  In this paper, we introduce a new method of sampling from transition
densities of diffusion processes including those unknown in closed forms by
solving a partial differential equation satisfied by the quotient of transition
densities. We demonstrate the performance of the developed method on processes
with known densities and the obtained results are consistent with theoretical
values. The method is applied to Wright-Fisher diffusions owing to their
importance in population genetics in studying interaction networks inherent in
genetic data. Diffusion processes with bounded drift and non degenerate
diffusion are considered as reference processes.
  $\bf {Key words}:$ Stochastic differential equation (SDE), Transition
density, Fokker-Planck partial differential equation, Aronson's bound,
Rejection sampling, Wright-Fisher diffusion.
