We introduce the problem of perpetual view generation - long-range generation of novel views corresponding to an arbitrarily long camera trajectory given a single image. This is a challenging problem that goes far beyond the capabilities of current view synthesis methods, which quickly degenerate when presented with large camera motions. Methods for video generation also have limited ability to produce long sequences and are often agnostic to scene geometry. We take a hybrid approach that integrates both geometry and image synthesis in an iterative render, refine, and repeat framework, allowing for long-range generation that cover large distances after hundreds of frames. Our approach can be trained from a set of monocular video sequences. We propose a dataset of aerial footage of coastal scenes, and compare our method with recent view synthesis and conditional video generation baselines, showing that it can generate plausible scenes for much longer time horizons over large camera trajectories compared to existing methods. Project page at https://infinite-nature.github.io/.