We propose a novel probabilistic direct structure-from-motion (SfM) method that combines black-box variational inference (BBVI) with the reparameterization trick. Unlike conventional approaches that rely on infinitesimal motion approximations and linearization, our method directly optimizes the nonlinear perspective projection model, achieving robust estimation even under large camera motions. By leveraging automatic differentiation, the BBVI formulation provides efficient, low-variance gradient estimation compared to REINFORCE-based methods. A hierarchical multi-resolution scheme further enhances stability and maintains implementation simplicity. Experimental results demonstrate that our approach successfully handles challenging wide-baseline scenarios while providing reliable, uncertainty-aware depth estimation.