Selective optical filters with high rejection levels are of fundamental importance for a wide range of advanced photonic circuits. However, the implementation of high-rejection on-chip optical filters is seriously hampered by phase errors arising from fabrication imperfections. Due to coherent interactions, unwanted phase-shifts result in detrimental destructive interferences that distort the filter response, whatever the chosen strategy (resonators, interferometers, Bragg filters, etc.). State-of-the-art high-rejection filters partially circumvent the sensitivity to phase errors by means of active tuning, complicating device fabrication and operation. Here, a new approach based on coherency-broken Bragg filters is proposed to overcome this fundamental limitation. Non-coherent interaction among modal-engineered waveguide Bragg gratings separated by single-mode waveguides is exploited to yield effective cascading, even in the presence of phase errors. This technologically independent approach allows seamless combination of filter stages with moderate performance free of active control, providing a dramatic increase of on-chip rejection. Based on this concept, on-chip non-coherent cascading of Si Bragg filters is experimentally demonstrated, achieving a light rejection exceeding 80 dB, the largest value reported for an all-passive silicon filter.