Not OP, but I wonder if the process would be in some way comparable to rigging a 3D model. There is well, you usually have some high-level input parameters, which influence joints on a predefined skeleton, which in turn determines the position of individual vertices in the 3D body. Finally, the 3D shape is used to render the actual pixels.

On each step, high-level parameters are combined with predefined weights to produce a more low-level output.

Seems, a similar transformation is going on here, except that the weights and the structure are somehow learned on its own.