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LyapuFlow improves control of generative models for inverse problems

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.

Sat 3 OctMachine Learning

The gist

Inverse problems are about working backward from observed data to find the cause. Generative models help by producing likely solutions, but guiding them to meet specific conditions is tricky. The authors developed LyapuFlow, which uses feedback control to steer these models toward solutions that obey constraints without retraining. This approach adjusts the sampling only when necessary, keeping the generative model's original behavior mostly intact and improving results in both scientific and image-related problems.

Open → 2610.04326v1