The fluctuation – dissipation theorem (FDT) is shown to provide a powerful resource for the analysis of stimulated light scattering from laser-driven density gratings, including stimulated Brillouin scattering (SBS) and its kinetic-regime extension. In the physical setting of stimulated light scattering by density gratings, the FDT establishes that the dynamics of disturbances induced in a medium by a laser-driven electrostrictive force unfolds via the same physical pathways as the dynamics of internal, spontaneous fluctuations in this medium at equilibrium. When integrated into a suitable kinetic framework, the FDT leads to a significant simplification of the analysis of stimulated light scattering, allowing the stimulated gain/loss spectrum to be found directly from the spectrum of spontaneous density fluctuations without the need to solve kinetic equations with an external-field term. Such FDT-based framework enables an accurate description of stimulated light scattering within a vast parameter space, recovering all the signature properties of sound-wave-mediated Stokes amplification in the hydrodynamic regime, providing a continuous crossover from the hydrodynamic to kinetic regime of stimulated scattering, and explaining distinctly different properties of kinetic stimulated scattering from density gratings, consistent with experiments on stimulated scattering in moderate-pressure gases. As important physical benchmarks, in the limits of vanishingly low and very high collision frequencies, this solution for the SBS gain recovers the FDT-transformed solutions of, respectively, the Vlasov and Navier – Stokes equations. This treatment sheds light on how the causality of density fluctuations is manifested in stimulated scattering and how the universality of Doppler broadening in the spectrum of spontaneous density fluctuations in the kinetic regime translates into the spectra of stimulated and coherent scattering.