You can use join for that:
SELECT c1.*, c2.* FROM conversation_user c1 INNER JOIN conversation_user c2 ON c1.conversation_id = c2.conversation_id WHERE c1.user_id != c2.user_id;
You can take a look at this SQLFiddle Example that is a bit more detailed. It shows an example of bringing the name of the users and one that filters by conversation.