# CL-DiffPhyCon: Closed-loop Diffusion Control of Complex Physical Systems

arXiv: https://arxiv.org/abs/2408.03124 · HTML: https://mlsanity.com/paper/2408.03124/

## Key facts

- Cited by 8 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 25 of its 43 references that are in the map.
- First posted on arXiv 31 Jul 2024.

## 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, 25 of 25)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [Is Conditional Generative Modeling all you need for Decision-Making?](https://mlsanity.com/paper/2211.15657/) (2022)
- [GenCast: Diffusion-based ensemble forecasting for medium-range weather](https://mlsanity.com/paper/2312.15796/) (2023)
- [Learning to Control PDEs with Differentiable Physics](https://mlsanity.com/paper/2001.07457/) (2020)
- [AR-Diffusion: Auto-Regressive Diffusion Model for Text Generation](https://mlsanity.com/paper/2305.09515/) (2023)
- [Rolling Diffusion Models](https://mlsanity.com/paper/2402.09470/) (2024)
- [Efficient collective swimming by harnessing vortices through deep reinforcement learning](https://mlsanity.com/paper/1802.02674/) (2018)
- [Optimal control of PDEs using physics-informed neural networks](https://mlsanity.com/paper/2111.09880/) (2021)
- [Behavior Proximal Policy Optimization](https://mlsanity.com/paper/2302.11312/) (2023)
- [Solving PDE-constrained Control Problems Using Operator Learning](https://mlsanity.com/paper/2111.04941/) (2021)
- [Continuous-Time Model-Based Reinforcement Learning](https://mlsanity.com/paper/2102.04764/) (2021)
- [Adaptive Online Replanning with Diffusion Models](https://mlsanity.com/paper/2310.09629/) (2023)
- [Compositional Generative Inverse Design](https://mlsanity.com/paper/2401.13171/) (2024)
- [DiffPhyCon: A Generative Approach to Control Complex Physical Systems](https://mlsanity.com/paper/2407.06494/) (2024)
- [How to Control Hydrodynamic Force on Fluidic Pinball via Deep Reinforcement Learning](https://mlsanity.com/paper/2304.11526/) (2023)
- [Efficient Navigation of a Robotic Fish Swimming Across the Vortical Flow Field](https://mlsanity.com/paper/2405.14251/) (2024)

## Built on by (most cited first, 8 of 8)

- [HJ-sampler: A Bayesian sampler for inverse problems of a stochastic process by leveraging Hamilton-Jacobi PDEs and score-based generative models](https://mlsanity.com/paper/2409.09614/) (2024)
- [Multi-modal Policies with Physics-informed Representations in Complex Fluid Environments](https://mlsanity.com/paper/2410.15250/) (2024)
- [Accelerated Sequential Flow Matching: A Bayesian Filtering Perspective](https://mlsanity.com/paper/2602.05319/) (2026)
- [CMP: Robust Whole-Body Tracking for Loco-Manipulation via Competence Manifold Projection](https://mlsanity.com/paper/2604.07457/) (2026)
- [Harnessing AI for Inverse Partial Differential Equation Problems: Past, Present, and Prospects](https://mlsanity.com/paper/2605.16966/) (2026)
- [Sample-Efficient Diffusion-based Control of Complex Physics Systems](https://mlsanity.com/paper/2502.17893/) (2025)
- [CloDS: Visual-Only Unsupervised Cloth Dynamics Learning in Unknown Conditions](https://mlsanity.com/paper/2602.01844/) (2026)
- [MetaColloc: Optimization-Free PDE Solving via Meta-Learned Basis Functions](https://mlsanity.com/paper/2605.12368/) (2026)

## Abstract (arXiv)

The control problems of complex physical systems have broad applications in science and engineering. Previous studies have shown that generative control methods based on diffusion models offer significant advantages for solving these problems. However, existing generative control approaches face challenges in both performance and efficiency when extended to the closed-loop setting, which is essential for effective control. In this paper, we propose an efficient Closed-Loop Diffusion method for Physical systems Control (CL-DiffPhyCon). By employing an asynchronous denoising framework for different physical time steps, CL-DiffPhyCon generates control signals conditioned on real-time feedback from the system with significantly reduced computational cost during sampling. Additionally, the control process could be further accelerated by incorporating fast sampling techniques, such as DDIM. We evaluate CL-DiffPhyCon on two tasks: 1D Burgers' equation control and 2D incompressible fluid control. The results demonstrate that CL-DiffPhyCon achieves superior control performance with significant improvements in sampling efficiency. The code can be found at https://github.com/AI4Science-WestlakeU/CL_DiffPhyCon.