The rate-determining step for the metal-catalyzed formation of filamentous carbon from hydrocarbons and carbon monoxide is commonly assumed to be diffusion of dissolved carbon through the metal particle. The driving force for the diffusion process has been proposed to be either an isothermal carbon concentration gradient or a temperature gradient, the latter leading to Soret diffusion (mass transfer due to a gradient in the chemical potential resulting from the temperature gradient) and, possibly, effects from the temperature dependence of the solubility of carbon. Metal carbides often have been postulated to play a role as intermediates. Mass transfer by these processes is examined and expressions for carbon deposition rate and activation energy are derived. Experimental results are consistent only with a mechanism in which the driving force for carbon diffusion is an isothermal carbon concentration gradient and in which metal carbides are not intermediates. The temperature gradient mechanism was found to conflict with the fact that for metals with a large negative heat of transport for carbon diffusion, such as alpha-Fe, temperature gradients of the type proposed (in which the gas-phase side of the particle is hotter than the carbon filament side) would lead to diffusion of carbon away from the carbon filament rather than towards it. A possible role for metal carbide intermediates is limited to Fe, Ni, and Co. However, measured activation energies for these metals are in good agreement only with those values predicted assuming metal carbides do not participate as intermediates.