A320 pilot reported an engine stall warning and other erratic readings so they diverted to a suitable airport.

Narrative

We were operating flight XXXX on Aircraft X from ZZZ1 to ZZZ2. We got an ECAM for ENG 1 STALL; despite the fact that all systems appeared to be operating normally. We ran the QRH procedure; which called for disconnecting the autothrust and retarding THR 1 to IDLE; which we did; with slightly erratic engine 1 indications. I [requested priority handling] with ATC and requested immediate descent; which we received. After activating the Eng Anti Ice (as per the directions for the current engine option in the QRH); we gradually began applying power to Eng 1. The ENG 1 STALL ECAM appeared again; and the Engine Pressure Ratio (EPR) and Exhaust Gas Temperature (EGT) gauges gave mildly erratic readings. Flight Attendant (FA) 3 reported that she heard unusual noises from that side of the aircraft; but FA 2 did not hear; see; or feel anything unusual.We returned THR 1 to idle and continued with the QRH; which dictated a shutdown and to land ASAP. Coordinating with Dispatch via satphone that we were overhead ZZZ in VMC; they advised us to divert to ZZZ; which we did. I communicated with the Inflight crew the nature of the situation and that we would be landing in ZZZ in 20 minutes. I then made an announcement to the passengers that we had a significant mechanical problem; and were making a precautionary landing in ZZZ. The First Officer (FO) and I set up for and briefed the approach to ZZZ; and ran the appropriate checklists. ATC vectored us for descent and the approach; which concluded in a safe landing. We stopped on the runway so that Crash Fire Rescue (CFR) could inspect the aircraft. After making a 'remain seated' announcement; I further explained to the passengers that the firefighters would check the aircraft; after which we would park at gate XX to examine the options for getting them to their destinations. CFR reported no damage or leaks visible from their inspection; and we taxied to the gate and parked the aircraft. The passengers disembarked without injury or incident.