  Smoothing of field configurations is highly important for precision
calculations of physical quantities on the lattice. We present a cooling method
based on Stochastic Quantization with a built-in UV momentum cutoff. The latter
is implemented via a UV-regularized, hence colored, noise term. Our method is
tested in a two-dimensional scalar field theory. We show, that UV modes can be
removed systematically without altering the physics content of the theory. The
approach has an interpretation in terms of the non-perturbative (Wilsonian)
renormalization group that facilitates the physics interpretation of the cutoff
procedure. It also can be used to define the maximal colored cooling applicable
without changing the theory.
