The question of whether quantum measurements reflect some underlying objective reality has no generally accepted answer. We show that a description of such reality is possible under natural conditions such as linearity and causality, although in terms of moments and cumulants of finite order and without relativistic invariance. The proposed construction of observations' probability distribution originates from weak, noninvasive measurements, with detection error replaced by some external finite noise. The noise allows us to construct microscopic objective reality, but remains dynamically decoupled and hence unobservable at the macroscopic level.