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Real low-resolution (LR) face images contain degradations which are too varied and complex to be captured by known downsampling kernels and signal-independent noises. So, in order to successfully super-resolve real faces, a method needs to be robust to a wide range of noise, blur, compression artifacts etc. Some of the recent works attempt to model these degradations from a dataset of real images using a Generative Adversarial Network (GAN). They generate synthetically degraded LR images and use them with corresponding real high-resolution(HR) image to train a super-resolution (SR) network using a combination of a pixel-wise loss and an adversarial loss. In this paper, we propose a two module super-resolution network where the feature extractor module extracts robust features from the LR image, and the SR module generates an HR estimate using only these robust features. We train a degradation GAN to convert bicubically downsampled clean images to real degraded images, and interpolate between the obtained degraded LR image and its clean LR counterpart. This interpolated LR image is then used along with it's corresponding HR counterpart to train the super-resolution network from end to end. Entropy Regularized Wasserstein Divergence is used to force the encoded features learnt from the clean and degraded images to closely resemble those extracted from the interpolated image to ensure robustness.