Deep neural networks (DNNs) are vulnerable to adversarial samples crafted by adding imperceptible perturbations to clean data, potentially leading to incorrect and dangerous predictions. Adversarial purification has been an effective means to improve DNNs robustness by removing these perturbations before feeding the data into the model. However, it faces significant challenges in preserving key structural and semantic information of data, as the imperceptible nature of adversarial perturbations makes it hard to avoid over-correcting, which can destroy important information and degrade model performance. In this paper, we break away from traditional adversarial purification methods by focusing on the clean data manifold. To this end, we reveal that samples generated by a well-trained generative model are close to clean ones but far from adversarial ones. Leveraging this insight, we propose Consistency Model-based Adversarial Purification (CMAP), which optimizes vectors within the latent space of a pre-trained consistency model to generate samples for restoring clean data. Specifically, 1) we propose a \textit{Perceptual consistency restoration} mechanism by minimizing the discrepancy between generated samples and input samples in both pixel and perceptual spaces. 2) To maintain the optimized latent vectors within the valid data manifold, we introduce a \textit{Latent distribution consistency constraint} strategy to align generated samples with the clean data distribution. 3) We also apply a \textit{Latent vector consistency prediction} scheme via an ensemble approach to enhance prediction reliability. CMAP fundamentally addresses adversarial perturbations at their source, providing a robust purification. Extensive experiments on CIFAR-10 and ImageNet-100 show that our CMAP significantly enhances robustness against strong adversarial attacks while preserving high natural accuracy.