Soft robots exhibit complex nonlinear dynamics with large degrees of freedom, making their modelling and control challenging. Typically, reduced-order models in time or space are used in addressing these challenges, but the resulting simplification limits soft robot control accuracy and restricts their range of motion. In this work, we introduce an end-to-end learning-based approach for fully dynamic modelling of any general robotic system that does not rely on predefined structures, learning dynamic models of the robot directly in the visual space. The generated models possess identical dimensionality to the observation space, resulting in models whose complexity is determined by the sensory system without explicitly decomposing the problem. To validate the effectiveness of our proposed method, we apply it to a fully soft robotic manipulator, and we demonstrate its applicability in controller development through an open-loop optimization-based controller. We achieve a wide range of dynamic control tasks including shape control, trajectory tracking and obstacle avoidance using a model derived from just 90 min of real-world data. Our work thus far provides the most comprehensive strategy for controlling a general soft robotic system, without constraints on the shape, properties, or dimensionality of the system.