  For a class of interacting particle systems in continuous space, we show that
finite-volume approximations of the bulk diffusion matrix converge at an
algebraic rate. The models we consider are reversible with respect to the
Poisson measures with constant density, and are of non-gradient type. Our
approach is inspired by recent progress in the quantitative homogenization of
elliptic equations. Along the way, we develop suitable modifications of the
Caccioppoli and multiscale Poincar\'e inequalities, which are of independent
interest.
