Magnetic Resonance Imaging (MRI) enables comprehensive evaluation through the integration of multiple modalities, providing diverse information to enhance diagnostic and therapeutic decision-making. However, radiation exposure and restricted equipment availability often lead to modality missing, requiring effective solutions. Existing synthesis methods remain inflexible in accommodating variable numbers of missing modalities and insufficient utilization of cross-modal information correlations. To address these limitations, we propose the unified multi-modal aggregated-masked diffusion network (UMADN) for multi-modal MRI synthesis with missing modalities. UMADN leverages an aggregated mask module to enable unified synthesis, accommodating arbitrary modality missing. Moreover, the Cross-Modal Interaction block employs the attention mechanism to explore cross-modal interactions while following multi-modal spatial consistency. Experimental results demonstrate that UMADN achieves superior performance compared with other competing methods in handling various scenarios of modality missing.