We investigate lattice Boltzmann (LB) modeling of multicomponent diffusion for finite Knudsen numbers. Analytic solutions for binary diffusion in narrow channels, where both molecular and Knudsen diffusion are of importance, are obtained for the standard and higher-order LB methods and validated against the results from the direct simulation Monte Carlo (DSMC) method. The LB methods are shown to reproduce the diffusion slip phenomena. In the DSMC method, while fluid particles are diffusely reflected on a wall, significant component slip and a kinetic boundary layer are observed. It is shown that a higher-order LB method accurately captures the characteristics observed in the DSMC method.