Why is diffusion Gaussian?

I was tracing Jascha Sohl-Dickstein’s original paper [1503.03585] Deep Unsupervised Learning using Nonequilibrium Thermodynamics. The intuition seems to come from physics and statistical mechanics which is fantastic. I am just wondering in life diffusion seems quickly leads to chaos, as there are some theories including butterfly effect which seems pretty true, so the eventual/inference “timeline” of distribution should have high entropy and not Gaussian, so why diffusion is Gaussian? Please share your thoughts!