Today I was doing some leisurely reading and stumbled upon Section 5.8 (on page 45) of Recommendation for Pair-Wise Key Establishment Schemes Using Discrete Logarithm Crypto
Well, consider that if two parties have the same cryptographic function, but don't have the same IV, they won't get the same results. So then, it seems like the proposal there is that the two parties get the same shared secret, and each generate, deterministically, an IV (that will be the same) and then they can communicate. That's just how I read it; but I've not actually read the document, and I'm not completely sure that my description is accurate; but it's how I'd start investigating.