Generative diffusion models can produce realistic images and videos, but making a specific edit or directing a particular movement remains challenging. This PhD seminar explores how to develop these capabilities, progressing from constructing useful training examples to using and controlling pretrained generative models. The research begins with improving visual supervision by connecting images with geometry and detailed language descriptions. It then turns to image editing, where suitable training examples are difficult to collect. By removing objects from photographs and reversing the resulting examples, we can train a model to add objects from written instructions. Keeping image editing as the goal, I next explore a different resource: the ability of pretrained video diffusion models to generate coherent changes over time. From a geometric perspective, these models implicitly represent the manifold of natural images—the space of plausible visual content. Expressing an edit as a gradual path along this manifold allows us to produce the requested change. Finally, video becomes the output we want to control. We develop a method that uses rough animations to specify the intended movement and a pretrained model to supply realistic detail and dynamics, enabling control over motion and appearance without additional training.