Two mechanisms can cause similar broadening of pulses in a pulse train: variable temporal/spectral phase in a train of identical pulses (a deterministic mechanism) and partial correlations between different frequency components of the pulses (a stochastic mechanism). We discuss methods to distinguish between these two fundamentally different mechanisms. We show that their roles can be separated, at least for an important class of fields known as Gaussian Schell-model pulses, using time-resolved intensity measurements of pulses passing through Michelson's interferometer.