mlsanityData to 7 Oct 2026

ImitationFlow: Learning Deep Stable Stochastic Dynamic Systems by Normalizing Flows

arXiv 2010.13129 ↗First posted 25 Oct 2020cs.LG cs.ROcited by 33

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Abstract (arXiv)

We introduce ImitationFlow, a novel Deep generative model that allows learning complex globally stable, stochastic, nonlinear dynamics. Our approach extends the Normalizing Flows framework to learn stable Stochastic Differential Equations. We prove the Lyapunov stability for a class of Stochastic Differential Equations and we propose a learning algorithm to learn them from a set of demonstrated trajectories. Our model extends the set of stable dynamical systems that can be represented by state-of-the-art approaches, eliminates the Gaussian assumption on the demonstrations, and outperforms the previous algorithms in terms of representation accuracy. We show the effectiveness of our method with both standard datasets and a real robot experiment.

Key facts. Cited by 33 papers in the map (data through 7 Oct 2026). First posted on arXiv 25 Oct 2020.

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Citing papers per year: 2021: 4; 2022: 6; 2023: 4; 2024: 8; 2025: 8; 2026: 3.

33 papers.

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  1. 2022SE(3)-DiffusionFields: Learning smooth cost functions for joint grasp and motion optimization through diffusioncited by 125
  2. 2024Riemannian Flow Matching Policy for Robot Motion Learningcited by 61
  3. 2024Deep Generative Models in Robotics: A Survey on Learning from Multimodal Demonstrationscited by 35
  4. 2022ProDMPs: A Unified Perspective on Dynamic and Probabilistic Movement Primitivescited by 25
  5. 2022Learning Implicit Priors for Motion Optimizationcited by 20
  6. 2024Fast and Robust Visuomotor Riemannian Flow Matching Policycited by 18
  7. 2022Learning Riemannian Stable Dynamical Systems via Diffeomorphismscited by 17
  8. 2021Composable Energy Policies for Reactive Motion Generation and Reinforcement Learningcited by 16
  9. 2024Neural Contractive Dynamical Systemscited by 14
  10. 2021Learning Stable Vector Fields on Lie Groupscited by 12
  11. 2022Continual Learning from Demonstration of Robotics Skillscited by 11
  12. 2024Learning Neural Contracting Dynamics: Extended Linearization and Global Guaranteescited by 11
21 more
  1. 2021Robot Skill Adaptation via Soft Actor-Critic Gaussian Mixture Modelscited by 9
  2. 2021RMP2: A Structured Composable Policy Class for Robot Learningcited by 8
  3. 2023Scalable and Efficient Continual Learning from Demonstration via a Hypernetwork-generated Stable Dynamics Modelcited by 6
  4. 2023PUMA: Deep Metric Imitation Learning for Stable Motion Primitivescited by 3
  5. 2024Fusion Dynamical Systems with Machine Learning in Imitation Learning: A Comprehensive Overviewcited by 3
  6. 2022Learning Stabilizable Deep Dynamics Modelscited by 2
  7. 2023Effect of Optimizer, Initializer, and Architecture of Hypernetworks on Continual Learning from Demonstrationcited by 2
  8. 2023Learning Orbitally Stable Systems for Diagrammatically Teachingcited by 1
  9. 2024Extended Neural Contractive Dynamical Systems: On Multiple Tasks and Riemannian Safety Regionscited by 1
  10. 2025Data-driven identification of nonlinear dynamical systems with LSTM autoencoders and Normalizing Flowscited by 1
  11. 2025Diffeomorphic Obstacle Avoidance for Contractive Dynamical Systems via Implicit Representationscited by 1
  12. 2025Robustly Invertible Nonlinear Dynamics and the BiLipREN: Contracting Neural Models with Contracting Inversescited by 1
  13. 2025KoopMotion: Learning Almost Divergence Free Koopman Flow Fields for Motion Planningcited by 1
  14. 2026Training-free score-based diffusion for parameter-dependent stochastic dynamical systemscited by 1
  15. 2024Imitation Learning-based Direct Visual Servoing using the Large Projection Formulationcited by 0
  16. 2025TamedPUMA: safe and stable imitation learning with geometric fabricscited by 0
  17. 2025Decision Flow Policy Optimizationcited by 0
  18. 2025A Robust Task-Level Control Architecture for Learned Dynamical Systemscited by 0
  19. 2025LILAD: Learning In-context Lyapunov-stable Adaptive Dynamics Modelscited by 0
  20. 2026Let the Dynamics Flow: Stable Flow Matching Dynamical Systemscited by 0
  21. 2026Robustly Invertible Nonlinear Dynamics and the BiLipREN: From Inversion-Based Control to Generative Trajectory Modellingcited by 0