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We present a method for learning to generate unbounded flythrough videos of natural scenes starting from a single view. This capability is learned from a collection of single photographs, without requiring camera poses or even multiple views of each scene. To achieve this, we propose a novel self-supervised view generation training paradigm where we sample and render virtual camera trajectories, including cyclic camera paths, allowing our model to learn stable view generation from a collection of single views. At test time, despite never having seen a video, our approach can take a single image and generate long camera trajectories comprised of hundreds of new views with realistic and diverse content. We compare our approach with recent state-of-the-art supervised view generation methods that require posed multi-view videos and demonstrate superior performance and synthesis quality. Our project webpage, including video results, is at infinite-nature-zero.github.io.