ABSTRACT We apply a Machine Learning technique known as Convolutional Denoising Autoencoder to denoise synthetic images of state-of-the-art radio telescopes, with the goal of detecting the faint, diffused radio sources predicted to characterize the radio cosmic web. In our application, denoising is intended to address both the reduction of random instrumental noise and the minimization of additional spurious artefacts like the sidelobes, resulting from the aperture synthesis technique. The effectiveness and the accuracy of the method are analysed for different kinds of corrupted input images, together with its computational performance. Specific attention has been devoted to create realistic mock observations for the training, exploiting the outcomes of cosmological numerical simulations, to generate images corresponding to LOFAR HBA 8 h observations at 150 MHz. Our autoencoder can effectively denoise complex images identifying and extracting faint objects at the limits of the instrumental sensitivity. The method can efficiently scale on large data sets, exploiting high-performance computing solutions, in a fully automated way (i.e. no human supervision is required after training). It can accurately perform image segmentation, identifying low brightness outskirts of diffused sources, proving to be a viable solution for detecting challenging extended objects hidden in noisy radio observations.