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Systematic compositionality, or the ability to adapt to novel situations by creating a mental model of the world using reusable pieces of knowledge, remains a significant challenge in machine learning. While there has been considerable progress in the language domain, efforts towards systematic visual imagination, or envisioning the dynamical implications of a visual observation, are in their infancy. We introduce the Systematic Visual Imagination Benchmark (SVIB), the first benchmark designed to address this problem head-on. SVIB offers a novel framework for a minimal world modeling problem, where models are evaluated based on their ability to generate one-step image-to-image transformations under a latent world dynamics. The framework provides benefits such as the possibility to jointly optimize for systematic perception and imagination, a range of difficulty levels, and the ability to control the fraction of possible factor combinations used during training. We provide a comprehensive evaluation of various baseline models on SVIB, offering insight into the current state-of-the-art in systematic visual imagination. We hope that this benchmark will help advance visual systematic compositionality.