Observations indicate that solar active region magnetic fields have a predominantly negative (positive) helicity in the northern (southern) hemisphere. This helicity is likely to have a subsurface origin. One possible explanation for the helicity is that the rising toroidal flux tube causing the active region collects flux from the general poloidal magnetic field of the Sun. This flux first wraps around the rising tube, then slowly penetrates it by turbulent diffusion. Here we present recent results concerning how this nonlinear diffusion proceeds. The models show that with a plausible choice of assumptions a mean twist comparable to the observations results.