Text-to-Image (T2I) diffusion models are widely recognized for their ability to generate high-quality and diverse images based on text prompts. However, despite recent advances, these models are still prone to generating unsafe images containing sensitive or inappropriate content, which can be harmful to users. Current efforts to prevent inappropriate image generation for diffusion models are easy to bypass and vulnerable to adversarial attacks. How to ensure that T2I models align with specific safety goals remains a significant challenge. In this work, we propose a novel, training-free approach, called Prompt-Noise Optimization (PNO), to mitigate unsafe image generation. Our method introduces a novel optimization framework that leverages both the continuous prompt embedding and the injected noise trajectory in the sampling process to generate safe images. Extensive numerical results demonstrate that our framework achieves state-of-the-art performance in suppressing toxic image generations and demonstrates robustness to adversarial attacks, without needing to tune the model parameters. Furthermore, compared with existing methods, PNO uses comparable generation time while offering the best tradeoff between the conflicting goals of safe generation and prompt-image alignment.
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