I will present the Auxiliary Field Diffusion Monte Carlo 
(AFDMC) method, that is an extension of the well known 
Diffusion Monte Carlo (DMC) to deal with nuclear systems.
The main difference between standard Hamiltonians and nuclear 
ones is that nucleon-nucleon interaction strongly depends 
on the spin and isospin states of nucleons that must be 
accurately included in the variational wave function.
As I will show, such dependence strongly limit the maximum 
number of nucleons that can be simulated by means of the very 
accurate techniques like Variational Monte Carlo (VMC) and 
Green's Function Monte Carlo (GFMC), because of the computational 
time needed to evaluate the wave function.
The AFDMC circumnavigates this limitation by sampling the 
spin/isospin states of nucleons by means of the Hubbard-Stratonovich 
transformation; this is realized by introducing auxiliary fields 
in addition to the spacial coordinates of nucleons.
The application of AFDMC to compute the ground state properties 
of both finite systems and infinite matter will be presented.