The structural solution problem can be a daunting and time-consuming task. Especially in the presence of impurity phases, current methods, such as indexing, become more unstable. In this work, the novel approach of semi-supervised learning is applied towards the problem of identifying the Bravais lattice and the space group of inorganic crystals. The reported semi-supervised generative deep-learning model can train on both labeled data, i.e. diffraction patterns with the associated crystal structure, and unlabeled data, i.e. diffraction patterns that lack this information. This approach allows the models to take advantage of the troves of unlabeled data that current supervised learning approaches cannot, which should result in models that can more accurately generalize to real data. In this work, powder diffraction patterns are classified into all 14 Bravais lattices and 144 space groups (the number is limited due to sparse coverage in crystal structure databases), which covers more crystal classes than other studies. The reported models also outperform current deep-learning approaches for both space group and Bravais lattice classification using fewer training data.