In this work, the question of the coherency matrix propagation of a light beam is addressed by means of the analysis of interpolation processes between two physical situations. These physical situations are defined according to the second order statistical properties of the underlying process. Two states of a light beam or the path in a medium to go from a physical situation at distance $z_1$ to another one at distance $z_2$ is related to the correlation between both these physical situations. Equivalence classes are derived from the definition of a group action on the set of coherency matrices. The geodesic curves on each equivalence class define the process of interpolation. The general solution is derived as a symbolic equation, and the solution is explicitly developed for the situation of uncorrelated statistical processes. Interpolating coherency matrix in this particular case describes the propagation of a light beam into a uniform nondepolarizing medium characterized by a differential Jones matrix determined by the far points of the interpolation curve up to a unitary matrix.