Diffusion in Hamiltonian systems with a modulation in the force amplitude is analyzed. The modulation of the force expands the spectrum and, hence, the diffusion region, provided that the Chirikov overlap parameter exceeds the threshold for stochasticity in the expanded domain. Analytical formulas for the diffusion coefficient are derived as a function of modulation parameters, and the results are compared with the numerical solutions of the dynamical equations. For periodic modulation there is no diffusion in the nonresonant region, while for an irregular modulation involving random changes in the particle phase space coordinates, the diffusion extends into the nonresonant region. The nonresonant diffusion coefficient is found to decrease at least as |υ−υp|-4, the detailed behavior being strongly dependent on the modulation parameters. Here, υ is the particle velocity and υp denotes the average phase velocity of the force spectrum.