ImitationFlow: Learning Deep Stable Stochastic Dynamic Systems by Normalizing Flows
Open accessAbstract
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.
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Encoder-decoder frameworks for motion primitives often struggle to generalize broadly across different scenarios.
“Nevertheless, these approaches often encounter challenges in achieving broad generalization across different scenarios.”
From LEGATO: Cross-Embodiment Imitation Using a Grasping Tool (2025) · cites this paper as [39]
The Introduction (page unavailable) says many state-dependent movement-primitive models do not ensure stable dynamics outside the demonstrated trajectories, limiting their use in real-world scenarios. This supports a narrower generalization concern, but the paper does not attribute it specifically to encoder-decoder frameworks or establish difficulty across different scenarios broadly. (LLM, conf=0.83)
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References 28 · Cited by 56
Research works printed but not linked: 8
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- [6]6. Y. Huang, L. Rozo, J. Silvério, and D. G. Caldwell, "Kernelized move- ment primitives," The International Journal of Robotics Research, vol. 38, no. 7, pp. 833-852, 2019.
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- Authors
- Urain, J., Ginesi, M., Tateo, D., & Peters, J.
- Affiliations
- Technische Universität Darmstadt (DE)
- University of Verona (IT)
- Venue
- 2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)
- Publisher
- IEEE
- Published
- 2020-10-24
- Pages
- 5231-5237
- ISSN
- 2153-0858 (ISSN-L)
- OpenAlex
- W3093968353
- Cited by
- 56
- References
- 28
- Citations by year
- 2026: 6 · 2025: 15 · 2024: 12 · 2023: 10 · 2022: 8 · 2021: 4 · 2020: 1
- FWCI
- 2.19
- Type
- conference paper
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Reinforcement Learning in Robotics
- Physical Sciences › Computer Science › Artificial Intelligence › Gaussian Processes and Bayesian Inference
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Model Reduction and Neural Networks
- Keywords
- normalizing flows, stochastic differential equations, Lyapunov stability, deep generative models, nonlinear dynamics, robot control, imitation learning
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