  We propose a novel four-coloring model which describes "frustrated
superfluidity" of $p$-band bosons in the diamond optical lattice. The
superfluid phases of the condensate wavefunctions on the diamond-lattice bonds
are mapped to four distinct colors at low temperatures. The fact that a
macroscopic number of states satisfy the constraints that four differently
colored bonds meet at the same site leads to an extensive degeneracy in the
superfluid ground state at the classical level. We demonstrate that the phase
of the superfluid wavefunction as well as the orbital angular momentum
correlations exhibit a power-law decay in the degenerate manifold that is
described by an emergent magnetostatic theory with three independent flux
fields. Our results thus provide a novel example of critical superfluid phase
with algebraic order in three dimensions. We further show that quantum
fluctuations favor a N\'eel ordering of orbital angular moments with broken
sublattice symmetry through the order-by-disorder mechanism.
