We study the problem of multilingual automated reply suggestions (RS) model serving many languages simultaneously. Multilingual models are often challenged by model capacity and severe data distribution skew across languages. While prior works largely focus on monolingual models, we propose Conditional Generative Matching models (CGM), optimized within a Variational Autoencoder framework to address challenges arising from multilingual RS. CGM does so with expressive message conditional priors, mixture densities to enhance multi-lingual data representation, latent alignment for language discrimination, and effective variational optimization techniques for training multi-lingual RS. The enhancements result in performance that exceed competitive baselines in relevance (ROUGE score) by more than 10% on average, and 16% for low resource languages. CGM also shows remarkable improvements in diversity (80%) illustrating its expressiveness in representation of multi-lingual data.