We prove that there exists a diffusion process whose invariant measure is t
he two-dimensional polymer measure nu(g). The diffusion is constructed by m
eans of the theory of Dirichlet forms on infinite-dimensional state spaces.
We prove the closability of the appropriate pre-Dirichlet form which is of
gradient type, using a general closability result by two of the authors. T
his result does not require an integration by parts formula (which does not
hold for the two-dimensional polymer measure nu(g)) but requires the quasi
-invariance of nu(g) along a basis of vectors in the classical Cameron-Mart
in space such that the Radon-Nikodym derivatives (have versions which) form
a continuous process. We also show the Dirichlet form to be irreducible or
equivalently that the diffusion process is ergodic under time translations
.