  Scaling laws of dust, HI gas and metal mass with stellar mass, specific star
formation rate and metallicity are crucial to our understanding of the buildup
of galaxies through their enrichment with metals and dust. In this work, we
analyse how the dust and metal content varies with specific gas mass
($M_{\text{HI}}$/$M_{\star}$) across a diverse sample of 423 nearby galaxies.
The observed trends are interpreted with a set of Dust and Element evolUtion
modelS (DEUS) - incluidng stellar dust production, grain growth, and dust
destruction - within a Bayesian framework to enable a rigorous search of the
multi-dimensional parameter space. We find that these scaling laws for galaxies
with $-1.0\lesssim \log M_{\text{HI}}$/$M_{\star}\lesssim0$ can be reproduced
using closed-box models with high fractions (37-89$\%$) of supernova dust
surviving a reverse shock, relatively low grain growth efficiencies
($\epsilon$=30-40), and long dus lifetimes (1-2\,Gyr). The models have
present-day dust masses with similar contributions from stellar sources
(50-80\,$\%$) and grain growth (20-50\,$\%$). Over the entire lifetime of these
galaxies, the contribution from stardust ($>$90\,$\%$) outweighs the fraction
of dust grown in the interstellar medium ($<$10$\%$). Our results provide an
alternative for the chemical evolution models that require extremely low
supernova dust production efficiencies and short grain growth timescales to
reproduce local scaling laws, and could help solving the conundrum on whether
or not grains can grow efficiently in the interstellar medium.
