Before revision:  Diffusion approximations are generally known to fail in this regard . It is shown that a diffusion approximation based on a quasi-steady-state reduction (stochastic averaging), which averages the internal state out and reduces the process to a continuous Markov process for the external state, provides unreliable accuracy. On the other hand, the QSA approximation is consistently accurate .
After revision:  Diffusion approximations are generally known to fail in this regard .