A nonlinear manifold learning algorithm based on Diffusion Maps (DMs) is employed in this work to identify the low-dimensional manifold embedding the fluidic pinball dynamics. Two-dimensional direct numerical simulations of the incompressible Navier-Stokes equations are performed to compute the viscous wake flow behind the fluidic pinball by varying the Reynolds number Re. Four different flow regimes are considered, spanning from periodic symmetric ( \(Re < 68\) ) to fully chaotic ( \(Re > 115\) ) conditions. By means of the Diffusion Maps embedding, the minimum set of DMs reduced coordinates (eigenvectors) necessary to represent the flow dynamics in all the regimes is found by projecting the high-dimensional simulation data into the reduced low-dimensional space. The nonlinear manifold lying in the state-space spanned by the three leading DMs coordinates is thus obtained by varying the Reynolds number Re, and its shape discussed in connection with the different physical mechanisms at play across all the flow regimes.