Pitch-up results from the aerodynamic center being offset from the thrust line. The wings produce drag that is offset from the thrust line & hence there is a turning (pitching) moment upwards (in the case of high-wing aircraft) toward the center of lift.

As speed increases, lift (& hence, drag) increases, thus changing (increasing) the pitching moment. Since speed is dependent on power, down thrust works (more or less) to cancel the pitching moment. The effect of downthrust is not directly proportional to throttle setting -- it is speed dependent, but it works fairly well across a usefull range of airspeeds.