We present a new clustering method, significance mode analysis (SigMA), for extracting co-spatial and co-moving stellar populations from large-scale surveys such as ESA Gaia. The method studies the topological properties of the density field in the multidimensional phase space. We validated SigMA on simulated clusters and find that it outperforms competing methods, especially in cases where many clusters are closely spaced. We applied the new method to Gaia DR3 data of the closest OB association to Earth, Scorpio-Centaurus (Sco-Cen), and find more than 13000 co-moving young objects, about 19% of which have a substellar mass. SigMA finds 37 co-moving clusters in Sco-Cen. These clusters are independently validated by their narrow Hertzsprung-Russell diagram sequences and, to a certain extent, by their association with massive stars too bright for Gaia, and are hence unknown to SigMA. We compared our results with similar recent work and find that the SigMA algorithm recovers richer populations, is able to distinguish clusters with velocity differences down to about 0.5km/s, and reaches cluster volume densities as low as 0.01sources/pc^3^. The 3D distribution of these 37 coeval clusters implies a larger extent and volume for the Sco-Cen OB association than typically assumed in the literature. Additionally, we find the association more actively star-forming and dynamically complex than previously thought. We confirm that the star-forming molecular clouds in the Sco-Cen region, namely, Ophiuchus, L134/L183, Pipe Nebula, Corona Australis, Lupus, and Chamaeleon, are part of the Sco-Cen association. The application of SigMA to Sco-Cen demonstrates that advanced machine learning tools applied to the superb Gaia data allows an accurate census of the young populations to be constructed, which in turn allows us to quantify their dynamics and recreate the recent star formation history of the local Milky Way.