This paper connects score-based generative modeling to the problem of predicting how a dynamical system responds to an external perturbation. The generalized fluctuation-dissipation theorem expresses that response using fluctuations in the unperturbed system and the score of its stationary distribution. Learning the score from time-series data removes the need to approximate that distribution as Gaussian. Tests on a spatial Ornstein-Uhlenbeck process, a stochastic Allen-Cahn equation, and two-dimensional Navier-Stokes flow demonstrate improved response estimates. Readers get the central theoretical connection and a data-driven recipe for predicting small-perturbation responses in systems with complicated statistics.