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

Sampling from Unknown Transition Densities of Diffusion processes