  The application of the diffusion Monte Carlo method to a strongly interacting
Fermi system as normal liquid $^3$He is explored. We show that the fixed-node
method together with the released-node technique and a systematic method to
analytically improve the nodal surface constitute an efficient strategy to
improve the calculation up to a desired accuracy. This methodology shows
unambiguously that backflow correlations, when properly optimized, are enough
to generate an equation of state of liquid $^3$He in excellent agreement with
experimental data from equilibrium up to freezing.
