Determination of fast structural changes of biomolecules is usually performed on crystalline samples in a time-resolved pump-probe experiment. Changes in the structure are found by the difference Fourier method using phases of a known reference structure. As we showed recently, such changes can also be determined from diffraction of uncrystallized molecules in random orientations. In this case, the difference in the angular correlations of the diffraction patterns is used to find structural changes. Similar to the difference Fourier method, there is no need for iterative phasing. We validated this approach previously with simulations in the absence of noise. In this paper, we show that the effects of noise can be adequately suppressed by averaging over a sufficiently large ensemble as they can be obtained using an X-ray free electron laser.