Diffusion models have achieved unprecedented success in image generation but pose increasing risks in terms of privacy, fairness, and security. A growing demand exists to \emph{erase} sensitive or harmful concepts (e.g., NSFW content, private individuals, artistic styles) from these models while preserving their overall generative capabilities. We introduce \textbf{SCORE} (Secure and Concept-Oriented Robust Erasure), a novel framework for robust concept removal in diffusion models. SCORE formulates concept erasure as an \emph{adversarial independence} problem, theoretically guaranteeing that the model's outputs become statistically independent of the erased concept. Unlike prior heuristic methods, SCORE minimizes the mutual information between a target concept and generated outputs, yielding provable erasure guarantees. We provide formal proofs establishing convergence properties and derive upper bounds on residual concept leakage. Empirically, we evaluate SCORE on Stable Diffusion and FLUX across four challenging benchmarks: object erasure, NSFW removal, celebrity face suppression, and artistic style unlearning. SCORE consistently outperforms state-of-the-art methods including EraseAnything, ANT, MACE, ESD, and UCE, achieving up to \textbf{12.5\%} higher erasure efficacy while maintaining comparable or superior image quality. By integrating adversarial optimization, trajectory consistency, and saliency-driven fine-tuning, SCORE sets a new standard for secure and robust concept erasure in diffusion models.