Image fusion aims to integrate complementary information from multiple source images to produce a more informative and visually consistent representation, benefiting both human perception and downstream vision tasks. Despite recent progress, most existing fusion methods are designed for specific tasks (i.e., multi-modal, multi-exposure, or multi-focus fusion) and struggle to effectively preserve source information during the fusion process. This limitation primarily arises from task-specific architectures and the degradation of source information caused by deep-layer propagation. To overcome these issues, we propose UniFusion, a unified image fusion framework designed to achieve cross-task generalization. First, leveraging DINOv3 for modality-consistent feature extraction, UniFusion establishes a shared semantic space for diverse inputs. Second, to preserve the understanding of each source image, we introduce a reconstruction-alignment loss to maintain consistency between fused outputs and inputs. Finally, we employ a bilevel optimization strategy to decouple and jointly optimize reconstruction and fusion objectives, effectively balancing their coupling relationship and ensuring smooth convergence. Extensive experiments across multiple fusion tasks demonstrate UniFusion's superior visual quality, generalization ability, and adaptability to real-world scenarios. Code is available at https://github.com/dusongcheng/UniFusion.