This paper proposes an end-to-end neural network model that fully utilizes the characteristic of uneven fog distribution to estimate visibility in fog images. Firstly, we transform the original single labels into discrete label distributions and introduce discrete label distribution learning on top of the existing classification networks to learn the difference in visibility information among different regions of an image. Then, we employ the bilinear attention pooling module to find the farthest visible region of fog in the image, which is incorporated into an attention-based branch. Finally, we conduct a cascaded fusion of the features extracted from the attention-based branch and the base branch. Extensive experimental results on a real highway dataset and a publicly available synthetic road dataset confirm the effectiveness of the proposed method, which has low annotation requirements, good robustness, and broad application space.