Although remote sensing image registration has been widely studied, accurate registration of multimodal remote sensing images is still challenging due to the presence of geometric deformation and radiometric differences between images of different modalities. We propose a two-stage coarse-to-fine registration network based on the U-Net network architecture. The network considers both the registration of large-scale affine transformations and local registration using flow field prediction, using flow field to fine tune affine registration. A Swin-U-KAN network is proposed for affine deformation, which embeds KAN convolution and Swin transformer into a U-net network with encoder-decoder structure. A U-Net network with parallel convolution blocks is proposed for fine registration of flow field prediction. The proposed network is evaluated on SAR-optical and infrared-optical image pairs with large-scale affine deformation, and compared with the current state-of-the-art registration methods. Experimental results show that the proposed network has good registration effect.