The free-draining properties of DNA normally make it impossible to separate nucleic acids by free-flow electrophoresis. However, little is known, either theoretically or experimentally, about the diffusion coefficient of DNA molecules during free-flow electrophoresis. In fact, many authors simply assume that the Nernst-Einstein relation between the mobility and the diffusion coefficient still holds under such conditions. In this paper, we present an experimental study of the diffusion coefficient of both ssDNA and dsDNA molecules during free-flow electrophoresis. Our results unequivocally show that a simplistic use of Nernst-Einstein's relation fails, and that the electric field actually has no effect on the thermal diffusion process. Finally, we compare the dependence of the diffusion coefficient upon DNA molecular size to results obtained previously by other groups and to Zimm's theory.