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There is growing concern over the safety of powerful diffusion models, as they are often misused to produce inappropriate, not-safe-for-work content or generate copyrighted material or data of individuals who wish to be forgotten. Many existing methods tackle these issues by heavily relying on text-based negative prompts or retraining the model to eliminate certain features or samples. In this paper, we take a radically different approach, directly modifying the sampling trajectory by leveraging a negation set (e.g., unsafe images, copyrighted data, or private data) to avoid specific regions of data distribution, without needing to retrain or fine-tune the model. We formally derive the relationship between the expected denoised samples that are safe and those that are unsafe, leading to our *safe* denoiser, which ensures its final samples are away from the area to be negated. We achieve state-of-the-art safety performance in large-scale datasets such as the CoPro dataset while also enabling significantly more cost-effective sampling than existing methodologies.