Infrared-visible image fusion plays a vital role in multi-modal vision tasks such as surveillance, navigation, and target recognition. While deep learning has advanced the field, most fusion networks are still empirically designed, lacking theoretical interpretability. To address this, we propose DLRF-Net, an end-to-end framework built upon a mathematically formulated low-rank decomposition model. By reformulating fusion as a constrained optimization problem, DLRF-Net embeds its solution into a structured convolutional network, effectively disentangling low-rank and sparse components for interpretable feature representation. A hierarchical loss further enforces multi-level constraints to preserve visible details and highlight infrared saliency. Experiments on benchmark datasets show that DLRF-Net outperforms state-of-the-art methods in both visual quality and quantitative metrics, while maintaining a compact architecture—validating the effectiveness of representation-guided network design.