Comparison between the L2 barycenter and the Wasserstein barycenter. The starting and final distributions are in blue and red, respectively. The black dashed distribution represents the barycenter calculated using the L2 distance, whereas the green dashed distribution is computed using the Wasserstein distance. The bottom panel illustrates the interpolation path of the Wasserstein barycenter for different a values, highlighting its transition from the starting distribution to the final one.