Interferometric Synthetic Aperture Radar (InSAR) provides subcentimetric measurements of surface displacements, which are key for characterizing and monitoring magmatic processes in volcanic regions. The abundant measurements of surface displacements in multitemporal InSAR data routinely acquired by SAR satellites can facilitate near real-time volcano monitoring on a global basis. However, the presence of atmospheric signals in interferograms complicates the interpretation of those InSAR measurements, which can even lead to a misinterpretation of InSAR signals and volcanic unrest. Given the vast quantities of SAR data available, an automatic InSAR data processing and denoising approach is required to separate volcanic signals that are cause of concern from atmospheric signals and noise. In this study, we employ a deep learning strategy that directly removes atmospheric and other noise signals from time-consecutive unwrapped surface displacements obtained through an InSAR time series approach using an end-to-end convolutional neural network (CNN) with an encoder-decoder architecture, modified U-net. The CNN is trained with simulated synthetic unwrapped surface displacement maps and is then applied to real InSAR data. Our proposed architecture is capable of detecting dynamic spatio-temporal patterns of volcanic surface displacements. We find that an ensemble-average strategy is recommended to stabilize detected results for varying deformation rates and signal-to-noise ratios (SNRs). A case study is also presented where this method is applied to InSAR data covering Masaya volcano, Nicaragua and the results are validated using continuous GPS data. The results confirm that our network can indeed efficiently suppress atmospheric and other noise to reveal the noise-free surface deformation.