Line intensity mapping (LIM) is a promising observational method to probe large-scale fluctuations of line emission from distant galaxies. Data from wide-field LIM observations allow us to study the large-scale structure of the universe as well as galaxy populations and their evolution. A serious problem with LIM is contamination by foreground/background sources and various noise contributions. We develop conditional generative adversarial networks (cGANs) that extract designated signals and information from noisy maps. We train the cGANs using 30,000 mock observation maps with assuming a Gaussian noise matched to the expected noise level of NASAs SPHEREx mission. The trained cGANs successfully reconstruct H{alpha} emission from galaxies at a target redshift from observed, noisy intensity maps. Intensity peaks with heights greater than 3.5 {sigma} noise are located with 60 % precision. The one-point probability distribution and the power spectrum are accurately recovered even in the noise-dominated regime. However, the overall reconstruction performance depends on the pixel size and on the survey volume assumed for the training data. It is necessary to generate training mock data with a sufficiently large volume in order to reconstruct the intensity power spectrum at large angular scales. Our deep-learning approach can be readily applied to observational data with line confusion and with noise.