An analytical treatment for the extraction of diffusion coefficients from gas effusion data considers several cases: (a) diffusion from spheres in which the initial gas distribution results from generation of gas within the sphere; (b) diffusion from spheres in which the initial gas distribution results from incomplete, external infusion; and (c) diffusion from collections of spheres of variable size. For the last, the size distribution functions examined are the square, the normal, and the log-normal distributions. The analytical models for extracting diffusion coefficients for the above initial conditions are developed. The deviations from the results of the simple classical analysis, which assumes uniform particle size and uniform initial gas concentration, are examined. It is shown that errors of factors of 1.5 to 100 can arise if the classical analysis is used.