The theory of photon counting histograms for fluorescent molecules diffusing through a laser spot is presented. Analytic expressions for the factorial cumulants of photon counts are obtained. For an arbitrary counting time window, it is shown how the exact histograms can be obtained by solving an appropriate reaction-diffusion equation. Our formalism reduces correctly when the molecules are immobile. The approximation used in fluorescence intensity multiple distribution analysis (FIMDA) is tested against the exact numerical solution of the problem. FIMDA works very well for a wide range of parameters except for small concentrations and long time windows.