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, we apply the novel approach of semi-supervised learning towards the problem of identifying the Bravais lattice and the space group of inorganic crystals. Our semi-supervised generative deep learning model can train on both labeled data -- diffraction patterns with the associated crystal structure -- and unlabeled data, diffraction patterns that lack this information. This approach allows our 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, we classify powder diffraction patterns into all 14 Bravais lattices and 144 space groups (we limit the number due to sparse coverage in crystal structure databases), which covers more crystal classes than other studies. Our models also drastically outperform current deep learning approaches for both space group and Bravais Lattice classification using less training data.