We present a general molecular-dynamics simulation scheme, based on the Nose thermostat, for sampling from arbitrary phase space distributions. We formulate numerical methods based on both Nose-Hoover and Nose-Poincare thermostats for two specific classes of distributions; namely, those that are functions of the system Hamiltonian and those for which position and momentum are statistically independent. As an example, we propose a generalized variable temperature distribution that is designed to accelerate sampling in molecular systems. (C) 2003 American Institute of Physics.