The aim of the lectures is to show how any dynamical semigroup on a von Neumann algebra, symmetric w.r.t. a trace, gives rise to a closed derivation with values in a tangent bi-modulus. The derivation is a differential square root of the Dirichlet form associated to the L 2 -generator, which in turn can be represented as a generalized laplacian, i.e. as the divergence of a derivation. Example will include negative definite functions on groups as well as the Dirac laplacian on riemannian manifold. In the second part of the talk we will construct a summable Fredholm module associated to the Dirichlet form. As a distinguished situation we will consider Fredholm modules constructed starting from diffusions on fractals.