Class AB power amplifier output signal
Because when the input is positive half cycle, the diode D1 is
  reversed biased


No, that's not true - the diode is always forward biased in normal operation; the resistors R1 and R2 ensure that this is the case.


  Why is there an output?


Because your analysis of the diodes being reverse biased was incorrect. For moderate signal levels the diodes will be forward biased at all times. If you went to extremes then this falls over but, even if the input voltage was a peak to peak amplitude that was only a little short of the power rail, the diodes would still be forward biased.