The modelling of the Stochastic Kinetics of biochemical networks by stochastic dierential equations (SDE) has been successfully used as a basis for statistical inference for such models. Since Monte Carlo based inference can be time consuming for SDEs, we suggest a dierent approximate approach. The idea is that a diusion model applies well to chemical kinetics, when the number of molecules of each type is large. In this limit, also the number fluctuations are small leading to a small diusion term compared to the drift. This suggests the application of a weak noise expansion.