Consideration of the physics and topology of the two-dimensional grain growth suggests that a stochastic expression is required for individual grain growth rates. Two sources for the stochastic behaviour are topological switching events and the average linear correlation between grain size and topological class. A size-based continuum stochastic formulation is presented on the basis of topological correlation. This analysis leads to a Fokker-Planck equation for the size distribution, which yields a unique self similar asymptotic state that is reached from arbitrary initial states. Grain size distributions obtained from these considerations arein good agreement with experimental observations.