Flight Instructor reported during taxi another aircraft taxied directly toward them and did not stop; requiring the Flight Instructor to move off centerline in order to avoid a collision.

Narrative

Was returning from an Instrument Cross-Country flight after landing on Runway XX and was given taxi instruction: 'Cross XXL at [Taxiway] 1 and continue [Taxiway] 2 to parking' - student read back clearance; we turned right onto [Taxiway] 2 toward parking at FBO; and saw another Cessna heading directly toward us. We immediately moved to the right of the taxiway; the other Cessna did not stop and continued straight at us while remaining on the centerline. They would have come straight into us if we did not move off to the right.I tried the other radio to see if we could hear any instructions being given that we were missing in the case of a broken radio but heard nothing. We then pulled into the parking area without incident. I confirmed with the student that we both heard the correct taxi clearance from the Ground controller - then after parking and securing; I asked another flight behind us if they had heard any abnormal instructions given to us on the ground frequency; and they said no. I applauded the student for immediately moving off to the right without hesitating; to avoid the oncoming aircraft.Although nothing really came from it; it is a good reminder to students and instructors to be on extra alert at all times on the airport surface (head up and eyes out) even after being given a taxi clearance.