  A recently introduced theoretical framework for modeling the dynamics of
X-ray amplified spontaneous emission is based on stochastic sampling of the
density matrix of quantum emitters and the radiation field, similarly to other
phase-space sampling techniques. While based on first principles and providing
valuable theoretical insights, the original stochastic differential equations
exhibit divergences and numerical instabilities. Here, we resolve this issue by
accounting the stochastic components perturbatively. The refined formalism
accurately reproduces the properties of spontaneous emission and proves
universally applicable for describing all stages of collective X-ray emission
in paraxial geometry, including spontaneous emission, amplified spontaneous
emission, and the non-linear regime. Through numerical examples, we analyze key
features of superfluorescence in one-dimensional approximation. Importantly,
single realizations of the underlying stochastic equations can be fully
interpreted as individual experimental observations of superfluorescence.
