Dataset Distillation as Pushforward Optimal Quantization

Dataset distillation aims to find a small synthetic training set, such that training on the synthetic data achieves similar performance to training on a larger training dataset. Early methods solve this by interpreting the distillation problem as a bi-level optimization problem. On the other hand, disentangled methods bypass pixel-space optimization by matching data distributions and using generative techniques, leading to better computational complexity in terms of size of both training and distilled datasets. We demonstrate that by using latent spaces, the empirically successful disentangled methods can be reformulated as an optimal quantization problem, where a finite set of points is found to approximate the underlying probability measure. In particular, we link disentangled dataset distillation methods to the classical problem of optimal quantization, and are the first to demonstrate consistency of distilled datasets for diffusion-based generative priors. We propose Dataset Distillation by Optimal Quantization (DDOQ), based on clustering in the latent space of latent diffusion models. Compared to a similar clustering method D4M, we achieve better performance and inter-model generalization on the ImageNet-1K dataset using the same model and with trivial additional computation, achieving SOTA performance in higher image-per-class settings. Using the distilled noise initializations in a stronger diffusion transformer model, we obtain competitive or SOTA distillation performance on ImageNet-1K and its subsets, outperforming recent diffusion guidance methods.