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We prove existence and uniqueness of solutions to a nonlinear stochasticevolution equation on the $d$-dimensional torus with singular $p$-Laplace-typeor total variation flow-type drift with general sublinear doublingnonlinearities and Gaussian gradient Stratonovich noise with divergence-freecoefficients. Assuming a weak defective commutator bound and acurvature-dimension condition, the well-posedness result is obtained in astochastic variational inequality setup by using resolvent and Dirichlet formmethods and an approximative It\^{o}-formula.

Stochastic evolution equations with singular drift and gradient noise via curvature and commutation conditions