The method of Parisi and Wu to quantize classical fields is applied to instanton solutions . I of euclidian non-linear theory in one dimension. The solution . = of the corresponding Langevin equation is built through a singular perturbative expansion in == 1Â2 in the frame of the center of mass of the instanton, where the difference . = &. I carries only fluctuations of the instanton form. The relevance of the method is shown for the stochastic K dV equation with uniform noise in space: the exact solution usually obtained by the inverse scattering method is retrieved easily by the singular expansion. A general diagrammatic representation of the solution is then established which makes a thorough use of regrouping properties of stochastic diagrams derived in scalar field theory. Averaging over the noise and in the limit of infinite stochastic time, we obtain explicit expressions for the first two orders in = of the perturbed instanton and of its Green function. Specializing to the Sine Gordon and . 4 models, the first anharmonic correction is obtained analytically. The calculation is carried to second order for the . 4 model, showing good convergence.