Learning low-dimensional latent state space dynamics models has proven powerful for enabling vision-based planning and learning for control. We introduce a latent dynamics learning framework that is uniquely designed to induce proportional controlability in the latent space, thus enabling the use of simple and well-known PID controllers. We show that our learned dynamics model enables proportional control from pixels, dramatically simplifies and accelerates behavioural cloning of vision-based controllers, and provides interpretable goal discovery when applied to imitation learning of switching controllers from demonstration. Notably, such proportional controlability also allows for robust path following from visual demonstrations using Dynamic Movement Primitives in the learned latent space.