The rapid development of AI models has led to a growing emphasis on enhancing their capabilities for complex input data such as videos. While large-scale video datasets have been introduced to support this growth, the unique challenges of reducing redundancies in video \textbf{sets} have not been explored. Compared to image datasets or individual videos, video \textbf{sets} have a two-layer nested structure, where the outer layer is the collection of individual videos, and the inner layer contains the correlations among frame-level data points to provide temporal information. Video \textbf{sets} have two dimensions of redundancies: within-sample and inter-sample redundancies. Existing methods like key frame selection, dataset pruning or dataset distillation are not addressing the unique challenge of video sets since they aimed at reducing redundancies in only one of the dimensions. In this work, we are the first to study Video Set Distillation, which synthesizes optimized video data by jointly addressing within-sample and inter-sample redundancies. Our Information Diversification and Temporal Densification (IDTD) method jointly reduces redundancies across both dimensions. This is achieved through a Feature Pool and Feature Selectors mechanism to preserve inter-sample diversity, alongside a Temporal Fusor that maintains temporal information density within synthesized videos. Our method achieves state-of-the-art results in Video Dataset Distillation, paving the way for more effective redundancy reduction and efficient AI model training on video datasets.