  Normally hyperbolic invariant manifolds theory provides an efficient tool for
proving diffusion in dynamical systems. In this paper we develop a methodology
for computer assisted proofs of diffusion in a-priori chaotic systems based on
this approach. We devise a method, which allows us to validate the needed
conditions in a finite number of steps, which can be performed by a computer by
means of rigorous-interval-arithmetic computations. We apply our method to the
generalized standard map, obtaining diffusion over an explicit range of
actions.
