We study the dynamics of sedimenting non-Brownian particles under steady-state conditions in two-dimensional geometry. We concentrate on the autocorrelation functions of the velocity fluctuations and the corresponding memory functions and diffusion coefficients as functions of ΦV for small but finite Reynolds numbers. For the numerical simulations we have chosen the model of Schwarzer [Phys. Rev. E 52, 6461 (1995)] where a continuum liquid phase is coupled through Stokesian friction to a discrete particle phase with volume fraction ΦV. We find that the steady-state velocity fluctuations are spatially highly anisotropic and the correlation functions parallel to gravity have nonexponential time dependence similar to that of purely dissipative systems with strong interactions. The corresponding memory functions also show nontrivial behavior. Diffusion along the direction of gravity is much faster than perpendicular to it, with the anisotropy decreasing as either the Reynolds number or the volume fraction increases.