# Dataset Distillation as Pushforward Optimal Quantization

arXiv: https://arxiv.org/abs/2501.07681 · HTML: https://mlsanity.com/paper/2501.07681/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 35 of its 58 references that are in the map.
- First posted on arXiv 13 Jan 2025.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 30 of 35)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Knowledge Distillation: A Survey](https://mlsanity.com/paper/2006.05525/) (2020)
- [Estimating Training Data Influence by Tracing Gradient Descent](https://mlsanity.com/paper/2002.08484/) (2020)
- [Deep Learning on a Data Diet: Finding Important Examples Early in Training](https://mlsanity.com/paper/2107.07075/) (2021)
- [Dataset Distillation by Matching Training Trajectories](https://mlsanity.com/paper/2203.11932/) (2022)
- [Dataset Condensation with Distribution Matching](https://mlsanity.com/paper/2110.04181/) (2021)
- [Model compression via distillation and quantization](https://mlsanity.com/paper/1802.05668/) (2018)
- [Dataset Meta-Learning from Kernel Ridge-Regression](https://mlsanity.com/paper/2011.00050/) (2020)
- [Dataset Distillation with Infinitely Wide Convolutional Networks](https://mlsanity.com/paper/2107.13034/) (2021)
- [Fast Computation of Wasserstein Barycenters](https://mlsanity.com/paper/1310.4375/) (2013)
- [Scaling Up Dataset Distillation to ImageNet-1K with Constant Memory](https://mlsanity.com/paper/2211.10586/) (2022)
- [Dataset Distillation using Neural Feature Regression](https://mlsanity.com/paper/2206.00719/) (2022)
- [Squeeze, Recover and Relabel: Dataset Condensation at ImageNet Scale From A New Perspective](https://mlsanity.com/paper/2306.13092/) (2023)
- [Dataset Distillation: A Comprehensive Review](https://mlsanity.com/paper/2301.07014/) (2023)
- [Score-Based Generative Models Detect Manifolds](https://mlsanity.com/paper/2206.01018/) (2022)
- [Dataset Distillation via Factorization](https://mlsanity.com/paper/2210.16774/) (2022)
- [Efficient Dataset Distillation Using Random Feature Approximation](https://mlsanity.com/paper/2210.12067/) (2022)
- [On the Diversity and Realism of Distilled Dataset: An Efficient Dataset Distillation Paradigm](https://mlsanity.com/paper/2312.03526/) (2023)
- [Remember the Past: Distilling Datasets into Addressable Memories for Neural Networks](https://mlsanity.com/paper/2206.02916/) (2022)
- [DREAM: Efficient Dataset Distillation by Representative Matching](https://mlsanity.com/paper/2302.14416/) (2023)
- [Data Distillation: A Survey](https://mlsanity.com/paper/2301.04272/) (2023)
- [Efficient Dataset Distillation via Minimax Diffusion](https://mlsanity.com/paper/2311.15529/) (2023)
- [D4M: Dataset Distillation via Disentangled Diffusion Model](https://mlsanity.com/paper/2407.15138/) (2024)
- [Dataset Distillation via the Wasserstein Metric](https://mlsanity.com/paper/2311.18531/) (2023)
- [Dataset Distillation via Curriculum Data Synthesis in Large Data Era](https://mlsanity.com/paper/2311.18838/) (2023)

## Built on by (most cited first, 1 of 1)

- [UniGeM: Unifying Data Mixing and Selection via Geometric Exploration and Mining](https://mlsanity.com/paper/2602.03772/) (2026)

## Abstract (arXiv)

Dataset distillation aims to find a synthetic training set such that training on the synthetic data achieves similar performance to training on real data, with orders of magnitude less computational requirements. Existing methods can be broadly categorized as either bi-level optimization problems that have neural network training heuristics as the lower level problem, or disentangled methods that bypass the bi-level optimization by matching distributions of data. The latter method has the major advantages of speed and scalability in terms of size of both training and distilled datasets. We demonstrate that when equipped with an encoder-decoder structure, 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 by minimizing the expected projection distance. In particular, we link existing disentangled dataset distillation methods to the classical optimal quantization and Wasserstein barycenter problems, demonstrating consistency of distilled datasets for diffusion-based generative priors. We propose Dataset Distillation by Optimal Quantization, based on clustering in a latent space. Compared to the previous SOTA method Dtextsuperscript4M, we achieve better performance and inter-model generalization on the ImageNet-1K dataset with trivial additional computation, and SOTA performance in higher image-per-class settings. Using the distilled noise initializations in a stronger diffusion transformer model, we obtain SOTA distillation performance on ImageNet-1K and its subsets, outperforming diffusion guidance methods.