Purpose: To substantially shorten the acquisition time required for quantitative 3D chemical exchange saturation transfer (CEST) and semisolid magnetization transfer (MT) imaging and allow for rapid chemical exchange parameter map reconstruction. Methods: Three-dimensional CEST and MT magnetic resonance fingerprinting (MRF) datasets of L-arginine phantoms, whole-brains, and calf muscles from healthy volunteers, cancer patients, and cardiac patients were acquired using 3T clinical scanners at 3 different sites, using 3 different scanner models and coils. A generative adversarial network supervised framework (GAN-CEST) was then designed and trained to learn the mapping from a reduced input data space to the quantitative exchange parameter space, while preserving perceptual and quantitative content. Results: The GAN-CEST 3D acquisition time was 42-52 seconds, 70% shorter than CEST-MRF. The quantitative reconstruction of the entire brain took 0.8 seconds. An excellent agreement was observed between the ground truth and GAN-based L-arginine concentration and pH values (Pearson's r > 0.97, NRMSE < 1.5%). GAN-CEST images from a brain-tumor subject yielded a semi-solid volume fraction and exchange rate NRMSE of 3.8$\pm$1.3% and 4.6$\pm$1.3%, respectively, and SSIM of 96.3$\pm$1.6% and 95.0$\pm$2.4%, respectively. The mapping of the calf-muscle exchange parameters in a cardiac patient, yielded NRMSE < 7% and SSIM > 94% for the semi-solid exchange parameters. In regions with large susceptibility artifacts, GAN-CEST has demonstrated improved performance and reduced noise compared to MRF. Conclusion: GAN-CEST can substantially reduce the acquisition time for quantitative semisolid MT/CEST mapping, while retaining performance even when facing pathologies and scanner models that were not available during training.