why variational inference in variational autoencoder if dealing with simple graphical model As far as I am reading about VAE, I always see a graphical model of Z --> X, 

I know P(X) can be intractable, but that would be if we would have many dependencies. But here is only Z. So why variational inference at first place?:)
I'm not sure if I get the question correctly, but we use variational inference, because we do have many dependencies. X and Z are usually high-dimensional vectors with complex relationships.