New Lyapunov Guidance Framework Stabilizes Generative AI Models

Flow matching is a powerful technique for learning complex data distributions, but adapting these pretrained generative flow models to new tasks typically requires computationally intensive retraining. While post-training guidance offers a more efficient alternative, existing methods often lack explicit stability guarantees and are largely heuristic. Researchers have developed LyaGuide, a novel Lyapunov-guided framework that addresses these limitations. LyaGuide reframes flow guidance as a Lyapunov control problem, establishing a theoretical equivalence between guided flow matching and Lyapunov control. This unification brings various guidance strategies, such as classifier, reward, and energy-based guidance, under a single, control-theoretic umbrella. A key innovation is the introduction of a pseudo-projection operator with a closed-form expression, which imbues learned or heuristic guidance terms with explicit stability guarantees. LyaGuide supports both model-driven (known Lyapunov function) and data-driven (adapted from task-specific data) settings, is compatible with existing guidance methods, and adds minimal computational overhead. Extensive experiments across diverse applications, including image inverse problems and reinforcement learning, demonstrate consistent improvements in sample quality, guidance fidelity, and robustness.