The Langevin diffusion is [reversible][1] 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][2]

In fact, random-walk based MCMC methods (like random walk Metropolis) with target density $\rho(x)$, can be viewed as weak approximations to the corresponding Langevin diffusion; see e.g. Theorem 5.1 of

[Metropolis integration schemes for self-adjoint diffusions][3]

In particular, random walk Metropolis doesn’t even explicitly involve the gradient of $U$, but by virtue of being reversible, can weakly approximate the Langevin diffusion.


  [1]: https://www.cambridge.org/core/journals/advances-in-applied-probability/article/abs/time-reversible-diffusions/6CEF3A3069A15D58C55FBB06D6F467D8
  [2]: https://projecteuclid.org/journalArticle/Download?urlid=bj%2F1178291835
  [3]: https://epubs.siam.org/doi/pdf/10.1137/130937470