Diffusion is the result of Brownian motion and must occur with a finite velocity. The earlier presented nonlinear diffusion equation, with diffusion coefficients that are directly proportional to the concentration of impurities, defines the maximum depth of penetration. For nonlinear diffusion from a constant source, the depth of the impurities’ penetration is directly proportional to the square root of the diffusion time. Profiles of nonlinear solutions differ from classical linear solutions on great distances and are in good fitting with experiment. We increased the accuracy of the approximate analytical solutions for nonlinear diffusion in the plane from a square infinite source with fixed initial impurity concentrations in the corners. The nonlinear diffusion equation for the solution was transformed by introducing similarity variables.