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We present an anomaly detection method using Wasserstein generative adversarial networks (WGANs) on optical galaxy images from the wide-field survey conducted with the Hyper Suprime-Cam (HSC) on the Subaru Telescope in Hawai'i. The WGAN is trained on the entire sample, and learns to generate realistic HSC-like images that follow the distribution of the training data. We identify images which are less well-represented in the generator's latent space, and which the discriminator flags as less realistic; these are thus anomalous with respect to the rest of the data. We propose a new approach to characterize these anomalies based on a convolutional autoencoder (CAE) to reduce the dimensionality of the residual differences between the real and WGAN-reconstructed images. We construct a subsample of ~9,000 highly anomalous images from our nearly million object sample, and further identify interesting anomalies within these; these include galaxy mergers, tidal features, and extreme star-forming galaxies. The proposed approach could boost unsupervised discovery in the era of big data astrophysics.