In this paper, we introduce new distributed diffusion algorithms to track a sequence of hidden random matrices that evolve on the special orthogonal group. The algorithms are based on the Adapt-then-Combine and the Random Exchange methods, and diffuse Gaussian approximations of posterior densities computed in the Lie algebra of the special orthogonal group. Simulation results show that, in a scenario with strongly nonlinear observation functions, the proposed algorithms perform similarly to the centralized particle filter estimator and can outperform competing Extended Kalman Filters.