  Using three dimensional Monte Carlo radiation transfer models of
photoionisation and dust scattering, we explore different components of the
widespread diffuse H$\alpha$ emission observed in the interstellar medium of
the Milky Way and other galaxies. We investigate the relative contributions of
H$\alpha$ from recombination emission in ionised gas and H$\alpha$ that
originates in H{\sc ii} regions near the Galactic midplane and scatters off
high altitude dust in the diffuse interstellar medium. For the radiation
transfer simulations we consider two geometries for the interstellar medium: a
three dimensional fractal geometry that reproduces the average density
structure inferred for hydrogen in the Milky Way, and a density structure from
a magneto hydrodynamic simulation of a supernovae driven turbulent interstellar
medium. Although some sight lines that are close to H{\sc ii} regions can be
dominated by scattered light, overall we find that less than $\sim 20\%$ of the
total H$\alpha$ intensity in our simulations can be attributed to dust
scattering. Our findings on the relative contribution of scattered H$\alpha$
are consistent with previous observational and theoretical analyses. We also
investigate the relative contributions of dust scattering and in situ
ionisation of high density dust clouds in the diffuse gas. Dust scattering in
these partially ionised clouds contribute $\sim 40\%$ to the total intensity of
H$\alpha$.
