From my research, I think what everything says is that the result of a zero knowledge proof (ZKP) is that the participants end up with a shared secret that can be used as a session key for a further symmetric encryption session between those two parties. And then, all of the articles say that you follow this up by starting up something like a Diffie-Helmann (DH) session.
If I just got a secure key from the ZKP - why do I need DH? Why don't I just expand the ZKP result and go from there?