李雅普诺夫引导：稳定生成流的统一框架
Lyapunov Guidance: A Unified Framework for Stabilizing Generative Flows
浏览论文内容
中文总结 AI 辅助
研究针对流匹配重新训练计算昂贵、现有训练后引导方法无稳定性保证的问题，提出LyaGuide框架，将流引导作为李雅普诺夫控制问题，统一多种引导策略，经实验验证其在多方面有改进且保持计算效率。
中文摘要 AI 辅助
流匹配已成为学习复杂数据分布的有效框架，但将预训练流模型应用于新任务通常需要计算昂贵的重新训练。训练后引导提供了一种更有效的替代方法，但现有方法大多是启发式的，没有明确的稳定性保证。我们提出了LyaGuide，一个统一的李雅普诺夫引导框架来解决这一限制，将流引导表述为李雅普诺夫控制问题。主要理论结果建立了引导流匹配与李雅普诺夫控制之间的等价关系，统一了多种引导策略。引入伪投影算子以确保李雅普诺夫条件，支持模型驱动和数据驱动两种设置。实验表明在样本质量等方面有持续改进且保持计算效率。
英文摘要
Flow matching has emerged as an effective framework for learning complex data distributions, but adapting pretrained flow models to new tasks often requires computationally expensive retraining. Post-training guidance provides a more efficient alternative, but existing methods are largely heuristic and offer no explicit stability guarantees. We address this limitation by proposing LyaGuide, a unified Lyapunov-guided framework that formulates flow guidance as a Lyapunov control problem. Our main theoretical result establishes an equivalence between guided flow matching and Lyapunov control, thereby unifying common guidance strategies, such as classifier guidance, reward guidance, and energy-based guidance, within a single control-theoretic framework. To enforce the Lyapunov condition, we introduce a pseudo-projection operator with a closed-form expression that endows learned or heuristic guidance terms with explicit stability guarantees. LyaGuide supports two practical settings: a model-driven setting, where the target guidance distribution is specified through a known Lyapunov function, and a data-driven setting, where the guidance is adapted from task-specific downstream data. LyaGuide is compatible with existing guidance methods, introduces minimal additional computational overhead, and is straightforward to integrate in practice. Extensive experiments on synthetic benchmarks, image inverse problems, reinforcement learning planning, and energy-based modeling demonstrate consistent improvements in sample quality, guidance fidelity, and robustness, while maintaining computational efficiency.
发表机构
- Imperial College London（伦敦帝国理工学院）
- Fudan University（复旦大学）
- Stanford University（斯坦福大学）
- MicroCyto（微赛生物）
机构由 AI 辅助整理，请以论文原文为准。
