Image fusion aims to effectively integrate complementary information from multi-modal images into a single image with enhanced representational capacity. However, simultaneously preserving structural semantics and texture details during the fusion process remains a significant challenge. To address this, we propose an innovative fusion framework based on frequency-domain decomposition and implicit space modeling, termed KMMF-Net. This method employs a lightweight Mamba network as the backbone to extract discriminative features from the input images. Subsequently, the extracted features are decomposed into high-frequency and low-frequency components using the Fast Fourier Transform (FFT). In the low-frequency branch, we introduce a KAN-based implicit space fusion strategy to project structural features from different modalities into a unified implicit space for alignment and integration. To further enhance structural consistency, a low-frequency enhancement module is designed to refine these features. In the high-frequency branch, a dedicated high-frequency enhancement module is constructed to reinforce texture and edge information, thereby better preserving fine details. Finally, the fused high- and low-frequency features are reconstructed into the final output image. Extensive experiments on infrared-visible and medical image fusion tasks demonstrate that KMMF-Net achieves state-of-the-art performance in both visual quality and objective metrics. This method offers a unified and interpretable solution for frequency-domain image fusion tasks. The code is available at https://github.com/fengjiawei123/KMMF-Net .