We report energy transfer experiments on poly(butyl methacrylate) (PBMA) latex films prepared from a 1:1 mixture of donor- and acceptor-labeled latex particles. In one set of samples, the particles contain low molecular weight polymer (M-w = 34 000) comparable to the entanglement molecular weight (M-e) of PBMA. For this sample, the extent of mixing f(m) (defined as the fractional increase in the energy transfer quantum yield) increased with time as t(1/2), consistent with diffusion that follows Fick's law. In the second set of experiments, involving polymer with M-w = 380 000 (M-w > 10M(e)), we observe a change in the time dependence of f(m). At early times, for values of f(m) < 0.2, f(w) scales as t(1/2). There is a sharp crossover to a t(1/4) scaling relationship for values of f(m) > 0.2. The most likely explanation of the early-time behavior is Fickian diffusion of the lowest molecular weight components of the broadly disperse polymer (M-w/M-n = 3). The scaling of f(m) with t1/4 does not appear to be consistent with the predictions of the theory of polymer diffusion across interfaces. The parameter f(m) is a measure of the number of monomers crossing the interface N(t). For diffusion across a planar interface, N(t) is predicted to increase as t(3/4) if the chain ends are uniform and as t(1/2) if they are segregated to the interface.