# PSM: Dataset Distillation Based on Precise Statistical Matching by Difficulty

arXiv: https://arxiv.org/abs/2609.34299 · HTML: https://mlsanity.com/paper/2609.34299/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 52 of its 63 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Builds on (most cited first, 30 of 52)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [ShuffleNet V2: Practical Guidelines for Efficient CNN Architecture Design](https://mlsanity.com/paper/1807.11164/) (2018)
- [An Empirical Study of Example Forgetting during Deep Neural Network Learning](https://mlsanity.com/paper/1812.05159/) (2018)
- [Dataset Condensation with Gradient Matching](https://mlsanity.com/paper/2006.05929/) (2020)
- [Dataset Distillation by Matching Training Trajectories](https://mlsanity.com/paper/2203.11932/) (2022)
- [Dataset Cartography: Mapping and Diagnosing Datasets with Training Dynamics](https://mlsanity.com/paper/2009.10795/) (2020)
- [Dataset Condensation with Distribution Matching](https://mlsanity.com/paper/2110.04181/) (2021)
- [How Does Batch Normalization Help Optimization?](https://mlsanity.com/paper/1805.11604/) (2018)
- [Dataset Condensation with Differentiable Siamese Augmentation](https://mlsanity.com/paper/2102.08259/) (2021)
- [Revisiting Batch Normalization For Practical Domain Adaptation](https://mlsanity.com/paper/1603.04779/) (2016)
- [Scaling Up Dataset Distillation to ImageNet-1K with Constant Memory](https://mlsanity.com/paper/2211.10586/) (2022)
- [Squeeze, Recover and Relabel: Dataset Condensation at ImageNet Scale From A New Perspective](https://mlsanity.com/paper/2306.13092/) (2023)
- [Batch Renormalization: Towards Reducing Minibatch Dependence in Batch-Normalized Models](https://mlsanity.com/paper/1702.03275/) (2017)
- [Towards Lossless Dataset Distillation via Difficulty-Aligned Trajectory Matching](https://mlsanity.com/paper/2310.05773/) (2023)
- [A Comprehensive Survey of Dataset Distillation](https://mlsanity.com/paper/2301.05603/) (2023)
- [On the Diversity and Realism of Distilled Dataset: An Efficient Dataset Distillation Paradigm](https://mlsanity.com/paper/2312.03526/) (2023)
- [Dataset Condensation with Contrastive Signals](https://mlsanity.com/paper/2202.02916/) (2022)
- [DREAM: Efficient Dataset Distillation by Representative Matching](https://mlsanity.com/paper/2302.14416/) (2023)
- [DataDAM: Efficient Dataset Distillation with Attention Matching](https://mlsanity.com/paper/2310.00093/) (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)
- [Generalized Large-Scale Data Condensation via Various Backbone and Statistical Matching](https://mlsanity.com/paper/2311.17950/) (2023)
- [Towards Understanding Regularization in Batch Normalization](https://mlsanity.com/paper/1809.00846/) (2018)

## Abstract (arXiv)

Dataset distillation (DD) condenses a large original dataset into a small distilled dataset with high training utility. Decoupled statistical matching methods substantially reduce distillation time and memory overhead while achieving strong performance. However, they typically supervise all distilled samples using running statistics estimated from the entire original dataset. These statistics mainly capture the average feature distribution while overlooking differences in sample difficulty, limiting their ability to characterize the difficulty structure of the original data. To address this issue, we propose Precise Statistical Matching (PSM) by difficulty. After pretraining, PSM uses the Global Precision Score (GPS) to estimate image difficulty, ranks the samples within each class, and partitions each class into IPC (images per class) difficulty groups. During distillation, Statistics Updated Again (SUA) updates the teacher's batch normalization (BN) running statistics through forward passes on original samples from each group, providing difficulty-specific supervision for the corresponding distilled batch. Meanwhile, Initial Sample Screening (ISS) initializes distilled samples using original images from the corresponding difficulty group, providing an effective starting point for precise matching. Experiments across multiple datasets and model architectures demonstrate that PSM broadens the difficulty range of distilled samples and improves downstream performance in most evaluated settings. Code will be released.