Sections of families of curves

Question

Let $R$ be a complete discrete valuation ring with fraction field, say $K$, $\pi:X \to \mathrm{Spec}(R)$ be a flat, projective, surjective morphism, where $X$ is a regular scheme of dimension $2$. Assume further that the generic fiber of $\pi$, $X_K:=X \times_R \mathrm{Spec}(K)$ is a smooth curve. The question is: If $X_K(\mathrm{Spec}(K)) \not= \emptyset$ then is $X(\mathrm{Spec}(R))\not= \emptyset$?