  Random diffusions are a popular tool in Monte-Carlo estimations, with well
established algorithms such as Walk-on-Spheres (WoS) going back several
decades. In this work, we introduce diffusion estimators for the problems of
angular synchronization and smoothing on graphs, in the presence of a rotation
associated to each edge. Unlike classical WoS algorithms, these estimators
allow for global estimations by propagating along the branches of multi-type
spanning forests, and we show that they can outperform standard
numerical-linear-algebra solvers in challenging instances, depending on the
topology and density of the graph.
