Multimodal fusion learning (MFL) has shown great potential in the medical domain, where we are faced with disparate data modalities such as imaging, clinical records, and omics. However, existing MFL strategies face several major challenges. First, they struggle to capture complex cross-modal interactions effectively, which in turn limits performance improvements. Second, they incur high computational costs, restricting their applicability in resource-constrained healthcare AI applications. Finally, they are often designed and evaluated for narrow, fixed modality configurations (e.g., imaging-only, or specific pairs such as image and omics), which limits evidence of their adaptability and generalizability to broader collections of heterogeneous medical modalities. To address these challenges, we propose a novel MFL framework - Cascaded Unified Representation Learning for Efficient Fusion Network (CURE) - a lightweight and scalable framework that progressively integrates various modalities through a novel efficient Hybrid Geometry Aware Fusion layer (HyFuse), where each HyFuse layer is sequentially learned for each modality, making the framework adaptable and generalizable. Within HyFuse, an efficient residual convolution module captures rich multi-scale features to ensure cost-effective learning, while a hybrid-space aware attention mixer learns coarse-to-fine structural cues to better preserve cross-modal relationships. Complementary learnable late-fusion and shared information refinement modules are then employed to learn robust modality-order-invariant shared representations, which in turn yields consistent performance improvements. Extensive evaluations on 16 public datasets show that CURE outperforms leading multimodal fusion methods, boosting performance by up to 3.97% and lowering computational costs by up to 87.8%, ensuring more effective and reliable predictions.

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