Dataset distillation aims to synthesize a compact subset of the original data, enabling models trained on it to achieve performance comparable to those trained on the original large dataset. Existing distribution-matching methods are confined to Euclidean spaces, making them only capture linear structures and overlook the intrinsic geometry of real data, e.g., curvature. However, high-dimensional data often lie on low-dimensional manifolds, suggesting that dataset distillation should have the distilled data manifold aligned with the original data manifold. In this work, we propose a geometry-aware distribution-matching framework, called \textbf{GeoDM}, which operates in the Cartesian product of Euclidean, hyperbolic, and spherical manifolds, with flat, hierarchical, and cyclical structures all captured by a unified representation. To adapt to the underlying data geometry, we introduce learnable curvature and weight parameters for three kinds of geometries. At the same time, we design an optimal transport loss to enhance the distribution fidelity. Our theoretical analysis shows that the geometry-aware distribution matching in a product space yields a smaller generalization error bound than the Euclidean counterparts. Extensive experiments conducted on standard benchmarks demonstrate that our algorithm outperforms state-of-the-art data distillation methods and remains effective across various distribution-matching strategies for the single geometries.

Dataset distillation has emerged as a promising paradigm that synthesizes compact, informative datasets capable of retaining the knowledge of large-scale counterparts, thereby addressing the substantial computational and storage burdens of modern model training. Conventional approaches typically rely on dense pixel-level representations, which introduce redundancy and are difficult to scale up. In this work, we propose GSDD, a novel and efficient sparse representation for dataset distillation based on 2D Gaussians. Instead of representing all pixels equally, GSDD encodes critical discriminative information in a distilled image using only a small number of Gaussian primitives. This sparse representation could improve dataset diversity under the same storage budget, enhancing coverage of difficult samples and boosting distillation performance. To ensure both efficiency and scalability, we adapt CUDA-based splatting operators for parallel inference and training, enabling high-quality rendering with minimal computational and memory overhead. Our method is simple yet effective, broadly applicable to different distillation pipelines, and highly scalable. Experiments show that GSDD achieves state-of-the-art performance on CIFAR-10, CIFAR-100, and ImageNet subsets, while remaining highly efficient encoding and decoding cost. Our code is available at https://github.com/j-cyoung/GSDatasetDistillation.

Dataset distillation (DD) promises compact yet faithful synthetic data, but existing approaches often inherit the inductive bias of a single teacher model. As dataset size increases, this bias drives generation toward overly smooth, homogeneous samples, reducing intra-class diversity and limiting generalization. We present PRISM (PRIors from diverse Source Models), a framework that disentangles architectural priors during synthesis. PRISM decouples the logit-matching and regularization objectives, supervising them with different teacher architectures: a primary model for logits and a stochastic subset for batch-normalization (BN) alignment. On ImageNet-1K, PRISM consistently and reproducibly outperforms single-teacher methods (e.g., SRe2L) and recent multi-teacher variants (e.g., G-VBSM) at low- and mid-IPC regimes. The generated data also show significantly richer intra-class diversity, as reflected by a notable drop in cosine similarity between features. We further analyze teacher selection strategies (pre- vs. intra-distillation) and introduce a scalable cross-class batch formation scheme for fast parallel synthesis. Code will be released after the review period.

Dataset distillation compresses large-scale datasets into compact, highly informative synthetic data, significantly reducing storage and training costs. However, existing research primarily focuses on balanced datasets and struggles to perform under real-world long-tailed distributions. In this work, we emphasize the critical role of soft labels in long-tailed dataset distillation and uncover the underlying mechanisms contributing to performance degradation. Specifically, we derive an imbalance-aware generalization bound for model trained on distilled dataset. We then identify two primary sources of soft-label bias, which originate from the distillation model and the distilled images, through systematic perturbation of the data imbalance levels. To address this, we propose ADSA, an Adaptive Soft-label Alignment module that calibrates the entangled biases. This lightweight module integrates seamlessly into existing distillation pipelines and consistently improves performance. On ImageNet-1k-LT with EDC and IPC=50, ADSA improves tail-class accuracy by up to 11.8% and raises overall accuracy to 41.4%. Extensive experiments demonstrate that ADSA provides a robust and generalizable solution under limited label budgets and across a range of distillation techniques. Code is available at: https://github.com/j-cyoung/ADSA_DD.git.

To address the computational and storage challenges posed by large-scale datasets in deep learning, dataset distillation has been proposed to synthesize a compact dataset that replaces the original while maintaining comparable model performance. Unlike optimization-based approaches that require costly bi-level optimization, distribution matching (DM) methods improve efficiency by aligning the distributions of synthetic and original data, thereby eliminating nested optimization. DM achieves high computational efficiency and has emerged as a promising solution. However, existing DM methods, constrained to Euclidean space, treat data as independent and identically distributed points, overlooking complex geometric and hierarchical relationships. To overcome this limitation, we propose a novel hyperbolic dataset distillation method, termed HDD. Hyperbolic space, characterized by negative curvature and exponential volume growth with distance, naturally models hierarchical and tree-like structures. HDD embeds features extracted by a shallow network into the Lorentz hyperbolic space, where the discrepancy between synthetic and original data is measured by the hyperbolic (geodesic) distance between their centroids. By optimizing this distance, the hierarchical structure is explicitly integrated into the distillation process, guiding synthetic samples to gravitate towards the root-centric regions of the original data distribution while preserving their underlying geometric characteristics. Furthermore, we find that pruning in hyperbolic space requires only 20% of the distilled core set to retain model performance, while significantly improving training stability. To the best of our knowledge, this is the first work to incorporate the hyperbolic space into the dataset distillation process. The code is available at https://github.com/Guang000/HDD.

"Cross" denotes the average test accuracy of trained AlexNet, VGG11,

Modern machine learning models heavily rely on large datasets that often include sensitive and private information, raising serious privacy concerns. Differentially private (DP) data generation offers a solution by creating synthetic datasets that limit the leakage of private information within a predefined privacy budget; however, it requires a substantial amount of data to achieve performance comparable to models trained on the original data. To mitigate the significant expense incurred with synthetic data generation, Dataset Distillation (DD) stands out for its remarkable training and storage efficiency. This efficiency is particularly advantageous when integrated with DP mechanisms, curating compact yet informative synthetic datasets without compromising privacy. However, current state-of-the-art private DD methods suffer from a synchronized sampling-optimization process and the dependency on noisy training signals from randomly initialized networks. This results in the inefficient utilization of private information due to the addition of excessive noise. To address these issues, we introduce a novel framework that decouples sampling from optimization for better convergence and improves signal quality by mitigating the impact of DP noise through matching in an informative subspace. On CIFAR-10, our method achieves a \textbf{10.0\%} improvement with 50 images per class and \textbf{8.3\%} increase with just \textbf{one-fifth} the distilled set size of previous state-of-the-art methods, demonstrating significant potential to advance privacy-preserving DD.

To address the larger computation and storage requirements associated with large video datasets, video dataset distillation aims to capture spatial and temporal information in a significantly smaller dataset, such that training on the distilled data has comparable performance to training on all of the data. We propose GVD: Guiding Video Diffusion, the first diffusion-based video distillation method. GVD jointly distills spatial and temporal features, ensuring high-fidelity video generation across diverse actions while capturing essential motion information. Our method's diverse yet representative distillations significantly outperform previous state-of-the-art approaches on the MiniUCF and HMDB51 datasets across 5, 10, and 20 Instances Per Class (IPC). Specifically, our method achieves 78.29 percent of the original dataset's performance using only 1.98 percent of the total number of frames in MiniUCF. Additionally, it reaches 73.83 percent of the performance with just 3.30 percent of the frames in HMDB51. Experimental results across benchmark video datasets demonstrate that GVD not only achieves state-of-the-art performance but can also generate higher resolution videos and higher IPC without significantly increasing computational cost.

Dataset distillation aims to create a compact dataset that retains essential information while maintaining model performance. Diffusion models (DMs) have shown promise for this task but struggle in low images-per-class (IPC) settings, where generated samples lack diversity. In this paper, we address this issue from an information-theoretic perspective by identifying two key types of information that a distilled dataset must preserve: ($i$) prototype information $\mathrm{I}(X;Y)$, which captures label-relevant features; and ($ii$) contextual information $\mathrm{H}(X | Y)$, which preserves intra-class variability. Here, $(X,Y)$ represents the pair of random variables corresponding to the input data and its ground truth label, respectively. Observing that the required contextual information scales with IPC, we propose maximizing $\mathrm{I}(X;Y) + β\mathrm{H}(X | Y)$ during the DM sampling process, where $β$ is IPC-dependent. Since directly computing $\mathrm{I}(X;Y)$ and $\mathrm{H}(X | Y)$ is intractable, we develop variational estimations to tightly lower-bound these quantities via a data-driven approach. Our approach, information-guided diffusion sampling (IGDS), seamlessly integrates with diffusion models and improves dataset distillation across all IPC settings. Experiments on Tiny ImageNet and ImageNet subsets show that IGDS significantly outperforms existing methods, particularly in low-IPC regimes. The code will be released upon acceptance.