EMB-145 First Officer reported unknown fumes in the flight deck and cabin.

Narrative

Initial incident on first leg of ZZZ-ZZZ1 out and back. Approximately 2 hours into the flight at cruise near ZZZ2 waypoint the captain and I smelled an abnormal odor lasting a minute or less. We checked all physical and systems indications available to us and instructed the FA's to do the same throughout the cabin and found no abnormalities. Odor never came back and we continued to our destination without further incident. For all we knew we may have possibly just flown through a peculiar odor that was outside the aircraft. At top of climb on return leg the odor returned. We again instructed the FA's forward to inspect and this time they noticed the odor near the front galley during their inspections. Once again we inspected physical locations as well as MFD (Multi-function Flight Display) / EICAS; this time with our o2 masks on. Smell once again went away. Passengers were aware and unaffected by situation. 15-20 mins later it came back more widespread throughout the aircraft and with the coffee maker and external factors ruled out and still with no source or indication we made the decision to run our memory items; QRC; QRH; request priority handling and divert to ZZZ3 ; conveniently the next fix on our flight plan. Our workload escalated while intermittent o2 mask mics further complicated things. We received expedited handling for ILS XXL while the FA's made standard landing preparations. Upon landing we were inspected by emergency vehicles and given a clean report. There was zero indication up front that we would not be able to exit the active runway and continued to the gate which we did; escorted by said vehicles. We then deplaned the passengers without further incident. After we caught our breath I performed my post flight walk around; contract maintenance conducted initial inspections and company departments were notified without a probable cause identified. Event: Fumes in cockpit and cabin.