mlsanityData to 7 Oct 2026

Manifold-Guided Lyapunov Control with Diffusion Models

arXiv 2403.17692 ↗First posted 26 Mar 2024cs.CV cs.LG math.DGcited by 1

On the map: Diffusion models → Diffusion and flow policies for robotics

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.

Key facts. Cited by 1 paper in the map (data through 7 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.

Builds on

19 of 23 references.

References · 19

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,694
  3. 2020Denoising Diffusion Implicit Modelscited by 9,655
  4. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  5. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  6. 2022DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Stepscited by 1,961
  7. 2022Diffusion Posterior Sampling for General Noisy Inverse Problemscited by 1,375
  8. 2022Diffusion Models: A Comprehensive Survey of Methods and Applicationscited by 1,107
  9. 2022Denoising Diffusion Restoration Modelscited by 951
  10. 2022Equivariant Diffusion for Molecule Generation in 3Dcited by 666
  11. 2022Improving Diffusion Models for Inverse Problems using Manifold Constraintscited by 501
  12. 2022PhysDiff: Physics-Guided Human Motion Diffusion Modelcited by 365
7 more
  1. 2023Manifold Preserving Guided Diffusioncited by 153
  2. 2020Neural Lyapunov Controlcited by 142
  3. 2023GibbsDDRM: A Partially Collapsed Gibbs Sampler for Solving Blind Inverse Problems with Denoising Diffusion Restorationcited by 58
  4. 2022Neural Lyapunov Control of Unknown Nonlinear Systems with Stability Guaranteescited by 39
  5. 2023Physics-Informed Neural Network Lyapunov Functions: PDE Characterization, Learning, and Verificationcited by 20
  6. 2020Automated and Sound Synthesis of Lyapunov Functions with SMT Solverscited by 10
  7. 2023Diffusion model based data generation for partial differential equationscited by 5

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026Manifold-Optimal Guidance: A Unified Riemannian Control View of Diffusion Guidancecited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025Dynamics-aware Diffusion Models for Planning and Control
  2. 2025Theoretical Closed-loop Stability Bounds for Dynamical System Coupled with Diffusion Policies
  3. 2024Denoising Diffusion-Based Control of Nonlinear Systems
  4. 2023Learning to Stabilize High-dimensional Unknown Systems Using Lyapunov-guided Exploration
  5. 2025DDAT: Diffusion Policies Enforcing Dynamically Admissible Robot Trajectories
  6. 2022Learning Solution Manifolds for Control Problems via Energy Minimization
  7. 2025Control Consistency Losses for Diffusion Bridges
  8. 2023Learning Lyapunov-Stable Polynomial Dynamical Systems through Imitation