Air carrier Captain reported the air conditioning PACK 1 was inoperative; then PACK 2 malfunctioned as well. As a result; the flight crew diverted to a nearby airport.

Narrative

Aircraft had Pack 1 Fault after blockout in ZZZZ; and PDM (Programmed Depot Maintenance) process added MEL for Pack 1 inoperative. When leveling off at FL370 cruise; FO noticed cabin altitude climbing through 8000 and cabin differential pressure at 7.1. (Abnormal indications). Pack 2 was visually confirmed selected on. Cabin altitude continued to climb at approximately 350 ft/min. Aircraft descended to FL 250 and cabin altitude continued to rise until ECAM indicated EXCESS CABIN ALTITUDE. After switching Pressure Regulator (per QRH); cabin still continued to rise. Subsequently; both Pressure Regulators Faulted and system reverted to Manual Pressurization. The switch to close valves was activated multiple times; although during the entire evolution; the Outflow Valves indicated full closed. When in Manual Pressuriztion; the valves also indicated closed. Crew had coordinated to continue descent with ATC and elected to divert to ZZZ. During descent to land; between approximately 13;000 and 10;000 feet; the noise of a pack increased and the outflow valves did start to modulate as the approach was started. Crew had donned oxygen masks when cabin altitude rose above 10;000 and removed oxygen masks after descending to 10;000 for diversion. Jumpseater was called to the cockpit (when cabin altitude initially above 10;000 feet) to ensure he was aware of depressurization and to assist crew. Jumpseater completed ACARS communication with dispatcher and obtained ATIS; called to ZZZ company ramp and overall greatly assisted crew. The approach and landing to ZZZ was uneventful. Cause: Subsequent maintenance troubleshooting identified faulty relay in pack valve operation.