In this talk we develop the theory of tamed spaces, which are Dirichlet spaces with distribution-valued lower bounds on the Ricci curvature, and investigate these from an Eulerian point of view. To this end we introduce singular perturbations of Dirichlet form by a broad class of distributions. The distributional Ricci bound is then formulated in terms of an integrated version of the Bochner inequality using the perturbed energy form and generalizing the well-known Bakry-Émery curvature-dimension condition. This talk is based on a joint work with M. Erbar, K.-T. Sturm and L. Tamanini.