  We present a finite temperature calculation of the transverse spin-diffusion
coefficient, $D_\bot$, in a dilute degenerate Fermi gas in the presence of a
small external magnetic field, $H$. While the longitudinal diffusion
coefficient displays the conventional low-temperature Fermi-liquid behavior,
$D_\parallel \propto T^{-2}$, the corresponding results for $D_\bot$ show three
separate regimes: (a) $D_\bot \sim H^{-2}$ for $T \ll H$; (b) $D_\bot \sim
T^{-2}$, $D_\bot /D_\parallel \neq 1$ for $T \gg H$ and large spin-rotation
parameter $\xi \gg 1$, and (c) $D_\bot = D_\parallel \propto T^{-2}$ for $T \gg
H$ and $\xi \ll 1$. Our results are qualitatively consistent with the available
experimental data in weakly spin-polarized $^3{\rm He}$ and $^3{\rm He} -
^4{\rm He}$ mixtures.
