In this paper we discuss various aspects of diffusion Monte Carlo methods u
sing a fixed number of walkers. First, a rigorous proof of the divergence o
f pure diffusion Monte Carlo (PDMC) methods (DMC without branching in which
the weights are carried along trajectories) is given. Second, a bias-free
Monte Carlo method combining DMC and PDMC approaches, and based on a minima
l stochastic reconfiguration of the population, is discussed. Finally, some
illustrative calculations for a system of coupled quantum rotators are pre
sented.