  We show that any non-relativistic quantum N-body dynamics problem with
pairwise interactions can be exactly reformulated in terms of N well behaved
1-body stochastic density equations. Specifically, the time evolving N-body
density matrix is written as an average of tensor products of 1-body densities
each of which obeys a stochastic evolution equation. Such decompositions can be
constructed for any mixture of fermions and bosons. The evolution equations for
the 1-body densities preserve norm, Hermiticity and positivity.
