A neural network-based approach is proposed both for reconstructing the focal spot intensity profile and for estimating the peak intensity of a high-power tightly focused laser pulse using the angular energy distributions of protons accelerated by the pulse from rarefied gases. For these purposes, we use a convolutional neural network architecture. Training and testing datasets are calculated using the test particle method, with the laser description in the form of Stratton–Chu integrals, which model laser pulses focused by an off-axis parabolic mirror down to the diffraction limit. To demonstrate the power and robustness of this method, we discuss the reconstruction of axially symmetric intensity profiles for laser pulses with intensities and focal diameters in the ranges of 10²¹–10²³ W cm^-2 and ∼(1–4)λ, respectively. This approach has prospects for implementation at higher intensities and with asymmetric laser beams, and it can provide a valuable diagnostic method for emerging extremely intense laser facilities.