Personalized text-to-image diffusion models have gained increasing attention because they can generate images that contain unique concepts based on limited training data. However, in continual learning scenarios, these models suffer from concept bleed-through, where newly introduced concepts frequently overwrite or interfere with the previously learned concepts. Previous studies have attempted to mitigate this issue at the model adaptation level; however, they failed to fully preserve the distinct semantic representations in the latent space. Thus, this paper proposes an adversarial perturbation-based training strategy to address concept bleed-through in continual learning for personalized diffusion models. The proposed method introduces adversarial perturbations into the training images, which strategically shifts their semantic representations in the latent space to ensure that the newly learned concepts remain distinct and do not interfere with the previously acquired knowledge. Unlike structural modifications to the model, the proposed method operates at the data level, which makes it broadly applicable to existing continual personalization frameworks without increasing model complexity. Experimental results demonstrate that the proposed method significantly improves concept separation while maintaining high image fidelity, offering a solution to enhance the reliability of continual learning in personalized generative models.