Tits-type alternative for groups generated by additive subgroups of affine varieties

Let $X$ be an affine algebraic variety defined over an algebraically closed field, and let $G$ be a subgroup of $\operatorname{Aut}(X)$ generated by a finite collection of $\mathbb{G}_{\mathrm{a}}$-subgroups $U_1,\ldots,U_k$. Tits-type alternative. Either $G$ contains a nonabelian free subgroup, or $G$ is a unipotent affine algebraic group. This is proposed as an analogue over arbitrary algebraically closed fields of the paper's theorem for affine algebraic surfaces over $\mathbb{C}$. The result is not established here; the cited arguments rely on results specific to varieties defined over $\mathbb{C}$, so the conjectural extension remains open.