Despite significant advancements in the area, adversarial robustness remains a critical challenge in systems employing machine learning models. The removal of adversarial perturbations at inference time, known as adversarial purification, has emerged as a promising defense strategy. To achieve this, state-of-the-art methods leverage diffusion models that inject Gaussian noise during a forward process to dilute adversarial perturbations, followed by a denoising step to restore clean samples before classification. In this work, we propose FlowPure, a novel purification method based on Continuous Normalizing Flows (CNFs) trained with Conditional Flow Matching (CFM) to learn mappings from adversarial examples to their clean counterparts. Unlike prior diffusion-based approaches that rely on fixed noise processes, FlowPure can leverage specific attack knowledge to improve robustness under known threats, while also supporting a more general stochastic variant trained on Gaussian perturbations for settings where such knowledge is unavailable. Experiments on CIFAR-10 and CIFAR-100 demonstrate that our method outperforms state-of-the-art purification-based defenses in preprocessor-blind and white-box scenarios, and can do so while fully preserving benign accuracy in the former. Moreover, our results show that not only is FlowPure a highly effective purifier but it also holds a strong potential for adversarial detection, identifying preprocessor-blind PGD samples with near-perfect accuracy.