[Proba] Latent variable: Directed or not?

[shouldsee]

I have this question when I read upon latent variable model, which assumes p(x|z) has a specific form (gaussian, multinomial, categorical, etc.), which corresponds to a directed edge z -> x. My question is whether it'd be possible to replace that with an undirected edge instead z -- x instead?

I am aware of markov random field with Ising model as one of its best rep. What are the most popular MRF LVM?