The key challenge of multi-domain translation lies in simultaneously encoding both the general knowledge shared across domains and the particular knowledge distinctive to each domain in a unified model. Previous work shows that the standard neural machine translation (NMT) model, trained on mixed-domain data, generally captures the general knowledge, but misses the domain-specific knowledge. In response to this problem, we augment NMT model with additional domain transformation networks to transform the general representations to domain-specific representations, which are subsequently fed to the NMT decoder. To guarantee the knowledge transformation, we also propose two complementary supervision signals by leveraging the power of knowledge distillation and adversarial learning. Experimental results on several language pairs, covering both balanced and unbalanced multi-domain translation, demonstrate the effectiveness and universality of the proposed approach. Encouragingly, the proposed unified model achieves comparable results with the fine-tuning approach that requires multiple models to preserve the particular knowledge. Further analyses reveal that the domain transformation networks successfully capture the domain-specific knowledge as expected.