- Abstract High energy scattering formulated as a classical branching process is considered within the framework of the QCD dipole model. Starting from Mueller's generating functional, we derive the high energy evolution law for the scattering amplitude. The amplitude's evolution is given by an infinite hierarchy of linear equations equivalent to the Balitsky's chain reduced to dipole operators. This new derivation of the hierarchy is the central result of the Letter. We also comment about target correlations which prevent the hierarchy from being expressed as the Balitsky–Kovchegov equation in closed form.