Aims. We revisit the color bimodality of galaxies using the extensive EFIGI morphological classification of nearby galaxies. Methods. The galaxy profiles from the Sloan Digital Sky Survey (SDSS) gri images were decomposed as a bulge and a disk by controlled profile modeling with the Euclid SourceXtractor++ software. The spectral energy distributions from our resulting gri SDSS photometry complemented with Galaxy Evolution Explorer (GALEX) NUV photometry were fitted with the ZPEG software and PEGASE.2 templates in order to estimate the stellar masses and specific star formation rates (sSFR) of whole galaxies as well as their bulge and disk components. Results. The absolute NUV−r color versus stellar mass diagram shows a continuous relationship between the present sSFR of galaxies and their stellar mass, which spans all morphological types of the Hubble sequence monotonously. Irregular galaxies to intermediate-type Sab spirals make up the “Blue Cloud” across 4 orders of magnitude in stellar mass but a narrow range of sSFR. This mass build-up of spiral galaxies requires major mergers, in agreement with their frequently perturbed isophotes. At high mass, the Blue Cloud leads to the “Green Plain”, dominated by S0a and Sa early-type spirals. It was formerly called the “Green Valley”, due to its low density, but we rename it because of its wide stretch and nearly flat density over ∼2 mag in NUV−r color (hence sSFR), despite a limited range of stellar mass (1 order of magnitude). The Green Plain links up the “Red Sequence”, containing all lenticular and elliptical galaxies with a 2 order of magnitude mass interval, and systematically higher masses for the ellipticals. We confirm that the Green Plain cannot be studied using u − r optical colors because it is overlayed by the Red Sequence, hence NUV data are necessary. Galaxies across the Green Plain undergo a marked growth by a factor 2 to 3 in their bulge-to-total mass ratio and a systematic profile change from pseudo to classical bulges, as well as a significant reddening due to star formation fading in their disks. The Green Plain is also characterized by a maximum stellar mass of 1011.7 M⊙ beyond which only elliptical galaxies exist, hence supporting the scenario of ellipticals partly forming by major mergers of massive disk galaxies. Conclusions. The EFIGI attributes indicate that dynamical processes (spiral arms and isophote distortions) contribute to the scatter of the Main Sequence of star-forming galaxies (Blue Cloud), via the enhancement of star formation (flocculence, HII regions). The significant bulge growth across the Green Plain confirms that it is a transition region, and excludes a predominantly quick transit due to rapid quenching. The high frequency of bars for all spirals as well as the stronger spiral arms and flocculence in the knee of the Green Plain suggest that internal dynamics, likely triggered by flybys or (mainly minor) mergers, may be the key to the bulge growth of massive disk galaxies, which is a marker of the aging of galaxies from star forming to quiescence. The Hubble sequence can then be considered as an inverse sequence of galaxy physical evolution.