Linearised fluctuating hydrodynamics describes effectively the concentration non-equilibrium fluctuations (NEF) arising during a diffusion process driven by a small concentration gradient. However, fluctuations in the presence of large gradients are not yet fully understood. Here we study the giant concentration NEF arising when a dense aqueous colloidal suspension is allowed to diffuse into an overlying layer of pure water. We use differential dynamic microscopy to determine both the statics and the dynamics of the fluctuations for several values of the wave-vector q. At small q, NEF are quenched by buoyancy, which prevents their full development and sets an upper timescale to their temporal relaxation. At intermediate q, the mean squared amplitude of NEF is characterised by a power law exponent −4, and fluctuations relax diffusively with diffusion coefficient D1. At large q, the amplitude of NEF vanishes and …