We introduce a class of interacting fermionic quantum models in d dimensions with nodal interactions that exhibit superdiffusive transport. We establish nonperturbatively that the nodal structure of the interactions gives rise to long-lived quasiparticle excitations that result in a diverging diffusion constant, even though the system is fully chaotic. Using a Boltzmann equation approach, we find that the charge mode acquires an anomalous dispersion relation at long wavelength ω ( q ) ∼ q z with dynamical exponent z = min [ ( 2 n + d ) / 2 n , 2 ] , where n is the order of the nodal point in momentum space. We verify our predictions in one-dimensional systems using tensor-network techniques.