Multimodal Variational Autoencoders (VAEs) represent a promising group of generative models that facilitate the construction of a tractable posterior within the latent space, given multiple modalities. Daunhawer et al. (2022) demonstrate that as the number of modalities increases, the generative quality of each modality declines. In this study, we explore an alternative approach to enhance the generative performance of multimodal VAEs by jointly modeling the latent space of unimodal VAEs using score-based models (SBMs). The role of the SBM is to enforce multimodal coherence by learning the correlation among the latent variables. Consequently, our model combines the superior generative quality of unimodal VAEs with coherent integration across different modalities.