We present InfinityGAN, a method to generate arbitrary-resolution images. The problem is associated with several key challenges. First, scaling existing models to a high resolution is resource-constrained, both in terms of computation and availability of high-resolution training data. Infinity-GAN trains and infers patch-by-patch seamlessly with low computational resources. Second, large images should be locally and globally consistent, avoid repetitive patterns, and look realistic. To address these, InfinityGAN takes global appearance, local structure and texture into account.With this formulation, we can generate images with resolution and level of detail not attainable before. Experimental evaluation supports that InfinityGAN generates imageswith superior global structure compared to baselines at the same time featuring parallelizable inference. Finally, we how several applications unlocked by our approach, such as fusing styles spatially, multi-modal outpainting and image inbetweening at arbitrary input and output resolutions