  We prove N\'{e}methi's conjecture: if $Y$ is a 3-manifold which is the
boundary of a plumbing of a tree of disk bundles over $S^2$, then the lattice
homology of $Y$ coincides with the Heegaard Floer homology of $Y$. We also give
a conjectural description of the $H_1(Y)/\mathrm{Tors}$ action when $b_1(Y)>0$.
