We consider the problem of generating exact samples at finitely many locations from the solution of a generic multidimensional stochastic differential equation (SDE) driven by Brownian motion at a given time. If the SDE can be transformed into one with a constant diffusion coefficient and gradient drift exact samples can be obtained by sequential acceptance / rejection. In general, in this talk, we will explain how to use the theory of rough paths to obtain such exact samples. This is the first generic algorithm for exact samples of generic multivariate diffusions.