# Manifold-Guided Lyapunov Control with Diffusion Models

arXiv: https://arxiv.org/abs/2403.17692 · HTML: https://mlsanity.com/paper/2403.17692/

## 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 19 of its 23 references that are in the map.
- First posted on arXiv 26 Mar 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, 19 of 19)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [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)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [Improving Diffusion Models for Inverse Problems using Manifold Constraints](https://mlsanity.com/paper/2206.00941/) (2022)
- [PhysDiff: Physics-Guided Human Motion Diffusion Model](https://mlsanity.com/paper/2212.02500/) (2022)
- [Manifold Preserving Guided Diffusion](https://mlsanity.com/paper/2311.16424/) (2023)
- [Neural Lyapunov Control](https://mlsanity.com/paper/2005.00611/) (2020)
- [GibbsDDRM: A Partially Collapsed Gibbs Sampler for Solving Blind Inverse Problems with Denoising Diffusion Restoration](https://mlsanity.com/paper/2301.12686/) (2023)
- [Neural Lyapunov Control of Unknown Nonlinear Systems with Stability Guarantees](https://mlsanity.com/paper/2206.01913/) (2022)
- [Physics-Informed Neural Network Lyapunov Functions: PDE Characterization, Learning, and Verification](https://mlsanity.com/paper/2312.09131/) (2023)
- [Automated and Sound Synthesis of Lyapunov Functions with SMT Solvers](https://mlsanity.com/paper/2007.10865/) (2020)
- [Diffusion model based data generation for partial differential equations](https://mlsanity.com/paper/2306.11075/) (2023)

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

- [Manifold-Optimal Guidance: A Unified Riemannian Control View of Diffusion Guidance](https://mlsanity.com/paper/2603.11509/) (2026)

## Abstract (arXiv)

This paper presents a novel approach to generating stabilizing controllers for a large class of dynamical systems using diffusion models. The core objective is to develop stabilizing control functions by identifying the closest asymptotically stable vector field relative to a predetermined manifold and adjusting the control function based on this finding. To achieve this, we employ a diffusion model trained on pairs consisting of asymptotically stable vector fields and their corresponding Lyapunov functions. Our numerical results demonstrate that this pre-trained model can achieve stabilization over previously unseen systems efficiently and rapidly, showcasing the potential of our approach in fast zero-shot control and generalizability.