The intense inner radiation belt at Jupiter (>50 MeV at 1.5 RJ) is generally accepted to be created by radial diffusion of electrons from further away from the planet. However, this requires a source with energies that exceed 1 MeV outside the orbit of the moon Io at 5.9 RJ, which has never been explained satisfactorily. Here we test the hypothesis that this source population could be formed from a very soft energy spectrum, by particle injection processes and resonant electron acceleration via whistler mode chorus waves. We use the British Antarctic Survey Radiation Belt Model to calculate the change in the electron flux between 6.5 and 15 RJ; these are the first simulations at Jupiter combining wave particle interactions and radial diffusion. The resulting electron flux at 100 keV and 1 MeV lies very close to the Galileo Interim Radiation Electron model spectrum after 1 and 10 days, respectively. The primary driver for the increase in the flux is cyclotron resonant acceleration by chorus waves. A peak in phase space density forms such that inside L≈9 radial diffusion transports electrons toward Jupiter, but outside L≈9 radial diffusion acts away from the planet. The results are insensitive to the softness of the initial energy spectrum but do depend on the value of the flux at the minimum energy boundary. We conclude by suggesting that the source population for the inner radiation belt at Jupiter could indeed be formed by wave-particle interactions.