We investigate a scaling limit of gradient stochastic dynamics
associated with Gibbs states in classical continuous systems
on ${\mathbb R}^d$, $d \ge 1$. The aim is to derive
macroscopic quantities from a given microscopic or mesoscopic system.
The scaling we consider has been investigated
by Brox (in 1980), Rost (in 1981), Spohn (in 1986) and Guo and Papanicolaou
(in 1985), under
the assumption that the underlying potential is in $C^3_0$ and
positive. We prove that the Dirichlet
forms of the scaled stochastic dynamics converge on a core of
functions to the Dirichlet form of a
generalized Ornstein--Uhlenbeck process. The proof is based on the
analysis and geometry on the configuration space which was
developed by Albeverio, Kondratiev and Röckner (in 1998),
and works for general
Gibbs measures of Ruelle type. Hence, the underlying potential may
have a singularity at the origin, only has to be bounded from
below and may not be compactly supported. Therefore, singular
interactions of physical interest are covered, as, for example,
the one given
by the Lennard--Jones
potential, which is studied in the theory of fluids. Furthermore,
using the Lyons--Zheng decomposition we give a simple proof for the
tightness of the scaled processes. We also prove that the
corresponding generators, however, do not converge in the $L^2$-sense.
This settles a conjecture formulated by Brox, by Rost and by Spohn.