  Low-surface-brightness galaxies (LSBGs) -- defined as systems that are
fainter than the surface-brightness limits of past wide-area surveys -- form
the overwhelming majority of galaxies in the dwarf regime (M* < 10^9 MSun).
Using NewHorizon, a high-resolution cosmological simulation, we study the
origin of LSBGs and explain why LSBGs at similar stellar mass show the large
observed spread in surface brightness. New Horizon galaxies populate a
well-defined locus in the surface brightness -- stellar mass plane, with a
spread of ~3 mag arcsec^-2, in agreement with deep SDSS Stripe data. Galaxies
with fainter surface brightnesses today are born in regions of higher
dark-matter density. This results in faster gas accretion and more intense star
formation at early epochs. The stronger resultant supernova feedback flattens
gas profiles at a faster rate which, in turn, creates shallower stellar
profiles (i.e. more diffuse systems) more rapidly. As star formation declines
towards late epochs (z<1), the larger tidal perturbations and ram pressure
experienced by these systems (due to their denser local environments)
accelerate the divergence in surface brightness, by increasing their effective
radii and reducing star formation respectively. A small minority of dwarfs
depart from the main locus towards high surface brightnesses, making them
detectable in past wide surveys. These systems have anomalously high
star-formation rates, triggered by recent, fly-by or merger-driven starbursts.
We note that objects considered extreme/anomalous at the depth of current
datasets, e.g. `ultra-diffuse galaxies', actually dominate the predicted dwarf
population and will be routinely visible in future surveys like LSST.
