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Vessel segmentation in medical images is one of the important tasks in the diagnosis of vascular diseases and therapy planning. Although learning-based segmentation approaches have been extensively studied, a large amount of ground-truth labels are required in supervised methods and confusing background structures make neural networks hard to segment vessels in an unsupervised manner. To address this, here we introduce a novel diffusion adversarial representation learning (DARL) model that leverages a denoising diffusion probabilistic model with adversarial learning, and apply it to vessel segmentation. In particular, for self-supervised vessel segmentation, DARL learns the background signal using a diffusion module, which lets a generation module effectively provide vessel representations. Also, by adversarial learning based on the proposed switchable spatially-adaptive denormalization, our model estimates synthetic fake vessel images as well as vessel segmentation masks, which further makes the model capture vessel-relevant semantic information. Once the proposed model is trained, the model generates segmentation masks in a single step and can be applied to general vascular structure segmentation of coronary angiography and retinal images. Experimental results on various datasets show that our method significantly outperforms existing unsupervised and self-supervised vessel segmentation methods.