This paper addresses passive inverse obstacle scattering problems with Neumann and Robin boundary conditions related to the Helmholtz equation in two and three space dimensions. The driving source is modeled as a Gaussian process, and the data of the inverse problems are correlations of total fields measure on a surface surrounding the scatterer and the source region. As a main result of this report, we establish uniqueness of the (spatially varying) strength of uncorrelated source processes given covariances of total fields. Moreover, we present numerical reconstruction results, both for source strengths and for shapes of scattering obstacles. This work builds on our previous study ( https://arxiv.org/abs/2410.06105 ) of Dirichlet boundary conditions, expanding the framework to handle Neumann and Robin boundary conditions.