The colour bimodality of galaxies provides an empirical basis for theories of galaxy evolution. However, the balance of processes that begets this bimodality has not yet been constrained. A more detailed view of the galaxy population is needed, which we achieve in this paper by using unsupervised machine learning to combine multidimensional data at two different epochs. We aim to understand the cosmic evolution of galaxy subpopulations by uncovering substructures within the colour bimodality. We choose a clustering algorithm that models clusters using only the most discriminative data available, and apply it to two galaxy samples: one from the second edition of the GALEX-SDSS-WISE Legacy Catalogue (GSWLC-2; z ∼ 0.06), and the other from the VIMOS Public Extragalactic Redshift Survey (VIPERS; z ∼ 0.65). We cluster within a nine-dimensional feature space defined purely by rest-frame ultraviolet-through-near-infrared colours. Both samples are similarly partitioned into seven clusters, breaking down into four of mostly star-forming galaxies (including the vast majority of green valley galaxies) and three of mostly passive galaxies. The separation between these two families of clusters suggests differences in the evolution of their galaxies, and that these differences are strongly expressed in their colours alone. The samples are closely related, with star-forming/green-valley clusters at both epochs forming morphological sequences, capturing the gradual internally driven growth of galaxy bulges. At high stellar masses, this growth is linked with quenching. However, it is only in our low-redshift sample that additional, environmental processes appear to be involved in the evolution of low-mass passive galaxies.