Abstract
Flow matching-based generative models have been integrated into the plug-and-play image restoration framework, and the resulting plug-and-play flow matching (PnP-Flow) model has achieved some remarkable empirical success for image restoration. However, the theoretical understanding of PnP-Flow lags its empirical success. In this paper, we derive a continuous limit for PnP-Flow, resulting in a stochastic differential equation (SDE) surrogate model of PnP-Flow. The SDE model provides two particular insights to improve PnP-Flow for image restoration: (1) It enables us to quantify the error for image restoration, informing us to improve step scheduling and regularize the Lipschitz constant of the neural network-parameterized vector field for error reduction. (2) It informs us to accelerate off-the-shelf PnP-Flow models via extrapolation, resulting in a rescaled version of the proposed SDE model. We validate the efficacy of the SDE-informed improved PnP-Flow using several benchmark tasks, including image denoising, deblurring, super-resolution, and inpainting. Numerical results show that our method significantly outperforms the baseline PnP-Flow and other state-of-the-art approaches, achieving superior performance across evaluation metrics.
Abstract (translated)
基于流匹配的生成模型已被集成到“即插即用”的图像恢复框架中，由此产生的即插即用流匹配（PnP-Flow）模型在图像恢复方面取得了显著的实际成功。然而，关于PnP-Flow的理论理解落后于其实际表现。在这篇论文中，我们为PnP-Flow推导出了一个连续极限，并得出了一种随机微分方程（SDE）替代模型来表示PnP-Flow。该SDE模型提供了两个特别的见解，以改进用于图像恢复的PnP-Flow：(1) 它使我们可以量化图像恢复中的误差，告知我们如何优化步长调度并调节神经网络参数化向量场的Lipschitz常数，从而减少误差。(2) 它还告诫我们可以通过外推加速现成的PnP-Flow模型，这导致了提议SDE模型的一个重缩放版本。我们使用包括图像去噪、去模糊、超分辨率和插值在内的多个基准任务来验证增强版PnP-Flow（基于SDE）的有效性。数值结果显示，我们的方法在评估指标上显著优于基线的PnP-Flow和其他最先进方法，实现了卓越的整体性能。
URL
https://arxiv.org/abs/2512.04283
