  In recent years, deep generative models have been shown to 'imagine'
convincing high-dimensional observations such as images, audio, and even video,
learning directly from raw data. In this work, we ask how to imagine
goal-directed visual plans -- a plausible sequence of observations that
transition a dynamical system from its current configuration to a desired goal
state, which can later be used as a reference trajectory for control. We focus
on systems with high-dimensional observations, such as images, and propose an
approach that naturally combines representation learning and planning. Our
framework learns a generative model of sequential observations, where the
generative process is induced by a transition in a low-dimensional planning
model, and an additional noise. By maximizing the mutual information between
the generated observations and the transition in the planning model, we obtain
a low-dimensional representation that best explains the causal nature of the
data. We structure the planning model to be compatible with efficient planning
algorithms, and we propose several such models based on either discrete or
continuous states. Finally, to generate a visual plan, we project the current
and goal observations onto their respective states in the planning model, plan
a trajectory, and then use the generative model to transform the trajectory to
a sequence of observations. We demonstrate our method on imagining plausible
visual plans of rope manipulation.
