Existing approaches for restoring weather-degraded images follow a fully-supervised paradigm and they require paired data for training. However, collecting paired data for weather degradations is extremely challenging, and existing methods end up training on synthetic data. To overcome this issue, we describe an approach for supervising deep networks that are based on CycleGAN, thereby enabling the use of unlabeled real-world data for training. Specifically, we introduce new losses for training CycleGAN that lead to more effective training, resulting in high-quality reconstructions. These new losses are obtained by jointly modeling the latent space embeddings of predicted clean images and original clean images through Deep Gaussian Processes. This enables the CycleGAN architecture to transfer the knowledge from one domain (weather-degraded) to another (clean) more effectively. We demonstrate that the proposed method can be effectively applied to different restoration tasks like de-raining, de-hazing and de-snowing and it outperforms other unsupervised techniques (that leverage weather-based characteristics) by a considerable margin.