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We propose a new generative model named adaptive cycle-consistent generative adversarial network, or Ad CycleGAN to perform image translation between normal and COVID-19 positive chest X-ray images. An independent pre-trained criterion is added to the conventional Cycle GAN architecture to exert adaptive control on image translation. The performance of Ad CycleGAN is compared with the Cycle GAN without the external criterion. The quality of the synthetic images is evaluated by quantitative metrics including Mean Squared Error (MSE), Root Mean Squared Error (RMSE), Peak Signal-to-Noise Ratio (PSNR), Universal Image Quality Index (UIQI), visual information fidelity (VIF), Frechet Inception Distance (FID), and translation accuracy. The experimental results indicate that the synthetic images generated either by the Cycle GAN or by the Ad CycleGAN have lower MSE and RMSE, and higher scores in PSNR, UIQI, and VIF in homogenous image translation (i.e., Y → Y) compared to the heterogenous image translation process (i.e., X → Y). The synthetic images by Ad CycleGAN through the heterogeneous image translation have significantly higher FID score compared to Cycle GAN (p < 0.01). The image translation accuracy of Ad CycleGAN is higher than that of Cycle GAN when normal images are converted to COVID-19 positive images (p < 0.01). Therefore, we conclude that the Ad CycleGAN with the independent criterion can improve the accuracy of GAN image translation. The new architecture has more control on image synthesis and can help address the common class imbalance issue in machine learning methods and artificial intelligence applications with medical images. Full article