Leaves of eudicots show tremendous morphological diversity. Remarkably different leaf morphologies may occur between closely-related species, as within-species variants, or even in the same plant. Diverse leaf shapes also emerge in molecular-level studies of reference plants including Arabidopsis thaliana, Cardamine hirsuta and tomato, where small genetic or hormonal changes yield significantly different forms. This lability of shapes, juxtaposed with similar molecular mechanisms underlying leaf development in reference plants, suggests that the striking diversity of eudicot leaves results from variations of a common generative program. Notably, this mechanism acts jointly on leaf shape and vasculature, patterning both marginal protrusions and corresponding veins in the blade. <br /><br /> Inspired by this perspective, we propose a geometric model of leaf development and diversity. It simulates development as a feedback between two processes: the dynamic patterning of growth centers at the leaf margin, and control of growth directions by veins associated with these points. Our models show that the spatial separation of the processes patterning and directing growth facilitates the generation of a wide range of leaf forms, from simple to lobed and compound. Additionally, transitions between different forms can be controlled in a continuous manner. These transitions reproduce frequently observed, and often drastic, changes in leaf form within the same plant or between closely related species. Our results highlight the flexible and self-organizing nature of leaf development, and provide a path towards an integrated understanding of their development and diversity.