Some producers of synthetic diamonds actually put a marking on them, labeling them as synthetic.
This does not prevent someone else to remove this marking though, just cutting the gem slightly smaller removing any superficial markings in the process, and selling it on as a natural stone.
As for the isotope ratios: that is a little more difficult, but could also be overcome when making artificial diamonds since you can get the proper isotope mixture using source materials enriched or depleted in specific isotopes to the point where it matches mined diamonds.
Diamonds are all about the percieved value, not about the actual cost of manufacture or mining, and hence the whole price of the things is not sustainable.
Compare this to other things once rare: Back in the 17th century or so aluminium metal was considered more valuable than gold, because it was very rare. You can google for stories about this and find many.
Aluminium as an atom is very common on earth, but before electricity it was very hard to produce it has a metal from ores like bauxite. Nowadays it's considered so cheap it's ideal for single use trays, foils and what not.
Diamond could easily go the same route as synthetic production improves. Most synthetic diamond nowadays is not made for gem stones but for industrial use in drills and such, but the techology keeps improving. I would not be surprised if really big (say 100 carat+) synthetic diamonds became available in a couple of decades.
Guess you'd have to find something more rare for your wedding bands, but at least we'd have an extra really hard material for useful applications.
