Achieving generative creativity in the context of visual data, i.e. the generation of novel and valuable images, is a long-standing goal in computer vision and artificial intelligence. Generative adversarial networks (GANs) are prominent deep generative models that can successfully generate visually-appealing images. However, the generated images are mostly simple memorisation or imitation of training samples, which exhibits limited generative creativity. To obtain higher-degree generative creativity, we focus on more challenging image-to-image generation tasks, in which the generated images are not only more practically valuable, but also more distinct from existing data. The challenges of achieving image-to-image generative creativity lie in three aspects: whether the generated images 1) are truly useful, especially for critical applications (e.g. in the field of medical imaging), and 2) can demonstrate a clear difference from training samples, and 3) are varied and diverse for one input image, which is a natural requirement for many image generation tasks. In this thesis, we aim to develop deep conditional adversarial networks for challenging image-to-image generation tasks, each of which respectively exhibits one type of image-to-image generative creativity. We make the following contributions. First, we propose EnrichGAN for fast compressed sensing magnetic resonance imaging (CS-MRI) reconstruction that exhibits enrichment creativity. We demonstrate that EnrichGAN qualitatively and quantitatively outperforms various conventional and state-of-the-art methods, with a much faster processing time that enables real-time applications. Second, we propose SimGAN for semantic image manipulation. It requires learning good mappings between visual and text features. We show that SimGAN achieves superior results on this challenging image-to-image generation task that demonstrates high-level transformative creativity. Finally, we propose DesignGAN for automating the process of shape-oriented bionic design. It requires learning to combine features of images from different domains, in an unsupervised fashion. We demonstrate that Design- GAN learns to achieve image-to-image combinatorial creativity.