Abstract We propose sphere generative adversarial network (GAN), a novel integral probability metric (IPM)-based GAN. Sphere GAN uses the hypersphere to bound IPMs in the objective function. Thus, it can be trained stably. On the hypersphere, sphere GAN exploits the information of higher-order statistics of data using geometric moment matching, thereby providing more accurate results. In the paper, we mathematically prove the good properties of sphere GAN. In experiments, sphere GAN quantitatively and qualitatively surpasses recent state-ofthe-art GANs for unsupervised image generation problems with the CIFAR-10, STL-10, and LSUN bedroom datasets. Source code is available at https://github.com/ pswkiki/SphereGAN.