Labeled sequence transduction is a task of transforming one sequence into another sequence that satisfies desiderata specified by a set of labels. In this paper we propose multi-space variational encoder-decoders, a new model for labeled sequence transduction with semi-supervised learning. The generative model can use neural networks to handle both discrete and continuous latent variables to exploit various features of data. Experiments show that our model provides not only a powerful supervised framework but also can effectively take advantage of the unlabeled data. On the SIGMORPHON morphological inflection benchmark, our model outperforms single-model state-of-art results by a large margin for the majority of languages.