The approximation of a Markov process by Markov chains has been an interesting topic for a long time. Up to our knowledge the known results were obtained under some additional regularity assumptions on the state spaces (e.g. locally compact separable space) and on the underlying transition semigroups (e.g. Feller semigroup). In this talk I am going to show that, based on my joint work with M. Röckner and W. Sun, any Hunt processes (in particular any conservative diffusions) on a general state space can be approximated by multivariate Poisson processes. The key point is that no additional regularity assumption is used.