Link prediction based on knowledge graph embeddings (KGE) aims to predict new triples to automatically construct knowledge graphs (KGs). However, recent KGE models achieve performance improvements by excessively increasing the embedding dimensions, which may cause enormous training costs and require more storage space. To address this challenge, we first conduct a theoretical analysis on the capacity of low-dimensional space for KG embeddings based on the principle of minimum entropy. Instead of training high-dimensional models, we propose MulDE, a novel knowledge distillation framework, which includes multiple low-dimensional hyperbolic KGE models as teachers and two student components, Junior and Senior. Under a novel iterative distillation strategy, the Junior component, a low-dimensional KGE model, asks teachers actively based on its preliminary prediction results, and the Senior component integrates teachers’ knowledge adaptively to train the Junior component based on two mechanisms: relation-specific scaling and contrast attention. The experimental results show that MulDE can effectively improve the performance and training speed of low-dimensional KGE models. The distilled 32-dimensional model is competitive compared to the state-or-the- art high-dimensional methods on several commonly-used datasets. The source code of our work is available on the GitHub.