Neural language models often fail to generate diverse and informative texts, limiting their applicability in real-world problems. While previous approaches have proposed to address these issues by identifying and penalizing undesirable behaviors (e.g., repetition, overuse of frequent words) from language models, we propose an alternative approach based on an observation: models primarily learn attributes within examples that are likely to cause degeneration problems. Based on this observation, we propose a new approach to prevent degeneration problems by training two models. Specifically, we first train a model that is designed to amplify undesirable patterns. We then enhance the diversity of the second model by focusing on patterns that the first model fails to learn. Extensive experiments on two tasks, namely language modeling and dialogue generation, demonstrate the effectiveness of our approach.