First of all, the original sentence does not specifically mean that both processes happen simultaneously. It may mean it, but it is only an interpretation.

Secondly, even if it is correct, the translated sentence does not have to be more precise than the original one.

Thirdly, if you want it to be precise, then you should re-arrange the whole thing. An example of that would be "mutual diffusion continues until thermal equilibrium is attained". This is taken out of any context so it may not be the best alternative for you.