Image-to-image translation is an ill-posed problem as unique one-to-one\nmapping may not exist between the source and target images. Learning-based\nmethods proposed in this context often evaluate the performance on test data\nthat is similar to the training data, which may be impractical. This demands\nrobust methods that can quantify uncertainty in the prediction for making\ninformed decisions, especially for critical areas such as medical imaging.\nRecent works that employ conditional generative adversarial networks (GANs)\nhave shown improved performance in learning photo-realistic image-to-image\nmappings between the source and the target images. However, these methods do\nnot focus on (i)~robustness of the models to out-of-distribution (OOD)-noisy\ndata and (ii)~uncertainty quantification. This paper proposes a GAN-based\nframework that (i)~models an adaptive loss function for robustness to OOD-noisy\ndata that automatically tunes the spatially varying norm for penalizing the\nresiduals and (ii)~estimates the per-voxel uncertainty in the predictions. We\ndemonstrate our method on two key applications in medical imaging:\n(i)~undersampled magnetic resonance imaging (MRI) reconstruction (ii)~MRI\nmodality propagation. Our experiments with two different real-world datasets\nshow that the proposed method (i)~is robust to OOD-noisy test data and provides\nimproved accuracy and (ii)~quantifies voxel-level uncertainty in the\npredictions.\n