Robotic fabric manipulation has applications in home robotics, textiles, senior care and surgery. Existing fabric manipulation techniques, however, are designed for specific tasks, making it difficult to generalize across different but related tasks. We extend the Visual Foresight framework to learn fabric dynamics that can be efficiently reused to accomplish different fabric manipulation tasks with a single goal-conditioned policy. We introduce VisuoSpatial Foresight (VSF), which builds on prior work by learning visual dynamics on domain randomized RGB images and depth maps simultaneously and completely in simulation. We experimentally evaluate VSF on multi-step fabric smoothing and folding tasks against 5 baseline methods in simulation and on the da Vinci Research Kit (dVRK) surgical robot without any demonstrations at train or test time. Furthermore, we find that leveraging depth significantly improves performance. RGBD data yields an 80% improvement in fabric folding success rate over pure RGB data. Code, data, videos, and supplementary material are available at https://sites.google.com/view/fabric-vsf/.