Summary The quantitative integration of nuclear measurements into the in-situ petrophysical and geophysical interpretation of rock formation has been difficult because of the lack of efficient algorithms to simulate them. We introduce and successfully implement a new method for rapid simulation of borehole neutron measurements using Monte Carlo-derived spatial flux sensitivity functions (FSFs) and diffusion flux-difference (DFD) approximations. The method calculates spatial sensitivity flux perturbations using flux-difference approximations of one-group neutron diffusion models. With appropriate boundary conditions, we implement the one-group, time-independent neutron diffusion solution for non-multiplying systems in cylindrical coordinates. The solution is differentiated with respect to neutron cross-section, thereby yielding an expression for flux-difference due to cross-section perturbations. Constant transport-correction factors for cross-section parameters in the diffusion model are calculated with a flux-fitting method. Thereafter, spatial responses are rapidly and accurately calculated using a first-order Rytov diffusion flux-difference (DFD) approximation. Examples of application indicate that neutron porosity logs can be efficiently simulated with the new method even in complex geometrical and physical conditions, with errors lower than 2.5 porosity units (p.u.) in highly-deviated wells.