Timepiece regulating mechanism including an energy storage means delivering an output torque (CS), via a train (3), to a wheel set (4) forming a magnetic escapement mechanism (10) with a resonator wheel set (5) subjected to the torque from a return means (6) and cooperating therewith, either directly or via a magnetic stop member (7), this magnetic escapement mechanism (10) being arranged to operate when the wheel set (4) receives a torque higher than or equal to a maintenance torque (CE), and the train (3) includes a torque regulating means (30) arranged to deliver to the wheel set (4) a constant torque comprised between 1.0 and 2.0 times the maintenance torque (CE), the torque regulating means (30) including a fusee (8) of continuously variable cross-section, from which unwinds a chain (9), wound by a drum (21), directly or indirectly driven by the energy storage means (2).