LyapuFlow: Controlling Generative Flows with Lyapunov Feedback for Inverse Problems
Abstract
Pretrained flow models are now widely used as generative priors in science and vision, where inference-time guidance enables test-time constraints without retraining. Existing methods use projection, posterior sampling, or iterative optimization of the generative trajectory. We propose LyapuFlow, an alternative based on Lyapunov feedback control. At each sampling step, LyapuFlow predicts the terminal sample towards which the current flow is evolving, and evaluates the constraint violation on this prediction. Then, we compute the minimum-norm control that satisfies a prescribed Lyapunov decrease condition. The resulting control remains inactive when the uncontrolled dynamics already reduce the constraint violation at the prescribed rate. Otherwise, it provides a corrective update within a feedback trust region that prevents the control from dominating the pretrained dynamics. We demonstrate LyapuFlow in both data and latent spaces, outperforming alternatives spanning different mechanisms for test-time constraint enforcement in scientific machine learning and image inverse problems.
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BibTeX
@misc{gwak2026lyapuflow,
title = {{LyapuFlow: Controlling Generative Flows with Lyapunov Feedback for Inverse Problems}},
author = {Minseon Gwak and Hans Hao-Hsun Hsu and Danielle C. Maddix and N. Benjamin Erichson},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.04326},
eprint = {2610.04326},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.04326},
}
RIS
TY - UNPB
TI - LyapuFlow: Controlling Generative Flows with Lyapunov Feedback for Inverse Problems
AU - Minseon Gwak
AU - Hans Hao-Hsun Hsu
AU - Danielle C. Maddix
AU - N. Benjamin Erichson
PY - 2026
DA - 2026/10/03
PB - arXiv
DO - 10.48550/arxiv.2610.04326
UR - https://arxiv.org/abs/2610.04326
AB - Pretrained flow models are now widely used as generative priors in science and vision, where inference-time guidance enables test-time constraints without retraining. Existing methods use projection, posterior sampling, or iterative optimization of the generative trajectory. We propose LyapuFlow, an alternative based on Lyapunov feedback control. At each sampling step, LyapuFlow predicts the terminal sample towards which the current flow is evolving, and evaluates the constraint violation on this prediction. Then, we compute the minimum-norm control that satisfies a prescribed Lyapunov decrease condition. The resulting control remains inactive when the uncontrolled dynamics already reduce the constraint violation at the prescribed rate. Otherwise, it provides a corrective update within a feedback trust region that prevents the control from dominating the pretrained dynamics. We demonstrate LyapuFlow in both data and latent spaces, outperforming alternatives spanning different mechanisms for test-time constraint enforcement in scientific machine learning and image inverse problems.
ER -