Image fusion seeks to integrate complementary information from multiple sources into a single, superior image. While traditional methods are fast, they lack adaptability and performance. Conversely, deep learning approaches achieve state-of-the-art (SOTA) results but suffer from critical inefficiencies: their reliance on slow, resource-intensive, patch-based training introduces a significant gap with full-resolution inference. We propose a novel hybrid framework that resolves this trade-off. Our method utilizes a learnable U-Net to generate a dynamic guidance map that directs a classic, fixed Laplacian pyramid fusion kernel. This decoupling of policy learning from pixel synthesis enables remarkably efficient full-resolution training, eliminating the train-inference gap. Consequently, our model achieves SOTA-comparable performance in about one minute on a RTX 4090 or two minutes on a consumer laptop GPU from scratch without any external model and demonstrates powerful zero-shot generalization across diverse tasks, from infrared-visible to medical imaging. By design, the fused output is linearly constructed solely from source information, ensuring high faithfulness for critical applications. The codes are available at https://github.com/Zirconium233/HybridFusion