Depth estimation is crucial for any underwater robotics system. In recent years, there have been significant advancements in monocular depth estimation. However, in underwater environments, light attenuation reduces visibility underwater, making it difficult to extract depth information from images. Water refraction causes objects to appear at different locations than their true positions, and this effect needs to be accounted for and corrected. Underwater environments often lack salient texture and features, which limits the effectiveness of traditional computer vision approaches. In this paper, we introduce the diffusion-adversarial prior learning model into underwater depth estimation. The model employs an adversarial learning denoising diffusion probability model to the challenge of monocular underwater depth estimate. In addition, DenoiseDep module in the model reinterprets depth estimation as a denoising diffusion process. In the specialized latent space encoded by the dedicated depth encoder and decoder, the initial random depth distribution is iteratively denoised to generate the depth map. This iterative denoising process aims to reduce noise and estimation errors, thereby enhancing the accuracy of depth estimation. Due to the significant differences between depth estimation and image generation tasks, we adopt a pattern of adversarial prior distribution, which utilizes a discriminator to impose constraints and guidance on the images based on the prior distribution. Experimental results on the FlSea underwater dataset show that our method accomplishes state-of-the-art(SOAT) performance in underwater scenes, with acceptable inference time.