The universal non-equilibrium properties of isolated quantum systems are usually explored by studying the transport of conserved quantities such as charge and spin, but energy transport has received less attention. Here we study infinite temperature energy transport in a kinetically constrained PXP model describing the Rydberg atomic quantum simulator. State-of-the-art numerical simulations, including exact diagonalization and time-evolution block-decimation methods, reveal the existence of two distinct transport regimes. At moderate times, the energy-energy correlation function displays periodic oscillations due to families of eigenstates forming distinct su(2) representations hidden within the spectrum. These families of eigenstates generalize the scar states of quantum many-body found in previous studies and imprint on infinite temperature energy transport. Later, we observe extensive hyperdiffusive transport regimes due to the proximity of nearby integrable points. Interestingly, strong deformation of his PXP model by chemical potentials does not restore diffusion, instead leading to a stable hyperdiffusive exponent z\approx3/2$. Our results suggest that constrained models are a potential host for new transport regimes and call for a better analytical understanding of their energy transport.