Learning](https://mlsanity.com/paper/2305.18459/) (2023)
- [Physics-Informed Diffusion Models](https://mlsanity.com/paper/2403.14404/) (2024)
- [DiffuserLite: Towards Real-time Diffusion Planning](https://mlsanity.com/paper/2401.15443/) (2024)
- [Diffusion Model Predictive Control](https://mlsanity.com/paper/2410.05364/) (2024)
- [Diffusion Predictive Control with Constraints](https://mlsanity.com/paper/2412.09342/) (2024)
- [Generating Behaviorally Diverse Policies with Latent Diffusion Models](https://mlsanity.com/paper/2305.18738/) (2023)
- [Diffusion Model for Planning: A Systematic Literature Review](https://mlsanity.com/paper/2408.10266/) (2024)
- [DDAT: Diffusion Policies Enforcing Dynamically Admissible Robot Trajectories](https://mlsanity.com/paper/2502.15043/) (2025)
- [Constraint-Aware Diffusion Models for Trajectory Optimization](https://mlsanity.com/paper/2406.00990/) (2024)
- [Physics-informed Score-based Diffusion Model for Limited-angle Reconstruction of Cardiac Computed Tomography](https://mlsanity.com/paper/2405.14770/) (2024)
- [Data-Driven Feedback Linearization using the Koopman Generator](https://mlsanity.com/paper/2210.05046/) (2022)
- [Denoising Diffusion-Based Control of Nonlinear Systems](https://mlsanity.com/paper/2402.02297/) (2024)
- [Diffusion-Based Forecasting for Uncertainty-Aware Model Predictive Control](https://mlsanity.com/paper/2503.15095/) (2025)

## Built on by (most cited first, 4 of 4)

- [Score Matching Diffusion Based Feedback Control and Planning of Nonlinear Systems](https://mlsanity.com/paper/2504.09836/) (2025)
- [Formal Safety Verification and Refinement for Generative Motion Planners via Certified Local Stabilization](https://mlsanity.com/paper/2509.19688/) (2025)
- [Provably Safe Generative Sampling with Constricting Barrier Functions](https://mlsanity.com/paper/2602.21429/) (2026)
- [Learning Robust Visuomotor Policies via Dynamics Alignment](https://mlsanity.com/paper/2510.27114/) (2025)

## Abstract (arXiv)

This paper addresses the problem of generating dynamically admissible trajectories for control tasks using diffusion models, particularly in scenarios where the environment is complex and system dynamics are crucial for practical application. We propose a novel framework that integrates system dynamics directly into the diffusion model's denoising process through a sequential prediction and projection mechanism. This mechanism, aligned with the diffusion model's noising schedule, ensures generated trajectories are both consistent with expert demonstrations and adhere to underlying physical constraints. Notably, our approach can generate maximum likelihood trajectories and accurately recover trajectories generated by linear feedback controllers, even when explicit dynamics knowledge is unavailable. We validate the effectiveness of our method through experiments on standard control tasks and a complex non-convex optimal control problem involving waypoint tracking and collision avoidance, demonstrating its potential for efficient trajectory generation in practical applications. Our code repository is available at www.github.com/darshangm/dynamics-aware-diffusion.