The Langevin diffusion is reversible with respect to the density $\rho(x)=e^{-U(x)}$. This property is more transparent when the SDE is written as $$ dX_t = \nabla \log \rho(X_t) dt + \sqrt{2} dW_t $$ and is the basis of MCMC methods based on Langevin diffusions; see e.g.
Exponential convergence of Langevin diffusions and their discrete approximations