  We construct geometric compactifications of the moduli space $F_{2d}$ of
polarized K3 surfaces, in any degree $2d$. Our construction is via KSBA theory,
by considering canonical choices of divisor $R\in |nL|$ on each polarized K3
surface $(X,L)\in F_{2d}$. The main new notion is that of a recognizable
divisor $R$, a choice which can be consistently extended to all central fibers
of Kulikov models. We prove that any choice of recognizable divisor leads to a
semitoroidal compactification of the period space, at least up to
normalization. Finally, we prove that the rational curve divisor is
recognizable for all degrees.
