Numerical simulations have grown to play a central role in modern sciences over the years. The ever improving technology of supercomputers has made large and precise models available. However, this accuracy is often limited by the cost of computational resources. Lowering the simulation's spatial resolution in order to conserve resources can lead to key processes being unresolved. We have shown in a previous study how insufficient spatial resolution of the proton cyclotron instability leads to a misrepresentation of ion dynamics in hybrid-Vlasov simulations. This leads to larger than expected temperature anisotropy and loss cone shaped velocity distribution functions. In this study, we present a sub-grid numerical model to introduce pitch-angle diffusion in a 3D Cartesian velocity space, at a spatial resolution where the relevant wave-particle interactions were previously not correctly resolved. We show that the method is successfully able to isotropize loss cone shaped velocity distribution functions, and that this method could be applied to simulations in order to save computational resources and still correctly model wave-particle interactions.