Let $(W,H,��)$ be the classical Wiener space on $\R^d$. Assume that $X=(X_t)$ is a diffusion process satisfying the stochastic differential equation $dX_t=��(t,X)dB_t+b(t,X)dt$, where $��:[0,1]\times C([0,1],\R^n)\to \R^n\otimes \R^d$, $b:[0,1]\times C([0,1],\R^n)\to \R^n$, $B$ is an $\R^d$-valued Brownian motion. We suppose that the weak uniqueness of this equation holds for any initial condition. We prove that any square integrable martingale $M$ w.r.t. to the filtration $(\calF_t(X),t\in [0,1])$ can be represented as $$ M_t=E[M_0]+\int_0^t P_s(X)��_s(X).dB_s $$ where $��(X)$ is an $\R^d$-valued process adapted to $(\calF_t(X),t\in [0,1])$, satisfying $E\int_0^t(a(X_s)��_s(X),��_s(X))ds

12 pages