If space is quantized, new grains could be emerging from an immaterial background and pushing things apart. The emergence of grains occurs continually and everywhere, but especially in sparse regions where it is less disruptive. Grains of quantized space would have discrete volume (just look around) but no other measurable properties so they are not detectable (there is nothing to measure!).
Occasionally, the unmeasured properties of some grains receive measured values and collapse down to discrete particles.