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. Previous studies have shown 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 independently trained 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 a better generative quality of unimodal VAEs with coherent integration across different modalities using the latent score-based model. In addition, our approach provides the best unconditional coherence.