A system for illuminating an environment with light that simulates natural light includes: a first light source which emits a beam of visible light; a diffused-light generator delimited by an inner surface, which receives the light beam, and an outer surface, the diffused-light generator being at least partially transparent to a long wavelength component of the beam of visible light. The diffused-light generator transmits diffused light from a short wavelength component of the beam of visible light, through the outer surface, the correlated color temperature of the transmitted light being lower than the CCT of the visible diffused light. The lighting system includes a dark box which hosts the first light source and is optically coupled to the environment via the diffused-light generator.