Molecular dynamics simulations for the penetrable-sphere model have been carried out over a wide range of the packing fraction φ and the repulsive energy parameter ε* to investigate the self-diffusion properties of the bounded repulsive fluids. The resulting self-diffusion data D are compared with theoretical approximations including Boltzmann and Enskog diffusion predictions in the gas kinetic theory. Empirical Enskog-like approximation based on the Enskog theory in the hard-sphere model we also proposed. The product of φD exhibits the transitional behavior from a nearly constant function of density in the lower repulsive system (ε*=0.25) where the soft-type collisions are dominant, to a rapidly decreasing function in the higher repulsive system (ε*=4.0) where most particle collisions are the hard-type reflections. For highly repulsive systems with high densities, a relatively poor agreement with our proposed prediction are observed due to the cluster-forming structure and phase transition from the fluid-like to the solid-like state in such bounded repulsive fluids.