The backbone of our model follows the general WGAN architecture which consists of two competing neural networks, the generator and the critic. The generator aims to produce samples which are similar to the ones in the training data given an atom composition chosen by the user, while the critic tries to assign low scores to the training and large scores to the generated samples. Both the generator and critic models are fully connected neural networks with core widths of 512 : 256 : 128 : 64 : 32 and 256 : 128 : 64 : 32 respectively. The generator takes 20 latent variables of random noise (see Supporting Information for results using 10 and 30 latent variables) as input and outputs 3N atoms coordinates ordered according to the list of requested atom types. The hyperparameters reported above are the result of a manual hyperparameter search and may be changed by the user. We note that the output of the generator does not satisfy permutation invariance, which is only handled later within the critic. We use leaky ReLU activation functions for both the generator and the critic, with the generator having an additional sigmoid activation applied to its output before being passed to the postprocessing step.