We examine the Landau free energy surface of a diblock copolymer melt using self-consistent field theory. The topography of its surface is found to exhibit a low-energy pathway connecting the local minima associated with the cylindrical (C) and spherical (S) morphologies. The pathway corresponds to an epitaxial transition where the periodicity of the two phases is matched with the cylinder axis oriented in one of the [111] directions of the bcc spheres. The energy barriers and stability limits are evaluated, and from them we conclude that the C <---->S transition should normally occur by a nucleation and growth mechanism. Based on the generally small energy barriers, we suggest that fluctuation effects are much stronger than previously anticipated. Furthermore, we examine the way the morphology evolves during a transition and discuss its signature in a small-angle scattering experiment.