Searching for topological states of quantum matter is at the forefront of ultracold atoms. Currently, consorted efforts are made to simulate famous electronic topological models that are non-interacting via loading atoms into the lowest s-band, assisted by synthetic magnetic flux or spin-orbit coupling. In contrast, in this talk we show that by loading atoms into the higher p-band of optical lattices, interaction among atoms could spontaneously generate topologically nontrivial states. First, focusing on the experimentally realized chiral bosonic p-wave superfluid, we show that it supports Dirac bosons in the elementary excitation spectra and a topological phase transition occurs due to further symmetry breaking from adding an extra lattice potential. Second, we find that topological odd-parity superfluidity robustly arises in a cold two-component Fermi gas with three rudimental aspects that are readily available in current cold atom experiments, namely: spin population imbalance, Feshbach resonance tuned s-wave interaction, and a spin-independent optical lattice.