LAUSR

We introduce in this paper a strategy to prove gradient estimates for some infinite-dimensional diffusions on $$L_2$$ L 2 -Wasserstein spaces. For a specific example of a diffusion on the $$L_2$$ L 2 -Wasserstein space of the torus, we get a Bismut-Elworthy-Li formula up to a remainder term and deduce a gradient estimate with a rate of blow-up of order $$\mathcal O(t^{-(2+\varepsilon )})$$ O ( t - ( 2 + ε ) ) .