Diffusion Dataset Condensation (D2C)

• Diffusion Dataset Condensation (D2C) is a method that creates a much smaller but effective training set by preserving the original data distribution’s support, local neighborhoods, and semantics.
• It employs a two-phase approach where a diverse subset is selected using diffusion difficulty and geometry-aware techniques, followed by enriching the samples with semantic and visual priors.
• Empirical evaluations demonstrate that D2C enables competitive generative performance with drastically reduced data sizes, optimizing training efficiency under constrained budgets.

Searching arXiv for the cited papers to ground the article in the current literature. Diffusion Dataset Condensation (D2C) denotes the construction of a substantially smaller training set that still supports effective diffusion-model training from scratch under constrained optimization budgets. In current usage, the term refers both to a general problem setting for generative modeling and, more narrowly, to the two-phase D\textsuperscript{2}C framework introduced for class-conditional image diffusion training. Across recent work, the central departure from classical discriminative condensation is consistent: diffusion models must preserve the structure of the data distribution itself—its support, local neighborhoods, mode coverage, semantics, and realism—rather than merely class-separating cues. This has led to several distinct formulations, including diffusion-difficulty-based selection with attached conditioning priors, geometry-aware real-subset selection via partial optimal transport, diffusion-generated candidate pools followed by subset extraction, and coreset compression followed by on-the-fly diffusion expansion (Huang et al., 8 Jul 2025, Cui et al., 4 Jun 2026, Li et al., 10 May 2025, Abbasi et al., 2024).

1. Problem setting and formal scope

The common problem setting starts from a large labeled dataset and asks for a much smaller representation that remains useful for downstream diffusion training. In the notation of D\textsuperscript{2}C, the full dataset is

$$\mathcal{D} = (\hat{\mathbf{X}}, \hat{\mathbf{Y}}) = \{(\hat{\mathbf{x}}_i, \hat{y}_i)\}_{i=1}^{|\mathcal{D}|},$$

and the condensed dataset is

$$\mathcal{D}^{\mathcal{S}} = (\mathbf{X}, \mathbf{Y}) = \{(\mathbf{x}_j, y_j)\}_{j=1}^{|\mathcal{D}^{\mathcal{S}}|}, \qquad |\mathcal{D}^{\mathcal{S}}| \ll |\mathcal{D}|.$$

For class-conditional generation, the same paper writes

$$\mathcal{D} = \bigcup_{y=1}^{C} \mathcal{D}_y,\qquad \mathcal{D}_y = \{x_i\}_{i=1}^{|\mathcal{D}_y|},$$

and evaluates condensation by image-generation quality metrics such as gFID, sFID, IS, Precision, and Recall rather than classification accuracy (Huang et al., 8 Jul 2025).

A closely related formulation appears in geometry-aware real subset selection for diffusion training. Given a labeled dataset

$T=\bigcup_{c=1}^{C}T_c,$

the goal is to select a much smaller real subset

$$S=\bigcup_{c=1}^{C}S_c,\qquad S_c\subset T_c,\qquad |S_c|\ll |T_c|,$$

typically with an equal number of selected samples per class. The downstream assumption is explicit: a diffusion model is then trained from scratch on $S$ under a limited training budget, and the subset should support generative performance close to that obtained from the full data (Cui et al., 4 Jun 2026).

The underlying diffusion objective in D\textsuperscript{2}C is the standard noise-prediction loss

$$\mathcal{L}_{\text{diff}} = \mathbb{E}_{\mathbf{x}_0\sim q_0(\mathbf{x}),\, \epsilon\sim\mathcal{N}(0,\mathbf{I}),\, t\sim \mathcal{U}[0,1]} \left[ \| \epsilon - \epsilon_\theta(\mathbf{x}_t, t, \mathbf{c}) \|_2^2 \right],$$

with forward noising

$$q_t(\mathbf{x}_t \mid \mathbf{x}_0) = \mathcal{N}(\mathbf{x}_t;\alpha_t \mathbf{x}_0,\sigma_t^2 \mathbf{I}), \qquad \mathbf{x}_t = \alpha_t \mathbf{x}_0 + \sigma_t \epsilon.$$

This formalization makes the central constraint plain: the condensed representation must remain a usable surrogate for a likelihood-based generative objective, not only for class prediction (Huang et al., 8 Jul 2025).

2. Methodological paradigms

Recent work uses markedly different condensed representations and roles for diffusion. The principal variants can be organized as follows.

Method	Condensed representation	Principal mechanism
D\textsuperscript{2}C (Huang et al., 8 Jul 2025)	Real-image subset with attached semantic and visual features	Select and Attach
Geometry-aware subset selection (Cui et al., 4 Jun 2026)	Compact subset of real images	One-sided partial OT with statistics and confidence regularization
Video condensation with diffusion (Li et al., 10 May 2025)	Representative subset of diffusion-generated synthetic videos	Generate synthetic pool, then select with VST-UNet or TAC-DT
Diffusion-augmented coreset expansion (Abbasi et al., 2024)	Real informative patches, seeds, and teacher soft labels	Patch coreset plus on-the-fly LDM expansion

D\textsuperscript{2}C, introduced as “Diffusion Dataset Condensation: Training Your Diffusion Model Faster with Less Data,” is explicit that its condensed dataset is not synthetic pixels optimized end-to-end. It is better described as an augmented subset of real samples plus attached side information. The framework has two phases: Select, which chooses a compact and diverse subset using a diffusion-difficulty score and interval sampling, and Attach, which enriches the chosen samples with semantic representations from a pretrained text encoder and visual representations from a pretrained vision encoder (Huang et al., 8 Jul 2025).

The geometry-aware method of 2026 pushes further toward real-subset selection and argues that the condensation objective itself must be redesigned around the needs of diffusion likelihood training. Its target object is a compact subset of real images whose feature-space arrangement preserves “distributional support geometry”: local neighborhoods, mode coverage, and support allocation. The paper treats previous ranking-based methods, including the prior diffusion-specific selector $D^2C$ of Huang et al., as inadequate because a scalar ranking collapses a high-dimensional, multimodal distribution (Cui et al., 4 Jun 2026).

The video formulation differs again. There, diffusion is used to generate a large synthetic candidate pool $\mathcal{S}_g=\mathcal{F}_\theta(\mathcal{T})$, with $$\mathcal{D}^{\mathcal{S}} = (\mathbf{X}, \mathbf{Y}) = \{(\mathbf{x}_j, y_j)\}_{j=1}^{|\mathcal{D}^{\mathcal{S}}|}, \qquad |\mathcal{D}^{\mathcal{S}}| \ll |\mathcal{D}|.$$0 generated synthetic videos per class, after which condensation is handled mainly as subset extraction from $$\mathcal{D}^{\mathcal{S}} = (\mathbf{X}, \mathbf{Y}) = \{(\mathbf{x}_j, y_j)\}_{j=1}^{|\mathcal{D}^{\mathcal{S}}|}, \qquad |\mathcal{D}^{\mathcal{S}}| \ll |\mathcal{D}|.$$1. This is a generate-then-select paradigm rather than direct optimization of final exemplars (Li et al., 10 May 2025).

The coreset-expansion line is adjacent rather than identical to direct D2C. It first stores informative low-resolution real patches and then uses a pretrained latent diffusion model to expand, super-resolve, and diversify them dynamically during student training. The stored distilled representation is procedural rather than a fixed set of final images (Abbasi et al., 2024).

3. Selection objectives and geometry preservation

The Select phase of D\textsuperscript{2}C is organized around a diffusion difficulty score. Using a pretrained class-conditional diffusion model, the method ranks each sample by a class-conditional likelihood proxy derived from diffusion loss: $$\mathcal{D}^{\mathcal{S}} = (\mathbf{X}, \mathbf{Y}) = \{(\mathbf{x}_j, y_j)\}_{j=1}^{|\mathcal{D}^{\mathcal{S}}|}, \qquad |\mathcal{D}^{\mathcal{S}}| \ll |\mathcal{D}|.$$2 Operationally, the score is effectively based on per-sample denoising MSE under a pretrained diffusion model. Samples are sorted class-wise and selected by interval sampling,

$$\mathcal{D}^{\mathcal{S}} = (\mathbf{X}, \mathbf{Y}) = \{(\mathbf{x}_j, y_j)\}_{j=1}^{|\mathcal{D}^{\mathcal{S}}|}, \qquad |\mathcal{D}^{\mathcal{S}}| \ll |\mathcal{D}|.$$3

with $$\mathcal{D}^{\mathcal{S}} = (\mathbf{X}, \mathbf{Y}) = \{(\mathbf{x}_j, y_j)\}_{j=1}^{|\mathcal{D}^{\mathcal{S}}|}, \qquad |\mathcal{D}^{\mathcal{S}}| \ll |\mathcal{D}|.$$4 for the 10K subset, $$\mathcal{D}^{\mathcal{S}} = (\mathbf{X}, \mathbf{Y}) = \{(\mathbf{x}_j, y_j)\}_{j=1}^{|\mathcal{D}^{\mathcal{S}}|}, \qquad |\mathcal{D}^{\mathcal{S}}| \ll |\mathcal{D}|.$$5 for the 50K subset, and $$\mathcal{D}^{\mathcal{S}} = (\mathbf{X}, \mathbf{Y}) = \{(\mathbf{x}_j, y_j)\}_{j=1}^{|\mathcal{D}^{\mathcal{S}}|}, \qquad |\mathcal{D}^{\mathcal{S}}| \ll |\mathcal{D}|.$$6 for the 100K subset. The stated rationale is a trade-off between learnability and diversity: very easy samples aid early convergence but under-cover the distribution, whereas very hard samples are cluttered or noisy and can destabilize training (Huang et al., 8 Jul 2025).

The geometry-aware alternative replaces scalar ranking with a distribution-alignment objective in representation space. Working class-wise, with selected embeddings $$\mathcal{D}^{\mathcal{S}} = (\mathbf{X}, \mathbf{Y}) = \{(\mathbf{x}_j, y_j)\}_{j=1}^{|\mathcal{D}^{\mathcal{S}}|}, \qquad |\mathcal{D}^{\mathcal{S}}| \ll |\mathcal{D}|.$$7 and full-data embeddings $$\mathcal{D}^{\mathcal{S}} = (\mathbf{X}, \mathbf{Y}) = \{(\mathbf{x}_j, y_j)\}_{j=1}^{|\mathcal{D}^{\mathcal{S}}|}, \qquad |\mathcal{D}^{\mathcal{S}}| \ll |\mathcal{D}|.$$8, it defines the pairwise cost

$$\mathcal{D}^{\mathcal{S}} = (\mathbf{X}, \mathbf{Y}) = \{(\mathbf{x}_j, y_j)\}_{j=1}^{|\mathcal{D}^{\mathcal{S}}|}, \qquad |\mathcal{D}^{\mathcal{S}}| \ll |\mathcal{D}|.$$9

The paper recalls balanced optimal transport,

$$\mathcal{D} = \bigcup_{y=1}^{C} \mathcal{D}_y,\qquad \mathcal{D}_y = \{x_i\}_{i=1}^{|\mathcal{D}_y|},$$0

but argues that this is ill-suited under severe compression because balanced OT forces all target mass to be matched. Its replacement is a one-sided partial optimal transport problem,

$$\mathcal{D} = \bigcup_{y=1}^{C} \mathcal{D}_y,\qquad \mathcal{D}_y = \{x_i\}_{i=1}^{|\mathcal{D}_y|},$$1

with

$$\mathcal{D} = \bigcup_{y=1}^{C} \mathcal{D}_y,\qquad \mathcal{D}_y = \{x_i\}_{i=1}^{|\mathcal{D}_y|},$$2

so that, when $$\mathcal{D} = \bigcup_{y=1}^{C} \mathcal{D}_y,\qquad \mathcal{D}_y = \{x_i\}_{i=1}^{|\mathcal{D}_y|},$$3, some target mass can remain unmatched (Cui et al., 4 Jun 2026).

The same method implements this through a dummy-source reformulation and entropy-regularized Sinkhorn iterations, then optimizes the one-sided transport loss

$$\mathcal{D} = \bigcup_{y=1}^{C} \mathcal{D}_y,\qquad \mathcal{D}_y = \{x_i\}_{i=1}^{|\mathcal{D}_y|},$$4

augmented by feature-statistics regularization

$$\mathcal{D} = \bigcup_{y=1}^{C} \mathcal{D}_y,\qquad \mathcal{D}_y = \{x_i\}_{i=1}^{|\mathcal{D}_y|},$$5

and semantic consistency / confidence regularization

$$\mathcal{D} = \bigcup_{y=1}^{C} \mathcal{D}_y,\qquad \mathcal{D}_y = \{x_i\}_{i=1}^{|\mathcal{D}_y|},$$6

The final class-wise objective is

$$\mathcal{D} = \bigcup_{y=1}^{C} \mathcal{D}_y,\qquad \mathcal{D}_y = \{x_i\}_{i=1}^{|\mathcal{D}_y|},$$7

This objective is optimized over discrete subset members by a two-stage procedure: greedy construction using marginal gains, followed by swap-based refinement. The paper’s interpretation is that one-sided POT concentrates transport on the dense, geometrically stable support while avoiding forced matching to low-density tails, thereby preserving the neighborhood and support geometry needed for score matching (Cui et al., 4 Jun 2026).

Taken together, these two lines expose a central conceptual divide within D2C. The original D\textsuperscript{2}C framework treats diffusion loss as a useful scalar proxy for sample usefulness. The geometry-aware critique treats that scalarization as fundamentally insufficient because distinct modes can share similar scores while nearby manifold points can be separated by ranking. This suggests that “difficulty” and “geometry” are not interchangeable design primitives in diffusion condensation.

4. Conditioning enrichment, generation, and expansion

The Attach phase of D\textsuperscript{2}C enriches each selected image with semantic and visual priors. For class $$\mathcal{D} = \bigcup_{y=1}^{C} \mathcal{D}_y,\qquad \mathcal{D}_y = \{x_i\}_{i=1}^{|\mathcal{D}_y|},$$8, a prompt $$\mathcal{D} = \bigcup_{y=1}^{C} \mathcal{D}_y,\qquad \mathcal{D}_y = \{x_i\}_{i=1}^{|\mathcal{D}_y|},$$9 is encoded by a pretrained T5 encoder to obtain

$T=\bigcup_{c=1}^{C}T_c,$0

These text features are fused with a learnable class embedding $T=\bigcup_{c=1}^{C}T_c,$1 through

$T=\bigcup_{c=1}^{C}T_c,$2

Instance-level visual priors are extracted with DINOv2-B,

$T=\bigcup_{c=1}^{C}T_c,$3

and truncated to the first $T=\bigcup_{c=1}^{C}T_c,$4 tokens. The diffusion model is then trained with semantic conditioning and an auxiliary projection loss

$T=\bigcup_{c=1}^{C}T_c,$5

leading to

$T=\bigcup_{c=1}^{C}T_c,$6

with default $T=\bigcup_{c=1}^{C}T_c,$7. In implementation, the framework uses a pretrained DiT-XL/2 for scoring, a T5 encoder for text features, DINOv2-B for visual features, and a Stable Diffusion VAE for latent encoding and decoding (Huang et al., 8 Jul 2025).

In video condensation, diffusion plays a different role. A pretrained class-conditional Latte model is fine-tuned on all real video datasets, using randomly sampled 16-frame clips. After training, it generates $T=\bigcup_{c=1}^{C}T_c,$8 synthetic videos per class to form a reusable candidate pool. Subset selection is then performed either by VST-UNet, a 4D U-Net operating on latent videos, or by TAC-DT, which embeds videos with pretrained VideoMAE, reduces dimensionality by PCA, applies BIRCH hierarchical clustering, and selects representative videos from clusters. The distilled output contains exactly VPC videos per class, with evaluations at VPC $T=\bigcup_{c=1}^{C}T_c,$9 (Li et al., 10 May 2025).

The coreset-expansion approach uses diffusion not for subset scoring but for procedural reconstruction and augmentation. For each informative patch $$S=\bigcup_{c=1}^{C}S_c,\qquad S_c\subset T_c,\qquad |S_c|\ll |T_c|,$$0, it first upsamples to $$S=\bigcup_{c=1}^{C}S_c,\qquad S_c\subset T_c,\qquad |S_c|\ll |T_c|,$$1, encodes into latent space $$S=\bigcup_{c=1}^{C}S_c,\qquad S_c\subset T_c,\qquad |S_c|\ll |T_c|,$$2, adds partial noise at level $$S=\bigcup_{c=1}^{C}S_c,\qquad S_c\subset T_c,\qquad |S_c|\ll |T_c|,$$3, and then performs a few reverse-diffusion steps with SDXL-Turbo. The resulting decoded image $$S=\bigcup_{c=1}^{C}S_c,\qquad S_c\subset T_c,\qquad |S_c|\ll |T_c|,$$4 is a high-resolution training view derived from the real patch anchor. The stored representation is effectively

$$S=\bigcup_{c=1}^{C}S_c,\qquad S_c\subset T_c,\qquad |S_c|\ll |T_c|,$$5

and the full-resolution images are regenerated on the fly during student training. The same work also introduces latent-space mixup,

$$S=\bigcup_{c=1}^{C}S_c,\qquad S_c\subset T_c,\qquad |S_c|\ll |T_c|,$$6

to further diversify diffusion-anchored augmentation (Abbasi et al., 2024).

These mechanisms clarify that the object being “condensed” varies substantially across the literature. In one case it is a real-image subset with side information; in another it is a subset of diffusion-generated videos; in another it is a low-resolution coreset plus procedural generation metadata. The shared goal is compressed training utility for downstream models, but the representation class is method-dependent.

5. Empirical performance and characteristic regimes

On ImageNet-1K, D\textsuperscript{2}C reports three retained-data budgets—10K, 50K, and 100K images, corresponding to 0.8%, 4.0%, and 8.0% of the training set—and evaluates on DiT-L/2, SiT-L/2, and SiT-XL/2 at 256×256 and 512×512. Its headline result is on SiT-XL/2 with 10K images: gFID-50K $$S=\bigcup_{c=1}^{C}S_c,\qquad S_c\subset T_c,\qquad |S_c|\ll |T_c|,$$7 at 40K iterations, without CFG, which the paper states is over 100× acceleration over REPA and 233× over vanilla SiT. At 50K images with CFG $$S=\bigcup_{c=1}^{C}S_c,\qquad S_c\subset T_c,\qquad |S_c|\ll |T_c|,$$8, it reports FID $$S=\bigcup_{c=1}^{C}S_c,\qquad S_c\subset T_c,\qquad |S_c|\ll |T_c|,$$9 at 180K steps. On 256×256 ImageNet with 10K images and 100K iterations, the framework reports DiT-L/2 FID $S$0 and SiT-L/2 FID $S$1, while the discriminative condensation baseline SRe\textsuperscript{2}L records $S$2 and $S$3, respectively. At 512×512 with 10K images and 100K iterations, D\textsuperscript{2}C reports DiT-L/2 gFID $S$4, sFID $S$5, IS $S$6, Precision $S$7, and Recall $S$8 (Huang et al., 8 Jul 2025).

The geometry-aware method evaluates the same ImageNet-1K setting but argues that the D\textsuperscript{2}C ranking objective preserves the wrong object for diffusion training. On ImageNet 256×256 with DiT-L/2 and 100K iterations, its FID-50K is $S$9 at the 10K budget, compared with $$\mathcal{L}_{\text{diff}} = \mathbb{E}_{\mathbf{x}_0\sim q_0(\mathbf{x}),\, \epsilon\sim\mathcal{N}(0,\mathbf{I}),\, t\sim \mathcal{U}[0,1]} \left[ \| \epsilon - \epsilon_\theta(\mathbf{x}_t, t, \mathbf{c}) \|_2^2 \right],$$0 for $$\mathcal{L}_{\text{diff}} = \mathbb{E}_{\mathbf{x}_0\sim q_0(\mathbf{x}),\, \epsilon\sim\mathcal{N}(0,\mathbf{I}),\, t\sim \mathcal{U}[0,1]} \left[ \| \epsilon - \epsilon_\theta(\mathbf{x}_t, t, \mathbf{c}) \|_2^2 \right],$$1; at 50K and 100K budgets it reports $$\mathcal{L}_{\text{diff}} = \mathbb{E}_{\mathbf{x}_0\sim q_0(\mathbf{x}),\, \epsilon\sim\mathcal{N}(0,\mathbf{I}),\, t\sim \mathcal{U}[0,1]} \left[ \| \epsilon - \epsilon_\theta(\mathbf{x}_t, t, \mathbf{c}) \|_2^2 \right],$$2 and $$\mathcal{L}_{\text{diff}} = \mathbb{E}_{\mathbf{x}_0\sim q_0(\mathbf{x}),\, \epsilon\sim\mathcal{N}(0,\mathbf{I}),\, t\sim \mathcal{U}[0,1]} \left[ \| \epsilon - \epsilon_\theta(\mathbf{x}_t, t, \mathbf{c}) \|_2^2 \right],$$3, compared with $$\mathcal{L}_{\text{diff}} = \mathbb{E}_{\mathbf{x}_0\sim q_0(\mathbf{x}),\, \epsilon\sim\mathcal{N}(0,\mathbf{I}),\, t\sim \mathcal{U}[0,1]} \left[ \| \epsilon - \epsilon_\theta(\mathbf{x}_t, t, \mathbf{c}) \|_2^2 \right],$$4 and $$\mathcal{L}_{\text{diff}} = \mathbb{E}_{\mathbf{x}_0\sim q_0(\mathbf{x}),\, \epsilon\sim\mathcal{N}(0,\mathbf{I}),\, t\sim \mathcal{U}[0,1]} \left[ \| \epsilon - \epsilon_\theta(\mathbf{x}_t, t, \mathbf{c}) \|_2^2 \right],$$5 for $$\mathcal{L}_{\text{diff}} = \mathbb{E}_{\mathbf{x}_0\sim q_0(\mathbf{x}),\, \epsilon\sim\mathcal{N}(0,\mathbf{I}),\, t\sim \mathcal{U}[0,1]} \left[ \| \epsilon - \epsilon_\theta(\mathbf{x}_t, t, \mathbf{c}) \|_2^2 \right],$$6. At 512×512 with DiT-L/2 and a 10K budget, it reports FID $$\mathcal{L}_{\text{diff}} = \mathbb{E}_{\mathbf{x}_0\sim q_0(\mathbf{x}),\, \epsilon\sim\mathcal{N}(0,\mathbf{I}),\, t\sim \mathcal{U}[0,1]} \left[ \| \epsilon - \epsilon_\theta(\mathbf{x}_t, t, \mathbf{c}) \|_2^2 \right],$$7, IS $$\mathcal{L}_{\text{diff}} = \mathbb{E}_{\mathbf{x}_0\sim q_0(\mathbf{x}),\, \epsilon\sim\mathcal{N}(0,\mathbf{I}),\, t\sim \mathcal{U}[0,1]} \left[ \| \epsilon - \epsilon_\theta(\mathbf{x}_t, t, \mathbf{c}) \|_2^2 \right],$$8, Precision $$\mathcal{L}_{\text{diff}} = \mathbb{E}_{\mathbf{x}_0\sim q_0(\mathbf{x}),\, \epsilon\sim\mathcal{N}(0,\mathbf{I}),\, t\sim \mathcal{U}[0,1]} \left[ \| \epsilon - \epsilon_\theta(\mathbf{x}_t, t, \mathbf{c}) \|_2^2 \right],$$9, and Recall $$q_t(\mathbf{x}_t \mid \mathbf{x}_0) = \mathcal{N}(\mathbf{x}_t;\alpha_t \mathbf{x}_0,\sigma_t^2 \mathbf{I}), \qquad \mathbf{x}_t = \alpha_t \mathbf{x}_0 + \sigma_t \epsilon.$$0, compared with $$q_t(\mathbf{x}_t \mid \mathbf{x}_0) = \mathcal{N}(\mathbf{x}_t;\alpha_t \mathbf{x}_0,\sigma_t^2 \mathbf{I}), \qquad \mathbf{x}_t = \alpha_t \mathbf{x}_0 + \sigma_t \epsilon.$$1, $$q_t(\mathbf{x}_t \mid \mathbf{x}_0) = \mathcal{N}(\mathbf{x}_t;\alpha_t \mathbf{x}_0,\sigma_t^2 \mathbf{I}), \qquad \mathbf{x}_t = \alpha_t \mathbf{x}_0 + \sigma_t \epsilon.$$2, $$q_t(\mathbf{x}_t \mid \mathbf{x}_0) = \mathcal{N}(\mathbf{x}_t;\alpha_t \mathbf{x}_0,\sigma_t^2 \mathbf{I}), \qquad \mathbf{x}_t = \alpha_t \mathbf{x}_0 + \sigma_t \epsilon.$$3, and $$q_t(\mathbf{x}_t \mid \mathbf{x}_0) = \mathcal{N}(\mathbf{x}_t;\alpha_t \mathbf{x}_0,\sigma_t^2 \mathbf{I}), \qquad \mathbf{x}_t = \alpha_t \mathbf{x}_0 + \sigma_t \epsilon.$$4 for $$q_t(\mathbf{x}_t \mid \mathbf{x}_0) = \mathcal{N}(\mathbf{x}_t;\alpha_t \mathbf{x}_0,\sigma_t^2 \mathbf{I}), \qquad \mathbf{x}_t = \alpha_t \mathbf{x}_0 + \sigma_t \epsilon.$$5. On SiT-L/2 at 512×512, it reports FID $$q_t(\mathbf{x}_t \mid \mathbf{x}_0) = \mathcal{N}(\mathbf{x}_t;\alpha_t \mathbf{x}_0,\sigma_t^2 \mathbf{I}), \qquad \mathbf{x}_t = \alpha_t \mathbf{x}_0 + \sigma_t \epsilon.$$6, IS $$q_t(\mathbf{x}_t \mid \mathbf{x}_0) = \mathcal{N}(\mathbf{x}_t;\alpha_t \mathbf{x}_0,\sigma_t^2 \mathbf{I}), \qquad \mathbf{x}_t = \alpha_t \mathbf{x}_0 + \sigma_t \epsilon.$$7, Precision $$q_t(\mathbf{x}_t \mid \mathbf{x}_0) = \mathcal{N}(\mathbf{x}_t;\alpha_t \mathbf{x}_0,\sigma_t^2 \mathbf{I}), \qquad \mathbf{x}_t = \alpha_t \mathbf{x}_0 + \sigma_t \epsilon.$$8, and Recall $$q_t(\mathbf{x}_t \mid \mathbf{x}_0) = \mathcal{N}(\mathbf{x}_t;\alpha_t \mathbf{x}_0,\sigma_t^2 \mathbf{I}), \qquad \mathbf{x}_t = \alpha_t \mathbf{x}_0 + \sigma_t \epsilon.$$9, compared with $D^2C$0, $D^2C$1, $D^2C$2, and $D^2C$3. Its ablations further show that removing $D^2C$4, $D^2C$5, or $D^2C$6, or replacing partial OT with balanced OT, degrades performance; the full model reaches FID $D^2C$7 at 10K images, compared with $D^2C$8 for balanced OT and $D^2C$9 without $\mathcal{S}_g=\mathcal{F}_\theta(\mathcal{T})$0. Runtime on ImageNet with 10K selected images is reported as 5.5 hours on 1 RTX 3090, versus 30.4 hours for DQ and 41.9 hours for $\mathcal{S}_g=\mathcal{F}_\theta(\mathcal{T})$1; with 8 GPUs it is 96 minutes, versus 238 minutes and 314 minutes (Cui et al., 4 Jun 2026).

The video literature reports a different evaluation regime because downstream training targets action recognition rather than diffusion generation quality. On MiniUCF at VPC $\mathcal{S}_g=\mathcal{F}_\theta(\mathcal{T})$2, VST-UNet achieves $\mathcal{S}_g=\mathcal{F}_\theta(\mathcal{T})$3 and TAC-DT $\mathcal{S}_g=\mathcal{F}_\theta(\mathcal{T})$4, compared with $\mathcal{S}_g=\mathcal{F}_\theta(\mathcal{T})$5 for the best prior FRePo+VD; the paper describes the largest gain as $\mathcal{S}_g=\mathcal{F}_\theta(\mathcal{T})$6. On HMDB51 at VPC $\mathcal{S}_g=\mathcal{F}_\theta(\mathcal{T})$7, VST-UNet gives $\mathcal{S}_g=\mathcal{F}_\theta(\mathcal{T})$8 and TAC-DT $\mathcal{S}_g=\mathcal{F}_\theta(\mathcal{T})$9. On Kinetics400 and SSv2, the main table reports top-5 improvements at both VPC $$\mathcal{D}^{\mathcal{S}} = (\mathbf{X}, \mathbf{Y}) = \{(\mathbf{x}_j, y_j)\}_{j=1}^{|\mathcal{D}^{\mathcal{S}}|}, \qquad |\mathcal{D}^{\mathcal{S}}| \ll |\mathcal{D}|.$$00 and $$\mathcal{D}^{\mathcal{S}} = (\mathbf{X}, \mathbf{Y}) = \{(\mathbf{x}_j, y_j)\}_{j=1}^{|\mathcal{D}^{\mathcal{S}}|}, \qquad |\mathcal{D}^{\mathcal{S}}| \ll |\mathcal{D}|.$$01. An ablation on MiniUCF shows that CE only yields $$\mathcal{D}^{\mathcal{S}} = (\mathbf{X}, \mathbf{Y}) = \{(\mathbf{x}_j, y_j)\}_{j=1}^{|\mathcal{D}^{\mathcal{S}}|}, \qquad |\mathcal{D}^{\mathcal{S}}| \ll |\mathcal{D}|.$$02, CE+Div $$\mathcal{D}^{\mathcal{S}} = (\mathbf{X}, \mathbf{Y}) = \{(\mathbf{x}_j, y_j)\}_{j=1}^{|\mathcal{D}^{\mathcal{S}}|}, \qquad |\mathcal{D}^{\mathcal{S}}| \ll |\mathcal{D}|.$$03, CE+Rep $$\mathcal{D}^{\mathcal{S}} = (\mathbf{X}, \mathbf{Y}) = \{(\mathbf{x}_j, y_j)\}_{j=1}^{|\mathcal{D}^{\mathcal{S}}|}, \qquad |\mathcal{D}^{\mathcal{S}}| \ll |\mathcal{D}|.$$04, and CE+Div+Rep $$\mathcal{D}^{\mathcal{S}} = (\mathbf{X}, \mathbf{Y}) = \{(\mathbf{x}_j, y_j)\}_{j=1}^{|\mathcal{D}^{\mathcal{S}}|}, \qquad |\mathcal{D}^{\mathcal{S}}| \ll |\mathcal{D}|.$$05, supporting the diversity and representativeness design (Li et al., 10 May 2025).

The diffusion-augmented coreset-expansion approach evaluates standard dataset distillation benchmarks by downstream classification accuracy. On ImageNet-1k it reports $$\mathcal{D}^{\mathcal{S}} = (\mathbf{X}, \mathbf{Y}) = \{(\mathbf{x}_j, y_j)\}_{j=1}^{|\mathcal{D}^{\mathcal{S}}|}, \qquad |\mathcal{D}^{\mathcal{S}}| \ll |\mathcal{D}|.$$06 at IPC $$\mathcal{D}^{\mathcal{S}} = (\mathbf{X}, \mathbf{Y}) = \{(\mathbf{x}_j, y_j)\}_{j=1}^{|\mathcal{D}^{\mathcal{S}}|}, \qquad |\mathcal{D}^{\mathcal{S}}| \ll |\mathcal{D}|.$$07 versus $$\mathcal{D}^{\mathcal{S}} = (\mathbf{X}, \mathbf{Y}) = \{(\mathbf{x}_j, y_j)\}_{j=1}^{|\mathcal{D}^{\mathcal{S}}|}, \qquad |\mathcal{D}^{\mathcal{S}}| \ll |\mathcal{D}|.$$08 for RDED, and $$\mathcal{D}^{\mathcal{S}} = (\mathbf{X}, \mathbf{Y}) = \{(\mathbf{x}_j, y_j)\}_{j=1}^{|\mathcal{D}^{\mathcal{S}}|}, \qquad |\mathcal{D}^{\mathcal{S}}| \ll |\mathcal{D}|.$$09 at IPC $$\mathcal{D}^{\mathcal{S}} = (\mathbf{X}, \mathbf{Y}) = \{(\mathbf{x}_j, y_j)\}_{j=1}^{|\mathcal{D}^{\mathcal{S}}|}, \qquad |\mathcal{D}^{\mathcal{S}}| \ll |\mathcal{D}|.$$10 versus $$\mathcal{D}^{\mathcal{S}} = (\mathbf{X}, \mathbf{Y}) = \{(\mathbf{x}_j, y_j)\}_{j=1}^{|\mathcal{D}^{\mathcal{S}}|}, \qquad |\mathcal{D}^{\mathcal{S}}| \ll |\mathcal{D}|.$$11. On ImageNette it reports $$\mathcal{D}^{\mathcal{S}} = (\mathbf{X}, \mathbf{Y}) = \{(\mathbf{x}_j, y_j)\}_{j=1}^{|\mathcal{D}^{\mathcal{S}}|}, \qquad |\mathcal{D}^{\mathcal{S}}| \ll |\mathcal{D}|.$$12 at IPC $$\mathcal{D}^{\mathcal{S}} = (\mathbf{X}, \mathbf{Y}) = \{(\mathbf{x}_j, y_j)\}_{j=1}^{|\mathcal{D}^{\mathcal{S}}|}, \qquad |\mathcal{D}^{\mathcal{S}}| \ll |\mathcal{D}|.$$13, $$\mathcal{D}^{\mathcal{S}} = (\mathbf{X}, \mathbf{Y}) = \{(\mathbf{x}_j, y_j)\}_{j=1}^{|\mathcal{D}^{\mathcal{S}}|}, \qquad |\mathcal{D}^{\mathcal{S}}| \ll |\mathcal{D}|.$$14 at IPC $$\mathcal{D}^{\mathcal{S}} = (\mathbf{X}, \mathbf{Y}) = \{(\mathbf{x}_j, y_j)\}_{j=1}^{|\mathcal{D}^{\mathcal{S}}|}, \qquad |\mathcal{D}^{\mathcal{S}}| \ll |\mathcal{D}|.$$15, and $$\mathcal{D}^{\mathcal{S}} = (\mathbf{X}, \mathbf{Y}) = \{(\mathbf{x}_j, y_j)\}_{j=1}^{|\mathcal{D}^{\mathcal{S}}|}, \qquad |\mathcal{D}^{\mathcal{S}}| \ll |\mathcal{D}|.$$16 at IPC $$\mathcal{D}^{\mathcal{S}} = (\mathbf{X}, \mathbf{Y}) = \{(\mathbf{x}_j, y_j)\}_{j=1}^{|\mathcal{D}^{\mathcal{S}}|}, \qquad |\mathcal{D}^{\mathcal{S}}| \ll |\mathcal{D}|.$$17, compared with $$\mathcal{D}^{\mathcal{S}} = (\mathbf{X}, \mathbf{Y}) = \{(\mathbf{x}_j, y_j)\}_{j=1}^{|\mathcal{D}^{\mathcal{S}}|}, \qquad |\mathcal{D}^{\mathcal{S}}| \ll |\mathcal{D}|.$$18, $$\mathcal{D}^{\mathcal{S}} = (\mathbf{X}, \mathbf{Y}) = \{(\mathbf{x}_j, y_j)\}_{j=1}^{|\mathcal{D}^{\mathcal{S}}|}, \qquad |\mathcal{D}^{\mathcal{S}}| \ll |\mathcal{D}|.$$19, and $$\mathcal{D}^{\mathcal{S}} = (\mathbf{X}, \mathbf{Y}) = \{(\mathbf{x}_j, y_j)\}_{j=1}^{|\mathcal{D}^{\mathcal{S}}|}, \qquad |\mathcal{D}^{\mathcal{S}}| \ll |\mathcal{D}|.$$20 for RDED. Its ablations further show that “Only text cond.” is weaker than anchored super-resolution, and that “Superres + Aug + Mixup” is strongest, reaching $$\mathcal{D}^{\mathcal{S}} = (\mathbf{X}, \mathbf{Y}) = \{(\mathbf{x}_j, y_j)\}_{j=1}^{|\mathcal{D}^{\mathcal{S}}|}, \qquad |\mathcal{D}^{\mathcal{S}}| \ll |\mathcal{D}|.$$21 on ImageWoof and $$\mathcal{D}^{\mathcal{S}} = (\mathbf{X}, \mathbf{Y}) = \{(\mathbf{x}_j, y_j)\}_{j=1}^{|\mathcal{D}^{\mathcal{S}}|}, \qquad |\mathcal{D}^{\mathcal{S}}| \ll |\mathcal{D}|.$$22 on ImageNette at IPC $$\mathcal{D}^{\mathcal{S}} = (\mathbf{X}, \mathbf{Y}) = \{(\mathbf{x}_j, y_j)\}_{j=1}^{|\mathcal{D}^{\mathcal{S}}|}, \qquad |\mathcal{D}^{\mathcal{S}}| \ll |\mathcal{D}|.$$23 (Abbasi et al., 2024).

A consistent empirical pattern runs across these works. The strongest gains typically occur under severe compression and limited training budgets. This suggests that D2C is especially consequential in the small-data, early-iteration regime, where sample selection quality, semantic enrichment, and geometry preservation materially alter the optimization trajectory.

6. Limitations, misconceptions, and open directions

A common misconception is that diffusion dataset condensation is synonymous with direct optimization of a tiny synthetic image set. The current literature does not support that equivalence. D\textsuperscript{2}C selects real images and attaches side information; the geometry-aware method selects only real images; the video method selects representative synthetic videos from a diffusion-generated pool; and the coreset-expansion method stores real patches plus procedural metadata rather than final images (Huang et al., 8 Jul 2025, Cui et al., 4 Jun 2026, Li et al., 10 May 2025, Abbasi et al., 2024).

A second misconception is that generic discriminative condensation transfers directly to diffusion training. The evidence cited by D\textsuperscript{2}C and by the geometry-aware critique points the other way. The former reports severe degradation when adapting SRe\textsuperscript{2}L to diffusion training, while the latter argues that ranking-based or prototype-based selectors fail because diffusion learning is sensitive to distortions of data support, relative relationships, and local structure rather than only to sample importance or class separation (Huang et al., 8 Jul 2025, Cui et al., 4 Jun 2026).

Current formulations also carry substantial assumptions. The geometry-aware method depends on a pretrained feature space whose geometry is assumed to correlate with the diffusion-relevant manifold, uses class-wise balanced selection, and includes a confidence regularizer that may inherit classifier biases; it is evaluated only on ImageNet-scale class-conditional generation. D\textsuperscript{2}C depends on a pretrained diffusion scorer, a pretrained text encoder, a pretrained vision encoder, and a pretrained VAE, and its appendix states that final performance upon convergence does not yet fully match baseline benchmarks in all cases. The video method relies on access to and fine-tuning of Latte, reports no formal generative quality metrics such as FVD, and leaves some details of VST-UNet under-specified. The coreset-expansion approach does not introduce a new diffusion-specific condensation loss; diffusion serves as a pretrained procedural generator, and runtime still grows with the number of patches due to repeated diffusion calls (Cui et al., 4 Jun 2026, Huang et al., 8 Jul 2025, Li et al., 10 May 2025, Abbasi et al., 2024).

Several broader implications follow from these constraints. One is that D2C is presently most mature for labeled, class-conditional settings with strong pretrained backbones and encoders. Another is that “what must be preserved” remains an open design question. D\textsuperscript{2}C emphasizes learnability balanced by interval-sampled difficulty, whereas geometry-aware selection emphasizes distributional support geometry, neighborhood structure, and mode coverage. A plausible implication is that future work will need to reconcile these views rather than treat them as mutually exclusive. The same literature also points toward expansion beyond ImageNet-scale image generation: D\textsuperscript{2}C explicitly mentions possible extension to 3D and video diffusion, while the video work already demonstrates that diffusion-based condensation can be reformulated around synthetic-pool selection in temporal domains (Huang et al., 8 Jul 2025, Li et al., 10 May 2025).

In its current form, Diffusion Dataset Condensation is best understood not as a single algorithm but as a research program that asks how much of a diffusion training set can be discarded, compressed, enriched, or procedurally regenerated without breaking the generative objective. The most technically developed answers so far revolve around three recurrent principles: preserve diffusion-relevant geometry, preserve enough semantic and visual conditioning to compensate for subsampling, and exploit generative priors only when they remain anchored to a faithful representation of the original data distribution.