The nonlinear properties of quasi-periodic photonic crystals based on the Thue-Morse sequence are investigated. The intrinsic spatial asymmetry of these one-dimensional structures for odd generation numbers results in bistability thresholds, which are sensitive to the propagation direction. Along with resonances of perfect transmission, this feature allows us to achieve strongly non-reciprocal propagation and to create an all-optical diode. The salient qualitative features of such optical diode action are readily explained through a simple coupled resonator model. The efficiency of a passive scheme that does not necessitate an additional short pump signal is compared to an active scheme where such a signal is required.