Right-angled Artin subgroups of the $C^{\mathrm{\infty }}$ diffeomorphism group of the real line

We prove that every right-angled Artin group embeds into the $C^{\mathrm{\infty }}$ diffeomorphism group of the real line. As a corollary, we show every limit group, and more generally every countable residually RAAG group, embeds into the $C^{\mathrm{\infty }}$ diffeomorphism group of the real line.