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A main challenge faced in the deep learning-based Underwater Image Enhancement (UIE) is that the ground truth high-quality image is unavailable. Most of the existing methods first generate approximate reference maps and then train an enhancement network with certainty. This kind of method fails to handle the ambiguity of the reference map. In this paper, we resolve UIE into distribution estimation and consensus process. We present a novel probabilistic network to learn the enhancement distribution of degraded underwater images. Specifically, we combine conditional variational autoencoder with adaptive instance normalization to construct the enhancement distribution. After that, we adopt a consensus process to predict a deterministic result based on a set of samples from the distribution. By learning the enhancement distribution, our method can cope with the bias introduced in the reference map labeling to some extent. Additionally, the consensus process is useful to capture a robust and stable result. We examined the proposed method on two widely used real-world underwater image enhancement datasets. Experimental results demonstrate that our approach enables sampling possible enhancement predictions. Meanwhile, the consensus estimate yields competitive performance compared with state-of-the-art UIE methods. Code available at https://github.com/zhenqifu/PUIE-Net.