Lipschitz control improves stability in image restoration models
Lipschitz-Controlled Flow Matching for Robust Image Restoration
Computer Vision and Pattern Recognition
Summary
Image restoration models can sometimes create shaky or unstable images when small changes happen to the input. The authors propose a new approach called LipsFlower that helps the model stay steady by limiting how much small changes can grow during restoration. They built a special tool called LipHDiT to enforce this limit and tested it on restoring blurred or damaged faces. Their method keeps the restored images looking good while making the process more stable and reliable.
What this means in practice
- •For image processing engineers: Improve the reliability of image restoration tools by reducing sensitivity to noise and input changes.
- •For computer vision developers: Build more stable generative image models that maintain quality under adversarial conditions.
Authors
Sedjro Salomon Hotegni, Konstantin Sonntag, Paul-Christian Bürkner, Sebastian Peitz
Abstract
Flow-matching models can produce high-quality image restorations, but their learned dynamics may amplify small input perturbations and make reconstructions unstable. We introduce LipsFlower to reduce this amplification. We derive stability bounds for Flow-from-$Y$, which initializes the ordinary differential equation from a noise-perturbed observation, as well as for observation-conditioned posterior sampling, which conditions the velocity field on the observation throughout integration. Based on this analysis, we develop LipHDiT, a Lipschitz-aware hourglass diffusion transformer that serves as the vector-field architecture of LipsFlower. LipHDiT incorporates stabilized approximate spectral normalization, bounded modulation, and convex residual mixing. We also use adversarial finite-radius gain regularization at sampled interpolation states to penalize excessive sensitivity to the state and, for conditional sampling, the observation. We test both formulations on blind face restoration, measuring adversarial robustness and the perceptual quality of the reconstructions. LipsFlower reduces perturbation amplification while keeping restoration quality competitive with the evaluated baselines. These results suggest that Lipschitz-aware flow matching can improve the stability of generative image restoration.