  Starting from the Gaia DR3 HR diagram, we derive the star formation history
(SFH) as a function of distance from the Galactic Plane within a cylinder
centred on the Sun with a 200~pc radius and spanning 1.3~kpc above and below
the Galaxy's midplane. We quantify both the concentration of the more recent
star formation in the Galactic Plane, and the age-related increase in the scale
height of the Galactic Disc stellar component, which is well-described by
power-laws with indices ranging from $1/2$ to $2/3$. The vertically-integrated
star formation rate falls from $(1.147 \pm 0.039)\times10^{-8}\,
\text{M}_{\odot} \text{yr}^{-1} \text{pc}^{-2}$ at earlier times down to $(6.2
\pm 3.0) \times10^{-9}\, \text{M}_{\odot} \text{yr}^{-1} \text{pc}^{-2}$ at
present times, but we find a significant peak of star formation in the 2 to 3
Gyr age bin. The total mass of stars formed per unit area over time is $118.7
\pm 6.2\, \text{M}_{\odot} \text{pc}^{-2}$, which is nearly twice the present
stellar mass derived from kinematics within 1~kpc from the Galactic Plane,
implying a high degree of matter recycling in successive generations of stars.
The method is then modified by adopting an age-dependent correlation between
the SFH across the different slices, which results in less noisy and more
symmetrical results without significantly changing the previously mentioned
quantities. This appears to be a promising way to improve SFH recovery in
external galaxies.
