We investigate the effect of chain architecture on the self-diffusion of poly(styrene)-poly(ethylene) triblock (PS-PE-PS or SES) and pentablock (PS-PE-PS-PE-PS or SESES) copolymers with a cylindrical domain structure (E cylinders). Transmission electron microscopy (TEM) and grazing-incidence small-angle X-ray scattering (GISAXS) are employed to reveal the microstructure of the block copolymer films, and dynamic secondary ion mass spectroscopy (DSIMS) is used to obtain diffusion coefficients. The triblock copolymer (SES) chains diffuse through a randomly oriented cylindrical structure via a "hopping" mechanism where the normalized diffusion coefficient D/D-0 (D is the diffusion coefficient of the block copolymer and D-0 is the diffusion coefficient of a disordered (hypothetical) block copolymer of similar M-w) decreases exponentially with the thermodynamic barrier chi N-PE, where chi is the Flory interaction parameter between styrene and ethylene and N-PE is the degree of polymerization of the poly(ethylene) block. However, the pentablock copolymer (SESES) diffuses via a "walking" mechanism through an ordered cylindrical structure which involves the activation of a single E block at a time to overcome the thermodynamic barrier. Both mechanisms have been reported previously for diblock and triblock copolymers, respectively. Hence, for a similar overall M-w the pentablock copolymer diffuses faster than the corresponding triblock copolymer. Moreover, a comparison is made between perpendicular and parallel diffusion in the pentablock copolymer as both mechanisms are observed due to a change in the cylinder orientation (from parallel to perpendicular cylinders) as a function of depth. The relative independence of the parallel diffusion on chi N-PE suggests that the thermodynamic barrier for perpendicular diffusion does not affect parallel diffusion coefficients. However, the normalized parallel and perpendicular diffusion coefficients of the SESES pentablock copolymer as well as the normalized perpendicular diffusion coefficient of the SES triblock copolymer are substantially less than the corresponding diffusion coefficients of a cylinder-forming diblock copolymer investigated by Cavicchi and Lodge at the same values of chi N-cyl, where N-cyl is the degree of polymerization of the cylinder block. This comparison suggests that entangled loops in the PE midblock cylinders impose additional entropic barriers to diffusion that are absent for diblock copolymers.