Dataset distillation, which compresses large-scale datasets into compact synthetic representations (i.e., distilled datasets), has become crucial for the efficient training of modern deep learning architectures. While existing large-scale dataset distillation methods leverage a pre-trained model through batch normalization statistics alignment, they neglect the essential role of covariance matrices in preserving inter-feature correlations, resulting in reduced diversity in the distilled datasets. In this paper, we propose a simple yet effective approach, Diversity-Enhanced Distribution Alignment (DEDA), which enhances the diversity of distilled data by leveraging inter-feature relationships. Our method first establishes Gaussian distribution alignment by matching the means and covariances of each class in the original dataset with those of the distilled dataset in the feature space of a pre-trained model. Since features within the last layer of a pre-trained model are often highly similar within each class, aligning distributions in this layer cannot obtain diversified distilled data, resulting in gradient starvation during downstream training tasks. To overcome this limitation, we introduce a regularizer that constrains the covariance matrix of the distilled data in the last layer to maximize diagonal elements while minimizing non-diagonal elements. Extensive evaluations across CIFAR-10/100, Tiny-ImageNet, and ImageNet-1K demonstrate state-of-the-art performance without additional computational overhead.