Could disorder enhance superconductivity? Close to the Anderson transition, electronic wave functions show a peculiar multifractal structure, predicted to enhance Cooper pairing. Here, the authors probe the weak disorder limit using an atomic monolayer of lead with high-resolution scanning tunneling spectroscopy. They show that mesoscopic spatial fluctuations of the electronic density of states indicate coherent diffusion of electrons. They use these energy-dependent fluctuations to reveal tiny energy gap fluctuations and to extract the elastic mean free path, dephasing length, as theoretically expected.