The mystery of the erratic motion of pollen grains suspended in water, named after its explorer, Robert Brown, was solved by Einstein in 1905. His kinetic theory, based upon lightwater molecules continuously bombarding the heavy pollen, provided not just an explanation of diffusion from the Newtonian mechanics, but also the most direct evidence yet for the existence of atoms and molecules. Since the discovery of quantum mechanics it has been a major challenge to verify the emergence of diffusion from the Schr¨odinger equation. In this talk I will report on a mathematically rigorous derivation of a diffusion equation as a long time scaling limit of a random Schr¨odinger equation in a weak, uncorrelated disorder potential.