I have no experience with the Nissin Di700, but the YN-622C triggers can communicate high speed sync, so it should work.
However if this is your first/only flash, you might be better off returning the Di700 and getting a Di700A and the Nissin Air 1 Commander, so you'll have a built-in receiver, rather than using an add-on one. The Di700A is the same price as the Di700 on B&H. The YN-622s will give you more flexibility in what lighting gear you might want to add to your triggering system, but built-in receivers have the advantage that you don't need to worry about external triggers or additional batteries.