B737 pilot reported a loud hissing sound in the cockpit; attributed to a broken and leaking oxygen mask at the observer's seat position. The oxygen system was depleted; and an immediate diversion was accomplished.

Narrative

During the climb out of ZZZ there was a sudden loud hissing sound which seems to come from somewhere in the flight deck. From previous Captain experience he suggested that the aircraft might have a bad seal. After verifying a positive rate of cabin climb and a positive Differential pressure; we concluded that the aircraft is pressurizing correctly. I pulled out my mask to have in handy in case of a sudden depressurization. The decision at the moment was to continue the flight.From my own past experience and due the abnormally loud noise (which could potentially cause fatigue if exposed to for a long period of time) I suggested it might be something else other than a seal and we agreed that once level at cruise I would get out of my seat and further investigate. Once leveled at 32;000 feet I transferred controls to the Captain and got up off my seat. I quickly noticed that the hissing sounds comes from the observer's mask; so I pulled it out to further check it; and the hissing sound stopped immediately. I looked up to the aft overhead panel and realized that our O2 gauge read 0. There was no prior alert or light associated; and both me and the Captain agreed that we verified it was full on the ground during preflight. The decision to divert was quick; and we decided to decent to a safer altitude and divert to ZZZ1. After a brief discussion we decided to [request priority handling]. Dispatcher; flight attendants; passengers and Maintenance were advised of the situation. About 20 minutes later the flight safely landed in ZZZ1. The aircraft was serviced and passengers accommodated. We later continued the flight to ZZZ2 once Maintenance replaced the empty O2 bottle and faulty observer's mask.