This Demonstration shows how a diffraction beam is formed by positive interference of a series of sine waves. You can change the number of waves and vary the phase increment between the component sine waves. This simulates the progressive difference in path length from components originating at different slits on a grating. Most phase increments (corresponding to different angles of the beam) result only in destructive interference, which explains the existence of a set of discrete diffraction angles.

Start with four waves and observe their destructive interference. As you increase the number of waves, there are more possibilities for destructive interference compared to constructive interference conditions. Is this similar to a noise signal with random phases? Also, remember, with a real grating you are observing intensity, which is proportional to the square of the electric field.