This paper presents an implementation of the phase vocoder within a Gaussian state-space framework. Rather than formulate the problem as a deterministic evolution of frequencies centered around a given bin, this evolution is treated stochastically by introducing noise into the dynamics matrix of the recursive state equation. This produces effects on the roughness of the input sound, which vary depending on the position within the matrix where the noise is added, how it is propagated throughout the matrix and further by the variance of the noise input.