We are interested in the asymptotic diffusion matrix A associated to a class of interacting particle systems in R^d. The models that we consider are reversible with respect to the Poisson measures and are of non-gradient type. Relying on the recent progress in quantitative stochastic homogenization for elliptic PDEs, we prove that finite-volume approximations of A converge at an algebraic rate. Furthermore, we show that A is smooth in the density of particles and obtain an explicit characterization of its derivatives. This talk is based on joint works with C. Gu (NYU Shanghai), J.-C. Mourrat (ENS Lyon) and M. Nitzschner (NYU Courant).