Quantum confinement effects are known to affect the behavior of molecules adsorbed in nanostructured materials. In order to study these effects on the transport of a single molecule through a nanotube, we present a quantum dynamics study on the diffusion of H2 in a narrow (8,0) carbon nanotube in the low pressure limit. Transmission coefficients for the elementary step of the transport process are calculated using the flux correlation function approach and diffusion rates are obtained using the single hopping model. The different time scales associated with the motion in the confined coordinates and the motion along the nanotube's axis are utilized to develop an efficient and numerically exact approach, in which a diabatic basis describing the fast motion in the confined coordinate is employed. Furthermore, an adiabatic approximation separating the dynamics of confined and unbound coordinates is studied. The results obtained within the adiabatic approximation agree almost perfectly with the numerically exact ones. The approaches allow us to accurately study the system's dynamics on the picosecond time scale and resolve resonance structures present in the transmission coefficients. Resonance enhanced tunneling is found to be the dominant transport mechanism at low energies. Comparison with results obtained using transition state theory shows that tunneling significantly increases the diffusion rate at T < 120 K.