LyapuFlow：利用李雅普诺夫反馈控制生成流以求解逆问题

中文摘要 AI 辅助

预训练流模型现已被广泛用作科学和视觉领域的生成先验，其中推理时引导能够在无需重新训练的情况下施加测试时约束。现有方法使用投影、后验采样或生成轨迹的迭代优化。我们提出LyapuFlow，一种基于李雅普诺夫反馈控制的替代方法。在每个采样步骤中，LyapuFlow预测当前流正在演化的终端样本，并评估该预测上的约束违反程度。然后，我们计算满足规定李雅普诺夫下降条件的最小范数控制。当无控制动力学已经以规定速率降低约束违反时，所得控制保持不活跃。否则，它在反馈信任区域内提供修正更新，以防止控制主导预训练动力学。我们在数据空间和潜在空间中展示了LyapuFlow，在科学机器学习和图像逆问题的测试时约束执行中，其性能优于涵盖不同机制的替代方法。

英文摘要

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.

发表机构

• Lawrence Berkeley National Lab（劳伦斯伯克利国家实验室）
• Georgia Institute of Technology（佐治亚理工学院）
• Siemens（西门子公司）
• International Computer Science Institute（国际计算机科学研究所）

机构由 AI 辅助整理，请以论文原文为准。