# Optimizing Distributional Geometry Alignment with Optimal Transport for Generative Dataset Distillation

arXiv: https://arxiv.org/abs/2512.00308 · HTML: https://mlsanity.com/paper/2512.00308/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 73 of its 97 references that are in the map.
- First posted on arXiv 29 Nov 2025.

## Builds on (most cited first, 30 of 73)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Robustness May Be at Odds with Accuracy](https://mlsanity.com/paper/1805.12152/) (2018)
- [Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model](https://mlsanity.com/paper/2212.00490/) (2022)
- [Dataset Condensation with Gradient Matching](https://mlsanity.com/paper/2006.05929/) (2020)
- [An Introduction to Convolutional Neural Networks](https://mlsanity.com/paper/1511.08458/) (2015)
- [Improving Diffusion Models for Inverse Problems using Manifold Constraints](https://mlsanity.com/paper/2206.00941/) (2022)
- [Dataset Distillation by Matching Training Trajectories](https://mlsanity.com/paper/2203.11932/) (2022)
- [Universal Guidance for Diffusion Models](https://mlsanity.com/paper/2302.07121/) (2023)
- [Dreaming to Distill: Data-free Knowledge Transfer via DeepInversion](https://mlsanity.com/paper/1912.08795/) (2019)
- [Dataset Condensation with Distribution Matching](https://mlsanity.com/paper/2110.04181/) (2021)
- [FreeDoM: Training-Free Energy-Guided Conditional Diffusion Model](https://mlsanity.com/paper/2303.09833/) (2023)
- [Diffusion models as plug-and-play priors](https://mlsanity.com/paper/2206.09012/) (2022)
- [Lipschitz-Margin Training: Scalable Certification of Perturbation Invariance for Deep Neural Networks](https://mlsanity.com/paper/1802.04034/) (2018)
- [Dataset Condensation via Efficient Synthetic-Data Parameterization](https://mlsanity.com/paper/2205.14959/) (2022)
- [Torchattacks: A PyTorch Repository for Adversarial Attacks](https://mlsanity.com/paper/2010.01950/) (2020)
- [Squeeze, Recover and Relabel: Dataset Condensation at ImageNet Scale From A New Perspective](https://mlsanity.com/paper/2306.13092/) (2023)

## Built on by (most cited first, 5 of 5)

- [DMGD: Train-Free Dataset Distillation with Semantic-Distribution Matching in Diffusion Models](https://mlsanity.com/paper/2605.03877/) (2026)
- [Ani3DHuman: Photorealistic 3D Human Animation with Self-guided Stochastic Sampling](https://mlsanity.com/paper/2602.19089/) (2026)
- [Geometry-Aware Dataset Condensation for Diffusion Model Training](https://mlsanity.com/paper/2606.05883/) (2026)
- [Beyond Dataset Distillation: Lossless Dataset Concentration via Diffusion-Assisted Distribution Alignment](https://mlsanity.com/paper/2603.27987/) (2026)
- [Revisiting On-policy Adversarial Black-Box Distillation: Calibrating Groupwise Reward Geometry for Effective Advantage Construction](https://mlsanity.com/paper/2609.39757/) (2026)

## Abstract (arXiv)

Dataset distillation seeks to synthesize a compact distilled dataset, enabling models trained on it to achieve performance comparable to models trained on the full dataset. Recent methods for large-scale datasets focus on matching global distributional statistics (e.g., mean and variance), but overlook critical instance-level characteristics and intraclass variations, leading to suboptimal generalization. We address this limitation by reformulating dataset distillation as an Optimal Transport (OT) distance minimization problem, enabling fine-grained alignment at both global and instance levels throughout the pipeline. OT offers a geometrically faithful framework for distribution matching. It effectively preserves local modes, intra-class patterns, and fine-grained variations that characterize the geometry of complex, high-dimensional distributions. Our method comprises three components tailored for preserving distributional geometry: (1) OT-guided diffusion sampling, which aligns latent distributions of real and distilled images; (2) label-image-aligned soft relabeling, which adapts label distributions based on the complexity of distilled image distributions; and (3) OT-based logit matching, which aligns the output of student models with soft-label distributions. Extensive experiments across diverse architectures and large-scale datasets demonstrate that our method consistently outperforms state-of-the-art approaches in an efficient manner, achieving at least 4% accuracy improvement under IPC=10 settings for each architecture on ImageNet-1K.