  The first measurements of differential branching fractions of inclusive
semileptonic ${B \to X_u \, \ell^+\, \nu_{\ell}}$ decays are performed using
the full Belle data set of 711 fb$^{-1}$ of integrated luminosity at the
$\Upsilon(4S)$ resonance and for $\ell = e, \mu$. Differential branching
fractions are reported as a function of the lepton momentum, the
four-momentum-transfer squared, light-cone momenta, the hadronic mass, and the
hadronic mass squared. They are obtained by subtracting the backgrounds from
semileptonic ${B \to X_c \, \ell^+\, \nu_{\ell}}$ decays and other processes,
and corrected for resolution and acceptance effects. The measured distributions
are compared to predictions from inclusive and hybrid ${B \to X_u \, \ell^+\,
\nu_{\ell}}$ calculations.
