We propose a “scotogenic” mechanism relating small neutrino mass and cosmological dark matter. Neutrinos are Dirac fermions with masses arising only in two-loop order through the sector responsible for dark matter. Two triality symmetries ensure both dark matter stability and strict lepton number conservation at higher orders. A global spontaneously broken U(1) symmetry leads to a physical Diracon that induces invisible Higgs decays which add up to the Higgs to dark matter mode. This enhances sensitivities to spin-independent WIMP dark matter search below class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269316305214&_mathId=si1.gif&_user=111111111&_pii=S0370269316305214&_rdoc=1&_issn=03702693&md5=057ab581da1769036e8a7078c35e0289" title="Click to view the MathML source">mh/2class="mathContainer hidden">class="mathCode">.