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arxiv: 2606.05883 · v2 · pith:HDTPFQBGnew · submitted 2026-06-04 · 💻 cs.CV

Geometry-Aware Dataset Condensation for Diffusion Model Training

Xiao Cui , Yulei Qin , Mo Zhu , Wengang Zhou , Hongsheng Li , Houqiang Li This is my paper

Pith reviewed 2026-06-28 02:05 UTC · model grok-4.3

classification 💻 cs.CV
keywords dataset condensationdiffusion modelsoptimal transportdata selectiongeometric alignmentimage generationdistribution matching
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The pith

Reformulating subset selection with one-sided partial optimal transport preserves geometric structure for diffusion model training from compact real datasets.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that standard dataset condensation techniques fail for diffusion models because they either produce low-fidelity synthetic samples or fail to maintain the distributional geometry that diffusion likelihood objectives depend on. It proposes to treat real subset selection as a geometry-aware alignment task solved with one-sided partial optimal transport, which matches a small subset to the full distribution while leaving low-density regions unmatched. Additional regularizers on feature statistics and semantic consistency, plus a two-stage optimization, further ensure fidelity. A sympathetic reader would care because this could enable training high-quality diffusion models on much smaller datasets, reducing the substantial computational resources typically required.

Core claim

The central claim is that by incorporating one-sided partial optimal transport into real subset selection, a compact subset can be aligned with the full data distribution while allowing unmatched mass in low-density regions, thereby preserving the geometric structure necessary for effective diffusion model training, and that complementing this with feature-statistics and semantic consistency regularization yields superior fidelity and distributional coverage compared to prior methods.

What carries the argument

One-sided partial optimal transport, which selectively aligns a compact subset with the full data distribution while permitting unmatched mass in low-density regions to maintain geometric structure.

If this is right

  • Superior performance in fidelity and coverage is achieved across different diffusion models, subset sizes, and resolutions.
  • The method enables effective training with real data subsets rather than synthetic ones.
  • A two-stage discrete optimization makes the alignment computationally feasible.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • This selective alignment might apply to other density-based generative models beyond diffusion.
  • It could lead to more efficient dataset curation pipelines for large-scale image generation tasks.
  • Testing on non-image domains like audio or text could reveal broader applicability.

Load-bearing premise

That the diffusion likelihood objectives specifically require preservation of the full distributional geometry in the condensed dataset, and that the proposed transport plus regularizers achieve this preservation better than alternatives.

What would settle it

Training a diffusion model on the proposed condensed dataset and comparing its sample quality and likelihood scores against models trained on randomly selected subsets or previous condensation methods; if no improvement is observed, the claim would be falsified.

Figures

Figures reproduced from arXiv: 2606.05883 by Hongsheng Li, Houqiang Li, Mo Zhu, Wengang Zhou, Xiao Cui, Yulei Qin.

Figure 1
Figure 1. Figure 1: Comparison of dataset condensation methods. (a) Syn￾thetic set generation methods create synthetic samples through continuous pixel optimization, often resulting in low-fidelity sam￾ples that are unsuitable for diffusion training. (b) Existing real subset selection methods use fixed criteria to select real samples but do not align the subset with the full data distribution. (c) Our alignment-driven selecti… view at source ↗
Figure 2
Figure 2. Figure 2: Illustration of the proposed pipeline. Mean–variance regularization aligns real and selected embeddings, and confidence regularization ensures semantic reliability. A dummy-source-augmented cost matrix is normalized via Sinkhorn iterations to obtain the one-sided POT alignment. The total objective, composed of these three components, is optimized using a two-stage strategy. into a single scalar and does no… view at source ↗
Figure 3
Figure 3. Figure 3: shows that our method reaches a substantially lower FID plateau compared with prior approaches, demonstrat￾ing that the selected subsets lead to more stable and faithful [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Visualization of generated images (golden retriever). 8 [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Visualization of the condensed subset selected by classical balanced OT (left) and one-sided partial OT (right) on a 2D toy dataset. Grey dots denote real samples, and blue dots denote selected condensed samples. mislead the alignment away from the high-density core manifold, resulting in redundant assignments and an over-dispersed condensed subset. In contrast, partial OT introduces a capacity relaxation … view at source ↗
Figure 6
Figure 6. Figure 6: Representative failure cases in large-scale datasets such as ImageNet (Russakovsky et al., 2015) that motivate confidence regularization. (a) Images containing multiple salient objects, where the labeled category is not visually dominant (images adapted from (Miyai et al., 2025)). (b) Genuinely mislabeled samples, where the assigned category is inconsistent with the actual visual content (images adapted fr… view at source ↗
Figure 7
Figure 7. Figure 7: t-SNE visualization comparing D2C (Huang et al., 2026) (left) and our method (right). We visualize the real data (gray) from class 0 (tench) of ImageNet and the selected subset samples (blue). In this visualization, D2C selects samples by uniformly spacing along a scalar difficulty ranking, which can lead to uneven coverage in the embedding distribution. In contrast, our one-sided partial OT–guided alignme… view at source ↗
Figure 8
Figure 8. Figure 8: Examples of 512 × 512 images generated by DiT-L/2 (Peebles & Xie, 2023) after 10K training iterations on a condensed dataset (10K data budget) selected by our method. 31 [PITH_FULL_IMAGE:figures/full_fig_p031_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Examples of 256 × 256 images generated by DiT-L/2 (Peebles & Xie, 2023) after 30K training iterations on a condensed dataset (50K data budget) selected by our method. for 30K iterations using our 50K-image condensed subset. The model produces diverse and semantically coherent images with well-preserved fine-grained details, illustrating that the larger budget enhances coverage of relatively low-density reg… view at source ↗
read the original abstract

Dataset condensation aims to construct compact datasets from real data via synthesis or selection. However, existing approaches are ill-suited for diffusion model training: synthetic data generation often yields low-fidelity samples unsuitable for authentic modeling, while real subset selection typically fails to preserve the distributional geometry required by diffusion likelihood objectives. To address this, we propose to reformulate real subset selection as a geometry-aware distribution alignment problem. By incorporating one-sided partial optimal transport, our method selectively aligns a compact subset with the full data distribution while allowing unmatched mass in low-density regions, ensuring the preserved geometric structure necessary for effective diffusion model training. To further ensure distributional fidelity, we complement geometric alignment with lightweight feature-statistics and semantic consistency regularization. An efficient two-stage discrete optimization strategy is proposed to achieve this alignment objective. Extensive experiments across diffusion variants, subset sizes, image resolutions, and training rounds show that our method achieves superior fidelity and distributional coverage in diffusion model training. Codes are available at https://github.com/2018cx/GADC.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The paper proposes reformulating real subset selection for dataset condensation as a geometry-aware distribution alignment problem using one-sided partial optimal transport. This selectively aligns a compact subset with the full data distribution while allowing unmatched mass in low-density regions, supplemented by feature-statistics and semantic consistency regularizers, and solved via an efficient two-stage discrete optimization. The authors claim this preserves the distributional geometry required by diffusion likelihood objectives and yields superior fidelity and coverage in experiments across diffusion variants, subset sizes, resolutions, and training rounds.

Significance. If the central claims hold with proper verification, the approach could meaningfully advance efficient diffusion model training by addressing limitations of synthetic data (low fidelity) and standard subset selection (poor geometry preservation). The code release at the provided GitHub link is a strength for reproducibility. However, without direct evidence isolating the OT contribution, the significance remains provisional.

major comments (1)
  1. [Experiments] Experiments (throughout, including claims of 'superior fidelity and distributional coverage'): no explicit post-selection geometry diagnostic is reported (e.g., empirical Wasserstein distance to the full distribution, mode-coverage statistic, or score-function alignment between subset and full data) that isolates the one-sided partial OT term from the regularizers or from simple diversity heuristics. Downstream FID/coverage numbers therefore cannot confirm that geometry preservation is what drives the gains, as required by the central claim.
minor comments (1)
  1. [Abstract] Abstract: the statement that 'extensive experiments show superior results' provides no quantitative numbers, baselines, error bars, or ablation details, which weakens the ability to assess the claims from the abstract alone.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the detailed and constructive review. The major comment raises an important point about isolating the contribution of the one-sided partial OT term, which we address below.

read point-by-point responses

  1. Referee: Experiments (throughout, including claims of 'superior fidelity and distributional coverage'): no explicit post-selection geometry diagnostic is reported (e.g., empirical Wasserstein distance to the full distribution, mode-coverage statistic, or score-function alignment between subset and full data) that isolates the one-sided partial OT term from the regularizers or from simple diversity heuristics. Downstream FID/coverage numbers therefore cannot confirm that geometry preservation is what drives the gains, as required by the central claim.

    Authors: We agree that the current experiments do not include explicit post-selection geometry diagnostics that directly isolate the one-sided partial OT contribution. In the revised manuscript we will add quantitative diagnostics, including the empirical Wasserstein distance between the selected subset and the full data distribution as well as mode-coverage statistics, computed both with and without the OT term (and against simple diversity baselines). These will be reported alongside the existing FID and coverage results to better substantiate the central claim that geometry preservation drives the observed gains. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is a proposed reformulation without self-referential reduction.

full rationale

The abstract and provided text present a novel reformulation of subset selection as a geometry-aware alignment problem solved via one-sided partial optimal transport plus regularizers and two-stage optimization. No equations, fitted parameters renamed as predictions, or self-citations appear in the given material that would reduce the claimed preservation of distributional geometry to an input by construction. The method is offered as an independent proposal for diffusion training, with downstream experiments cited as validation rather than tautological restatements. This is the common case of a self-contained algorithmic contribution.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that diffusion training requires geometric structure preservation that prior methods lose; no free parameters or invented entities are mentioned in the abstract.

axioms (1)
  • domain assumption Diffusion likelihood objectives require preserved distributional geometry that existing condensation methods fail to maintain.
    Stated directly in the abstract as the motivation for the new formulation.

pith-pipeline@v0.9.1-grok · 5710 in / 1154 out tokens · 20444 ms · 2026-06-28T02:05:13.564786+00:00 · methodology

discussion (0)

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Reference graph

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