Dataset Distillation seeks to summarize a large dataset by generating a reduced set of synthetic samples. While there has been much success at distilling small datasets such as CIFAR-10 on smaller neural architectures, Dataset Distillation methods fail to scale to larger high-resolution datasets and architectures. In this work, we introduce \textbf{D}ataset \textbf{D}istillation with \textbf{D}omain \textbf{S}hift (\textbf{D3S}), a scalable distillation algorithm, made by reframing the dataset distillation problem as a \textit{domain shift} one. In doing so, we derive a universal bound on the distillation loss, and provide a method for efficiently approximately optimizing it. We achieve state-of-the-art results on Tiny-ImageNet, ImageNet-1k, and ImageNet-21K over a variety of recently proposed baselines, including high cross-architecture generalization. Additionally, our ablation studies provide lessons on the importance of validation-time hyperparameters on distillation performance, motivating the need for standardization.