New results unearthed from urtexts of quantum state diffusion
  Thirty years ago, the present author discussed pure state unraveling (stochastic quantum trajectories) of Markovian open system dynamics. The fact that he considered all positive dynamics, not restricted for the Lindblad-Gorini-Kossakowski-Sudarshan complete-positive subclass, has remained unnoticed so far. Here we point out the importance of the transition rate operator and the merit of invariant (representation-independent) approach, with reference to invariant condition of positive dynamics and extension of quantum state diffusion beyond complete-positive dynamics. A new result, description of all diffusive unravelings of positive dynamics directly follows. 
Lajos Di\'osi
quant-ph