We investigate the nuclear many-body problem through two projects. First, we develop a novel method for calculating the second-order perturbation theory correction to the ground state energy of a nuclear-many system in a Diffusion Monte Carlo calculation. Higher perturbative corrections are difficult to calculate in most \textit{ab initio} many-body methods since they are usually concerned with calculating only the ground state energy. By mapping the calculation of the second-order correction to an evolution in imaginary time using Diffusion Monte Carlo, we calculate these terms for the first time in a continuum nuclear context. We employ our new method to investigate the perturbativeness of modern nuclear interactions derived from chiral effective field theory. The second project approaches the nuclear many-body problem within a lattice formalism. We apply Auxiliary Field Quantum Monte Carlo which is used widely for the study of condensed matter systems and modify it to study nuclear systems.