Sedjro Salomon Hotegni, Konstantin Sonntag, Paul-Christian Bürkner, Sebastian Peitz
原文摘要
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.
In this paper, we present a Koopman autoencoder-based least-squares policy iteration (KAE-LSPI) algorithm for reinforcement learning (RL). The KAE-LSPI algorithm is based on reformulating the so-called least-squares fixed-point approximation method in terms of extended dynamic mode decomposition (EDMD), thereby enabling automatic feature learning via the Koopman autoencoder (KAE) framework. The approach is motivated by the lack of a systematic procedure for selecting features or kernels in linear RL techniques. Unlike previous approaches, no features or kernels need to be fixed a priori in our method. We discuss the theoretical convergence of KAE-LSPI under suitable assumptions, similar to kernel-based least-squares policy iteration (KLSPI). We empirically compare our method with two existing algorithms: least-squares policy iteration (LSPI) and KLSPI. In particular, for the chainwalk problem, the resulting policies are either optimal or nearly optimal for both three approaches. For the cart-pole system, KAE-LSPI outperforms the other two approaches in terms of policy performance.