  A diffusion Monte Carlo algorithm is introduced that can determine the
correct nodal structure of the wave function of a few-fermion system and its
ground-state energy without an uncontrolled bias. This is achieved by confining
signed random walkers to the points of a uniform infinite spatial grid,
allowing them to meet and annihilate one another to establish the nodal
structure without the fixed-node approximation. An imaginary-time propagator is
derived rigorously from a discretized Hamiltonian, governing a non-Gaussian,
sign-flipping, branching, and mutually annihilating random walk of particles.
The accuracy of the resulting stochastic representations of a fermion wave
function is limited only by the grid and imaginary-time resolutions and can be
improved in a controlled manner. The method is tested for a series of model
problems including fermions in a harmonic trap as well as the He atom in its
singlet or triplet ground state. For the latter case, the energies approach
from above with increasing grid resolution and converge within
$0.015~{E}_\text{h}$ of the exact basis-set-limit value with a statistical
uncertainty of $10^{-5}~{E}_\text{h}$ without an importance sampling or Jastrow
factor.
