<p>The rapid advancement of machine learning techniques has motivated research exploring their application to geostatistical modeling. Generative adversarial networks (GANs) are a machine learning framework based on training two neural networks known as a generator and a discriminator simultaneously and by an adversarial process to generate models that reproduce the underlying distribution of the training data. This paper explores the application of a GAN with deep convolutional neural networks to generate geological models of categorical variables. An ensemble of training images is used to train the generator to produce fake models that are not distinguishable from real ones, while the discriminator is trained simultaneously to distinguish between the real and fake models. The trained network can process random inputs and generate realizations that honor the spatial continuity of the training images. Conditioning to drill hole data is also integrated into the training process to generate an ensemble of conditional realizations that can capture the geological uncertainty. In this paper, a comprehensive overview of the theoretical foundation of a GAN is provided. A case study is developed to demonstrate application of a GAN to produce multiple realizations of a conceptual geological model informed by drill hole data and training models. A comparison with multiple point statistics (MPS) is conducted to assess the performance of the GAN.</p>