Distribution-Aware Diverse Content Upsampling

• The paper introduces a two-stage method that fills low-density gaps in data while rigorously preserving the original distribution.
• It employs techniques like k-DPP, k-means++ seeding, and diffusion-based strategies to enhance sample diversity and mitigate clustering artifacts.
• Empirical evaluations across image, point cloud, and domain adaptation tasks show improvements in generalization, accuracy, and perceptual quality.

Distribution-aware diverse content upsampling refers to a class of techniques for increasing data density or resolution—whether in point clouds, images, or datasets—while simultaneously enforcing both statistical fidelity to the original data distribution and maximizing diversity across the newly generated content. The core principle is to guide upsampling so that the produced samples not only fill gaps and increase variety but also avoid deviating from the true data manifold, thus preventing the introduction of unrealistic or clustered artifacts. Modern approaches integrate manifold modeling, sampling theory, optimal transport, diffusion modeling, and distribution-matching energy functions to attain both uniform coverage and diversity, yielding strong empirical benefits in cross-domain generalization, downstream accuracy, and perceptual quality.

1. Motivation and Problem Definition

Distribution-aware diverse content upsampling arises in response to the failures of naïve upsampling or data expansion methods, which often worsen generalization or perceptual quality by introducing bias, redundancy, or mode collapse. For example, in synthetic image quality assessment, reference images selected for upsampling can overrepresent clustered regions of feature space, undermining regression on real-world data (Li et al., 1 Jan 2026). Similarly, point cloud upsampling from sparse, non-uniform scans may yield unevenly distributed points that cluster or miss regions of the surface manifold (Fang et al., 16 Apr 2025).

A common theme is the prevalence of clustered or under-diverse synthetic data when using grid or random selection, leading to discontinuities in the feature (or geometric) manifold, lower coverage of the data distribution, and increased generalization gap. Distribution-aware diverse upsampling directly targets these issues by:

• Measuring the support and density of the observed data/dataset in (pretrained) feature space or local geometric patch space.
• Filling low-density or “gapped” regions with new content while maintaining global and local distribution support.
• Assigning pseudo-labels or statistical weights to generated samples via principled interpolation, thus preserving distributional semantics.

2. Methodological Frameworks

Approaches span structured manifold modeling, probabilistic sampling, diffusion-based sample expansion, and explicit diversity-maximization. Key instantiations include:

2.1 Distribution-aware content selection in feature space

In SynDR-IQA, distribution-aware diverse content upsampling (DDCUp) is defined as a two-stage procedure for augmenting synthetic reference sets (Li et al., 1 Jan 2026):

• Compute a feature extractor $f(\cdot) \in \mathbb{R}^d$ and measure pairwise distances over the reference set.
• Select candidate images from a large pool that (a) are not too close to any existing reference, (b) are not outliers, and (c) are mutually separated, i.e., lie in low-density gaps within the convex hull of the originals.
• Accepted references are paired with synthetic distortions and pseudo-labels generated by weighted interpolation from the neighborhood of existing labels.

Mathematically, this operates by constraining the minimum and maximum distances between new candidates, guaranteeing increased diversity without distributional drift.

2.2 Distribution-aligned, diversity-aware sampling

For domain adaptation and dataset balancing, diversity-driven upsampling relies on structured sampling algorithms:

• k-Determinantal Point Processes (k-DPPs): These maximize the determinant (and thus the volume) spanned by the selected minibatch in feature space, promoting a subset that is both diverse and representative. Weighting individual samples allows controlled upsampling of minority or underrepresented classes while maintaining global distribution proportions (Napoli et al., 2024).
• k-means++ seeding: This probabilistically selects initialization points for clustering or minibatch assembly, biasing each selection toward maximal feature-space separation from previously chosen examples.

Both strategies can integrate per-example weights inversely proportional to class frequency, thus upsampling rare data modalities and reducing bias.

2.3 Manifold-constrained generative modeling

Point cloud upsampling via local manifold distribution fitting uses Gaussian Mixture Models (GMMs) on local (tangent-projected) surface patches (Fang et al., 16 Apr 2025). Here:

• Each neighborhood patch is modeled as a $K$-component GMM, parameterized with unconstrained weights and covariance factors.
• The set of local mixtures is viewed as points on a statistical manifold, and a Fisher–Rao geodesic distance is minimized between input and upsampled output mixtures to ensure global distributional consistency.
• An explicit distribution loss penalizes divergence from the original distribution, enforcing both uniform coverage and mode diversity.

2.4 Diffusion-based distribution-aware expansion

In image and dataset expansion, diffusion models are guided toward the true data manifold by hierarchical prototype-based energy functions (Zhu et al., 2024):

• Prototypes at class and group levels summarize manifold structure, and the sample’s clean reconstruction in latent space is forced toward these prototypes via energy gradients during reverse diffusion steps.
• The total guidance comprises both class- and group-level terms, and energy injection is staged at semantically meaningful timesteps to avoid early-stage instability or late-stage ineffectiveness.

Diffusion-driven approaches are also extended via explicit diversity-seeking terms: pairwise repulsion between N candidate outputs during sampling (e.g., clamped distance penalties) maximizes semantic spread without distributional drift (Cohen et al., 2023).

3. Detailed Algorithmic Procedures

3.1 Algorithmic summary for DDCUp (Li et al., 1 Jan 2026)

• Compute median ($\mu$) and max ($\delta$) inter-reference distances in feature space.
• For each candidate, accept if all distances to original references are within $(\mu, \delta)$, and also beyond $\mu$ from all previously accepted new references.
• For each new reference, produce distorted variants (with respect to all synthetic distortion types and levels), assigning pseudo-labels via a distance-weighted softmax interpolation from the k-nearest original references.
• Complexity is $O(M^2)$ for reference selection per $M$ candidates.

3.2 Distribution-aware diffusion sampling (Zhu et al., 2024)

• Extract class and group prototypes from features via clustering.
• At a chosen reverse diffusion step, compute energy as sum of Euclidean distances between the clean latent and both levels of prototypes.
• Nudge the sample in latent space with gradient descent on the energy, iterating as part of the reverse diffusion chain.
• Empirically, application at roughly the 60% (semantic) mark in sampling yields optimum results.

3.3 Diversity-seeking diffusion for upsampling (Cohen et al., 2023)

• For each reverse diffusion timestep, generate $N$ concurrent samples.
• At each step, compute nearest neighbor in feature space for each candidate, apply a clamped repulsive loss to steer samples apart.
• The repulsion parameter and threshold are tuned to balance diversity with data consistency.
• Quantitative metrics include LPIPS diversity, NIQE, and LR-PSNR for super-resolution tasks.

3.4 Diverse Score Distillation (DSD) for super-resolution (Xu et al., 2024)

• For each independent sample, fix a random DDIM ODE seed, induce associated noise at each timestep.
• Build interpolated states combining the optimized variable and path-specific noise, calculate the difference of score (noise) predictions at adjacent steps.
• The overall loss is the expectation over per-seed, per-timestep score differences, augmented with a strict data-fidelity loss matching the downsampled output to the low-res observation.
• Multiple diverse outputs are obtained by independently optimizing with distinct initial seeds, ensuring both fidelity and multimodality by construction.

4. Theoretical Implications and Bounds

Analytical results in synthetic-to-real IQA demonstrate that increasing the number of distinct, well-separated clusters $m$ directly decreases the generalization upper bound:

$$|R(f) − R_{\text{emp}}(f)| \leq 2 \operatorname{Rad}_m(\mathcal{F}) + \sqrt{\frac{2 \ln(2/\delta)}{m}} + \sqrt{\frac{\eta \ln(2/\delta)}{8m} + \frac{2 \ln(2/\delta)}{3m}}$$

where $\eta$ measures cluster redundancy (Li et al., 1 Jan 2026). DDCUp increases $m$ without proportionally increasing redundancy, thus provably reducing the generalization gap.

For diversity-based sampling, quantization error (total distance to nearest minibatch exemplar) and mean absolute percentage error for MMD estimation are both substantially reduced compared to uniform random sampling, leading to lower estimation bias and variance in distributional alignment (Napoli et al., 2024).

5. Empirical Evidence and Performance

Illustrative empirical results include:

• For IQA, DDCUp increases the cross-dataset SRCC average by more than 3% (from 0.7155 baseline to 0.7387) in synthetic-to-authentic settings (Li et al., 1 Jan 2026).
• For point cloud upsampling, manifold-constrained methods reduce Chamfer distance, Jensen–Shannon divergence, and Uniformity metrics beyond prior state-of-the-art baselines (e.g., CD = $2.742 \times 10^{-3}$ with notable improvement over PUGeo/APUNet) (Fang et al., 16 Apr 2025).
• For data expansion using distribution-aware diffusion, absolute classification accuracy gains reach +30.7%, with FID reductions on benchmarks (Zhu et al., 2024).
• For diversity-driven batch sampling in domain adaptation, both k-means++ and k-DPP improve test-domain accuracy by 4–5 percentage points and reduce quantization error and MMD estimation error compared to random selection (Napoli et al., 2024).
• In image super-resolution, DSD-based upsampling achieves LPIPS diversity values 7× higher than standard mode-seeking methods, with negligible loss in PSNR/SSIM (Xu et al., 2024).

Ablations consistently show that removing distributional or diversity constraints leads to mode clustering, reduced coverage, and degraded generalization, affirming the necessity of both components.

6. Visualization and Interpretation

Visualization of the reference-feature space in DDCUp reveals that newly added references populate the boundary and low-density regions between clusters, augmenting manifold coverage without introducing outliers or shifting the support (Li et al., 1 Jan 2026). For manifold modeling in point clouds, qualitative figures show that distribution-constrained generation eliminates spurious point clusters and enhances geometric uniformity (Fang et al., 16 Apr 2025).

In diffusion-based guidance methods, qualitative samples exhibit retention of class-specific structure and avoidance of hallucinated or out-of-distribution artifacts, with improvements visible in both perceptual spread and faithfulness to the input semantics (Zhu et al., 2024, Xu et al., 2024).

7. Applications and Future Directions

Distribution-aware diverse content upsampling underpins advances in:

• Cross-domain and out-of-distribution generalization (e.g., synthetic-to-authentic BIQA, domain adaptation).
• Geometric reconstruction (point cloud upsampling, 3D object completion).
• Data-efficient training pipelines (data expansion for deep learning).
• Image restoration and generation (super-resolution, inpainting with meaningful diversity).

A plausible implication is that future developments will further unify data-driven prototype modeling with implicit generative priors, enabling plug-in distributionally constrained modules for any data modality. Open directions include integrating density-aware downsampling for redundancy mitigation, extending prototype hierarchies, and exploring joint probabilistic and adversarial objectives for optimal diversity-fidelity tradeoff.

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Key references: (Li et al., 1 Jan 2026, Fang et al., 16 Apr 2025, Zhu et al., 2024, Napoli et al., 2024, Cohen et al., 2023, Xu et al., 2024).