The translational motion of atoms in a liquid confined between two plane parallel repulsive walls is studied by computer simulation. It is shown that the motion perpendicular to the walls cannot be described in a strict sense by the conventional diffusion equation even if the diffusion constant is generalized to a space dependent diffusion tensor. Instead, for the anisotropic case, a system of linear coupled rate equations is proposed, whose time-independent rate transition matrix is shown to be necessarily spatially asymmetric, with the equilibrium mean static density as its zero eigenvalue eigenvector. This accurately describes the transverse atomic motion for times considerably larger than the velocity autocorrelation time without the need to empirically input the mean static density. This theory is tested by computer simulation and found within statistical error to be a valid quasi-microscopic description of the (slower) stochastic atomic motion. The evolution of the anisotropic self-diffusion propagators towards the quasi-periodic mean density profile is studied in detail as a function of the initial starting position.