Recent advancements in text-to-image (T2I) models have greatly benefited from large-scale datasets, but they also pose significant risks due to the potential generation of unsafe content. To mitigate this issue, researchers proposed unlearning techniques that attempt to induce the model to unlearn potentially harmful prompts. However, these methods are easily bypassed by adversarial attacks, making them unreliable for ensuring the safety of generated images. In this paper, we propose Diffusion Unlearning Optimization (DUO), a novel framework for removing NSFW content from T2I models while preserving their performance on unrelated topics. DUO employs a preference optimization approach using curated paired image data, ensuring that the model learns to remove unsafe visual concepts while retain unrelated features. Furthermore, we introduce an output-preserving regularization term to maintain the model's generative capabilities on safe content. Extensive experiments demonstrate that DUO can robustly defend against various state-of-the-art red teaming methods without significant performance degradation on unrelated topics, as measured by FID and CLIP scores. Our work contributes to the development of safer and more reliable T2I models, paving the way for their responsible deployment in both closed-source and open-source scenarios.