An earlier equivalent-particle theory, describing the propagation of a self-focused light channel at an oblique angle of incidence to the interface separating two nonlinear dielectric media [A. B. Aceves, J. V. Moloney, and A. C. Newell, J. Opt. Soc. Am. B 5, 559 (1988); Phys. Lett. A 129, 231 (1988); Phys. Rev. A 39, 1809 (1989); 39, 1828 (1989)], is extended to include diffusion of the nonlinear excitation within each medium. The theory replaces the computationally intensive problem of beam propagation by the much simpler and intuitive picture of the motion of an equivalent particle in an equivalent potential. This simpler Newtonian dynamical problem provides quantitative information on the asymptotes of the reflected, transmitted, or trapped channels as well as the stability of the latter as a function of increasing diffusion length. Our main results are that increased diffusion makes light transmission more difficult and tends to wash out the local equilibria of the equivalent potential representing unstable or stable TE nonlinear surface waves. © 1990 The American Physical Society.