Mechanistic interpretability reveals that safety-critical behaviors (e.g., alignment, jailbreak, backdoor) in Large Language Models (LLMs) are grounded in specialized functional components. However, existing safety attribution methods struggle with generalization and reliability due to their reliance on heuristic, domain-specific metrics and search algorithms. To address this, we propose \ourmethod, a unified safety interpretability framework that identifies functionally complete safety circuits in LLMs via optimization. Unlike methods focusing on isolated heads or neurons, \ourmethod introduces differentiable binary masks to extract multi-granular circuits through gradient descent on safety datasets, while integrates Safety Circuit Tuning to utilize these sparse circuits for efficient safety fine-tuning. We validate \ourmethod in two key scenarios in LLM safety: \textbf{(1) backdoor attacks}, identifying a backdoor circuit with 0.42\% sparsity, whose ablation eradicates the Attack Success Rate (ASR) from 100\% $\to$ 0.4\% while retaining over 99\% general utility; \textbf{(2) safety alignment}, localizing an alignment circuit with 3.03\% heads and 0.79\% neurons, whose removal spikes ASR from 0.8\% $\to$ 96.9\%, whereas excluding this circuit during helpfulness fine-tuning maintains 96.5\% safety retention.

Recent advances in deep neural networks (DNNs) have led to remarkable success across a wide range of tasks. However, their susceptibility to adversarial perturbations remains a critical vulnerability. Existing diffusion-based adversarial purification methods often require intensive iterative denoising, severely limiting their practical deployment. In this paper, we propose Diffusion Bridge Distillation for Purification (DBLP), a novel and efficient diffusion-based framework for adversarial purification. Central to our approach is a new objective, noise bridge distillation, which constructs a principled alignment between the adversarial noise distribution and the clean data distribution within a latent consistency model (LCM). To further enhance semantic fidelity, we introduce adaptive semantic enhancement, which fuses multi-scale pyramid edge maps as conditioning input to guide the purification process. Extensive experiments across multiple datasets demonstrate that DBLP achieves state-of-the-art (SOTA) robust accuracy, superior image quality, and around 0.2s inference time, marking a significant step toward real-time adversarial purification.