Smooth volume form on quotient of Lie group

Question

I consider a compact Lie group $K$ and a closed subgroup $K'$. Let $\mu_K$ be the probability Haar measure on $K$ and let $\omega_{K}$ be the associated left-invariant volume form. I consider the quotient $X = K / K'$, which is a compact manifold, and I equip it with the push-forward measure $\sigma = \pi_* \mu_K$ under the natural projection map $\pi : K \rightarrow X$, $k \mapsto k K'$. This gives a $K$-invariant probability measure on $X$. My question is, if the measure $\sigma$ is still associeted with a smooth non-vanishing top-dimensional form $\omega_\sigma$ on $X$ and how one can see this. Thank you.