Form understanding is a challenging problem which aims to recognize semantic entities from the input document and their hierarchical relations. Previous approaches face a significant difficulty dealing with the complexity of the task, thus treat these objectives separately. To this end, we present a novel deep neural network to jointly perform both Entity Labeling and link prediction in an end-to-end fashion. Our model extends the Multi-stage Attentional U-Net architecture with the Part-Intensity Fields and Part-Association Fields for link prediction, enriching the spatial information flow with the additional supervision from Entity Linking. We demonstrate the effectiveness of the model on the \textit{Form Understanding in Noisy Scanned Documents} \textit{(FUNSD)} dataset, where our method substantially outperforms the original model and state-of-the-art baselines in both Entity Labeling and Entity Linking task.