A controller for an internal combustion engine is configured to execute a regeneration process of burning and removing particulate matter accumulated in an exhaust purification device, a determination process of determining that a deviation between a first change amount and a second change amount is less than or equal to a threshold, the first change amount and the second change amount being change amounts per unit time of the temperature of exhaust gas on the upstream side and the downstream side of the exhaust purification device, respectively, and an anomaly diagnosing process that determines that the exhaust purification device is in a detached state when the determination process determines that the deviation is less than or equal to the threshold. The controller is configured to not execute the determination process during a period from the end of the regeneration process to when a post-regeneration execution condition is met.