We present a framework for visual action planning of complex manipulation tasks with high-dimensional state spaces such as manipulation of deformable objects. Planning is performed in a low-dimensional latent state space that embeds images. We define and implement a Latent Space Roadmap (LSR) which is a graph-based structure that globally captures the latent system dynamics. Our framework consists of two main components: a Visual Foresight Module (VFM) that generates a visual plan as a sequence of images, and an Action Proposal Network (APN) that predicts the actions between them. We show the effectiveness of the method on a simulated box stacking task as well as a T-shirt folding task performed with a real robot.