Path integral molecular dynamics (PIMD) is a method to incorporate quantum mechanics into molecular dynamics by mapping each quantum particle onto a classical representation . Combining electronic structure theory with PI methods is exceedingly computationally expensive as each particle is represented by several classical replicas, each requiring a separate on-the-fly electronic structure calculation. For this reason, high-level electronic structure calculations coupled with quantum nuclear dynamics have only recently been made possible. Thanks to the recent development of neural network potentials (NNPs), an extensive study using a high-quality functional beyond local DFT is feasible even when combined with path-integral molecular dynamics. For instance, the densities of water as predicted by NNP trained on revPBE0-D3 data agree with the experiment to within 3% for both liquid water and ice Ih and Ic. Accurate and efficient quantum vibrational spectra of water can also be obtained for bulk and interfacial systems. Recently, quantum dynamics simulations with forces from a fifth-rung electronic structure level have provided an accurate determination of the structure, diffusion, and vibrational features of water and aqueous solvated electron . In this work, the structural and dynamical properties of bulk water have been studied by means of MD and PIMD simulations via an NNP. Radial distribution functions, diffusion, and vibrational dynamics were investigated at different temperatures. At ambient conditions, MP2 theory predicts overstructured liquid water, which might be due to an incomplete basis set. It is found that experimental structural properties and the diffusion coefficients are in better agreement with simulations at 340 K.