    # In the multimodal setting we assume the N modalities, $x_{1}, x_{2}, ..., x_{N}$, are conditionally independent given the common latent variable, z. That is we assume a generative model of the form $p_{\theta}(x_{1}, x_{2}, ..., x_{N}, z) = p(z)p_{\theta}(x_{1}|z)p_{\theta}(x_{2}|z)$$p_{\theta}(x_{N}|z)$. The conditional independence assumptions in the generative model imply a relation among joint- and simgle-modality posteriors. That is, the joint posterior is a procuct of individual posteriors, with an additional quotient by the prior.  
