We consider a gradient, speed-change, symmetric exclusion process on the discrete torus $T^d_n$, $d\leq 3$, whose empirical measure evolves, on the diffusive scale, according to a non-linear parabolic equation. We prove that, starting from a sequence of initial states whose relative entropy with respect to the inhomogeneous product measure associated with the initial profile is o(n^{d/2}), and whose density fluctuation field converges, the density fluctuation field converges, in $L^1(0,T; H_{-r})$, to the solution of a linear stochastic partial differential equation with time-dependent coefficients driven by a conservative space-time white noise. Joint work with S. Sethuraman.