The combination of energy-dispersive X-ray spectroscopy (EDX) and electron tomography is a powerful approach to retrieve the 3D elemental distribution in nanomaterials, providing an unprecedented level of information for complex, multi-component systems, such as semiconductor devices, as well as catalytic and plasmonic nanoparticles. Unfortunately, the applicability of EDX tomography is severely limited because of extremely long acquisition times and high electron irradiation doses required to obtain 3D EDX reconstructions with an adequate signal-to-noise ratio. One possibility to address this limitation is intelligent denoising of experimental data using prior expectations about the objects of interest. Herein, this approach is followed using the deep learning methodology, which currently demonstrates state-of-the-art performance for an increasing number of data processing problems. Design choices for the denoising approach and training data are discussed with a focus on nanoparticle-like objects and extremely noisy signals typical for EDX experiments. Quantitative analysis of the proposed method demonstrates its significantly enhanced performance in comparison to classical denoising approaches. This allows for improving the tradeoff between the reconstruction quality, acquisition time and radiation dose for EDX tomography. The proposed method is therefore especially beneficial for the 3D EDX investigation of electron beam-sensitive materials and studies of nanoparticle transformations.