Unified synthesis of missing MRI sequences facilitates robust image analysis in brain tumor patients when imaging data are incomplete. We present a unified framework based on the Mixture of Multimodal Hierarchical Variational Autoencoders (MMHVAE), which performs cross-modal MRI synthesis with arbitrary missing sequences. MMHVAE leverages a hierarchical latent representation and a mixture of unimodal posteriors to flexibly model incomplete inputs. For the MICCAI 2025 BraSyn challenge, our approach synthesizes one randomly missing sequence from the remaining three, while addressing inter-center acquisition variability through contrast harmonization. On the BraSyn validation set, the method achieves high-quality synthesis with Structural Similarity Index Measures (SSIM) exceeding \(99.7\%\) in tumor regions and promising Dice scores in downstream tumor segmentation tasks. These results demonstrate the potential of MMHVAE as a unified solution for brain MRI synthesis in the presence of missing sequences.