We present a theory for describing the evolution of a galaxy caused by stochastic events such as weak mergers, transient spiral structure, orbiting blobs, etc. This noise excites large-scale patterns that drives the evolution of the galactic density profile. In dark-matter haloes, the repeated stochastic perturbations preferentially ring the lowest-order modes of the halo with only a very weak dependence on the details of their source. Shaped by these modes, the profile quickly takes on a nearly self-similar form. We show that this form has the features of the “universal profile” reported by Navarro, Frenk, & White independent of initial conditions in a companion paper. In this sense, this noise-driven process is a near-equilibrium form of violent relaxation.