Deep learning has recently been successfully applied to lithography hotspot detection. However, automatic correction of the detected hotspots into non-hotspots has not been explored. This problem is challenging because the standard supervised learning requires a training dataset with pairs of hotspots and non-hotspots, which is impractical to collect because lithography hotspots involve diverse and complicated lithographic pattern properties. In this paper, we propose a new framework for lithography hotspot correction with a deep generative network combined with a learning strategy optimized for lithography patterns. Our key idea is to learn to translate hotspots to non-hotspots and vice versa, simultaneously. In this way, the training dataset does not have to be paired, and hotspot patterns in variety of background can be learned. Our method does not require the understanding of the cause of hotspots and can correct hotspots that are difficult to recognize by conventional approaches. For evaluation, we propose to synthesize a training dataset that reflects a variety of real-world lithography patterns. Experimental results show that our framework can correct hotspot images with comparable quality as a conventional complicated process, while significantly reducing the overall processing time.