The question is a little bit confusing because I would think you’d expect the contrary: the faster the diffusion, the larger the depletion region (DR for short). So I am not sure what your line of thinking is, therefore, I will take a very general approach, and remind some stuff that I’m can’t be certain you’ve heard about.
Mostly, I want to start by making sure that, if you admit the situation depicted in your drawing as a starting point, you understand why it forms a barrier to further diffusion. As drawn, you have negative net charges on the p-side of the DR and positive charges on the n-side. I assume you know that such a charge distribution will create an electric field pointing form + to -. Now let’s say that an electron from the n-side wants to take a hike on the p-side. The electric field as oriented will push it away (electrons are negatively charged). Same goes for holes from the p-side who would dare try to diffuse to the n-side. So the point to remember: having a depletion region blocks further diffusion.
Other reminder before answering: how the DR forms. 531
When a free electron arrives in the p side from the n side, it encounters sooo many holes that it immediately wanna get intimate and recombine. This additional electron from the n-side is now stuck in the p-side and therefore starts to build up the negative charge that you see on your drawing.
Those being established, you should start to see that the size of the DR is a trade-off between the rate of two processes: rate of recombination and rate of diffusion. Imagine if you have a super fast diffusion and really slow recombination: electrons would have time to sprint wherever they want before they recombine, and therefore would recombine anywhere in the p-zone, and your idea would be true (charges all over, in case of super fast diffusion). On the contrary, if recombination happens instantly, then the electrons/holes recombine right at the gate of their new region. This recombination process creates charges and stops further diffusion of other charges as established above. Therefore, if diffusion is very slow (or recombination very fast), the depletion region is smaller. In real life, recombination happens on much smaller timescales than diffusion, so the DR is always pretty thin. But the exact size varies on the materials used and does depend in good part on the tradeoff discussed: slow diffusion, thin DR, fast diffusion, larger DR. 969