We examine coherence properties of small-area, intrinsically stationary statistical pulses propagating in amplifying media in the vicinity of an optical resonance. Any such medium acts as a coherent linear amplifier, amplifying and reshaping the pulse. We show that an initially nearly incoherent Gaussian Schell-model pulse becomes almost fully coherent and its state of coherence becomes nearly uniform across the temporal profile as the pulse propagates into the amplifying medium. (C) 2013 Optical Society of America