We describe a method for learning a group of continuous transformation operators to traverse smooth nonlinear manifolds. The method is applied to model how natural images change over time and scale. The group of continuous transform operators is represented by a basis that is adapted to the statistics of the data so that the infinitesimal generator for a measurement orbit can be produced by a linear combination of a few basis elements. We illustrate how the method can be used to efficiently code time-varying images by describing changes across time and scale in terms of the learned operators.