In order to minimize the computational resources necessary for a given level of accuracy in a Lagrangian Vortex Particle Method, a novel particle core size adaptivity scheme has been created. The method adapts locally to the solution while preventing large particle size gradients, and optionally adapts globally to focus effort on important regions. It is implemented in the diffusion solver, which uses the Vorticity Redistribution Method, by allowing and accounting for variations in the core radius of participating particles. We demonstrate the effectiveness of this new method on the diffusion of a δ-function and impulsively started flow over a circular cylinder at Re = 9,500. In each case, the adaptive method provides solutions with marginal loss of accuracy but with substantially fewer computational elements.