In elastic macromolecules, the value of the short-time diffusion coefficient depends on the choice of the point the displacement of which is tracked. On the other hand, the experimentally more relevant long-time diffusion coefficient is independent of the reference point, but its estimation usually requires computationally expensive Brownian dynamics simulations. Here we show how to obtain a precise estimate of the long-time diffusion coefficient of elastic macromolecules in a fast and robust manner, without invoking Brownian dynamics.