We study the horizontal expansion of vertically confined ultracold atoms in the presence of disorder. Vertical confinement allows us to realize a situation with a few coupled harmonic oscillator quantum states. The disordered potential is created by an optical speckle at an angle of 30° with respect to the horizontal plane, resulting in an effective anisotropy of the correlation lengths of a factor of 2 in that plane. We observe diffusion leading to non-Gaussian density profiles. Diffusion coefficients, extracted from the experimental results, show anisotropy and strong energy dependence, in agreement with numerical calculations.