Lyapunov Guidance: A Unified Framework for Stabilizing Generative Flows
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 energ...
| Authors | Jingdong Zhang, Xinze Li, Yize Jiang et al. |
|---|---|
| Primary category | cs.LG |
| Published | 15 July 2026 |
| Last updated at source | 15 July 2026 |
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