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The proposed method combines a control on galaxy shape parameters offered by analytic models with realistic surface brightness distributions learned from real<jats:italic>Hubble<\/jats:italic>Space Telescope observations by deep generative models. We simulate a galaxy field of 0.4\u2006deg<jats:sup>2<\/jats:sup>as it will be seen by the<jats:italic>Euclid<\/jats:italic>visible imager VIS, and we show that galaxy structural parameters are recovered to an accuracy similar to that for pure analytic S\u00e9rsic profiles. Based on these simulations, we estimate that the<jats:italic>Euclid<\/jats:italic>Wide Survey (EWS) will be able to resolve the internal morphological structure of galaxies down to a surface brightness of 22.5\u2006mag\u2006arcsec<jats:sup>\u22122<\/jats:sup>, and the<jats:italic>Euclid<\/jats:italic>Deep Survey (EDS) down to 24.9\u2006mag\u2006arcsec<jats:sup>\u22122<\/jats:sup>. This corresponds to approximately 250 million galaxies at the end of the mission and a 50% complete sample for stellar masses above 10<jats:sup>10.6<\/jats:sup>\u2006<jats:italic>M<\/jats:italic><jats:sub>\u2299<\/jats:sub>(resp. 10<jats:sup>9.6<\/jats:sup>\u2006<jats:italic>M<\/jats:italic><jats:sub>\u2299<\/jats:sub>) at a redshift<jats:italic>z<\/jats:italic>\u2004\u223c\u20040.5 for the EWS (resp. EDS). 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