DETR introduces a simplified one-stage framework for scene graph generation (SGG). However, DETR-based SGG models face two challenges: i) Sparse supervision, as each image typically contains fewer than 10 relation annotations, while the models employ over 100 relation queries. This sparsity arises because each ground truth relation is assigned to only one single query during training. ii) False negative samples, since one ground truth relation may have multiple queries with similar matching scores. These suboptimally matched queries are simply treated as negative samples, causing the loss of valuable supervisory signals. As a response, we devise Hydra-SGG, a one-stage SGG method that adopts a new Hybrid Relation Assignment. This assignment combines a One-to-One Relation Assignment with a newly introduced IoU-based One-to-Many Relation Assignment. Specifically, each ground truth is assigned to multiple relation queries with high IoU subject-object boxes. This Hybrid Relation Assignment increases the number of positive training samples, alleviating sparse supervision. Moreover, we, for the first time, empirically show that self-attention over relation queries helps reduce duplicated relation predictions. We, therefore, propose Hydra Branch, a parameter-sharing auxiliary decoder without a self-attention layer. This design promotes One-to-Many Relation Assignment by enabling different queries to predict the same relation. Hydra-SGG achieves state-of-the-art performance with 10.6 mR@20 and 16.0 mR@50 on VG150, while only requiring 12 training epochs. It also sets a new state-of-the-art on Open Images V6 and and GQA.