A320 flight crew reported a malfunction with cargo door. Flight crew diverted and landed safely.

Narrative

Climbing through approximately 12;000ft we received 2 ECAMs simultaneously; DOOR AFT CARGO and COND AFT CRG HEAT FAULT. We cleared the first ECAM; DOOR; and then cleared the second; COND. We immediately decided since we were climbing through altitudes where oxygen may be needed; to descend to 10;000 immediately; and continue to investigate the issue and run our procedures and checklists. We then reviewed our manifest and saw no live animals were onboard and reviewed our cabin pressurization. Cabin pressurization appeared normal at 10;000ft and level. We decided at that point we could continue since the checklist advised no pilot action required". As we reinitiated the climb after our ECAM procedures and checklist review; I kept looking at the Door page and Press page. I determined that I cannot guarantee the condition or position of the aft cargo door; decided we could be loosing cargo or have sustained damage. I had a discussion with my First Officer about it and we decided to divert and advise ATC. ZZZ seemed to be the best option; so we made a 180 degree turn direct ZZZ advising ATC; Dispatch; Crew; and Cabin of our intentions to divert to ZZZ. We prepared for runway XXR per ATC request; preparing the FMCs and running out descent checklist. Upon discovering the runway length to be shorter than XXR and we were overweight; we queried ATC for our need for XXR or alternative longer runway. We ran the Landing; Overweight Checklist; Landing Checklist and landed with out incident on runway XXR. The Fire Chief inspected the airplane on Taxiway 1 and said the Aft Cargo Door latch handle appeared to be out and open and there appeared to be damage to the door. We decided to taxi back to the gate and have them follow us. Once parked at the gate; I decided to deplane the airplane while Mx (Maintenance) inspections occurred and we could debrief with the cabin crew. We coordinated with local Mx; Maintenance Control; and the Chief Pilot until our duty period timed out."