A deterioration diagnosis apparatus to be applied to an exhaust gas purification apparatus including a first exhaust gas purification device provided in an exhaust passage of an internal combustion engine capable of operating in a lean-burn mode and including a hydrogen production catalyst that brings about a water gas shift reaction using a reducing agent produced by combustion of air-fuel mixture when the air-fuel ratio of the air-fuel mixture is equal to a predetermined rich air-fuel ratio lower than the theoretical air-fuel ratio, a second exhaust gas purification device provided in the exhaust passage downstream of said first exhaust gas purification device and including a selective catalytic reduction catalyst that stores oxygen in exhaust gas when the air-fuel ratio of the exhaust gas is a lean air-fuel ratio higher than the theoretical air fuel ratio and desorbs oxygen stored therein when the air-fuel ratio of the exhaust gas is lower than the theoretical air-fuel ratio, a first air-fuel ratio sensor that measures a physical quantity correlating with the air-fuel ratio of the exhaust gas flowing into said second exhaust gas purification device, and a second air-fuel ratio sensor that measures a physical quantity correlating with the air-fuel ratio of the exhaust gas flowing out of said second exhaust gas purification device, the deterioration diagnosis apparatus comprising: a control unit configured to start an induction process, which is a process of inducing a water gas shift reaction in said first exhaust gas purification device by controlling the operation state of the internal combustion engine in such a way as to change the air-fuel ratio of the air-fuel mixture to said predetermined rich-air fuel ratio and to terminate said induction process when a fuel integration value, which is a value obtained by integrating the fuel injection quantity from the time at which desorption of the oxygen stored in said first exhaust gas purification device is completed, reaches a specific quantity; and a diagnosis unit configured to integrate a sensor output difference defined as a difference between the measurement value of said first air-fuel ratio sensor and the measurement value of said second air-fuel ratio sensor over the period through which said induction process is performed to obtain an integrated sensor output difference defined as the sum total of the sensor output difference over the period through which said induction process is performed and diagnoses deterioration of said second exhaust gas purification device using the integrated sensor output difference as a parameter, wherein said control unit is configured to obtain a degree of deterioration of said hydrogen production catalyst and to control the operation state of the internal combustion engine in such a way as to make a quantity of the reducing agent supplied to said first exhaust gas purification device, during the period through which said induction process is performed, larger by increasing the specific quantity or by lowering the air-fuel ratio, when the degree of deterioration obtained is high than when the degree of deterioration obtained is low, wherein said hydrogen production catalyst has an oxygen storage capability of storing oxygen in the exhaust gas when the air-fuel ratio of the exhaust gas is a lean air-fuel ratio higher than the theoretical air-fuel ratio and desorbing oxygen stored therein when the air-fuel ratio of the exhaust gas is equal to or lower than the theoretical air-fuel ratio. a control unit configured to start an induction process, which is a process of inducing a water gas shift reaction in said first exhaust gas purification device by controlling the operation state of the internal combustion engine in such a way as to change the air-fuel ratio of the air-fuel mixture to said predetermined rich-air fuel ratio and to terminate said induction process when a fuel integration value, which is a value obtained by integrating the fuel injection quantity from the time at which desorption of the oxygen stored in said first exhaust gas purification device is completed, reaches a specific quantity; and a diagnosis unit configured to integrate a sensor output difference defined as a difference between the measurement value of said first air-fuel ratio sensor and the measurement value of said second air-fuel ratio sensor over the period through which said induction process is performed to obtain an integrated sensor output difference defined as the sum total of the sensor output difference over the period through which said induction process is performed and diagnoses deterioration of said second exhaust gas purification device using the integrated sensor output difference as a parameter, wherein said control unit is configured to obtain a degree of deterioration of said hydrogen production catalyst and to control the operation state of the internal combustion engine in such a way as to make a quantity of the reducing agent supplied to said first exhaust gas purification device, during the period through which said induction process is performed, larger by increasing the specific quantity or by lowering the air-fuel ratio, when the degree of deterioration obtained is high than when the degree of deterioration obtained is low, wherein said hydrogen production catalyst has an oxygen storage capability of storing oxygen in the exhaust gas when the air-fuel ratio of the exhaust gas is a lean air-fuel ratio higher than the theoretical air-fuel ratio and desorbing oxygen stored therein when the air-fuel ratio of the exhaust gas is equal to or lower than the theoretical air-fuel ratio.