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REVIEW 3 major objections 5 minor 127 references

The paper claims that by assigning unlabeled examples a trivial label ∅ and training one score model over the augmented label space, the sampling distribution of a conditional diffusion model converges to PX|Y at a rate dominated by the unl

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2026-08-01 20:16 UTC pith:ESLWYNOT

load-bearing objection Sensible method with real finite-sample rates, but the strict-improvement claim depends on an unverified transfer assumption that is close to the conclusion. the 3 major comments →

arxiv 2607.16685 v1 pith:ESLWYNOT submitted 2026-07-18 stat.ML cs.LG

Semi-Supervised Conditional Diffusion via Label Augmentation

Jin Su , Yuan Gao , Yong Zhou , Jian Huang This is my paper
classification stat.ML cs.LG MSC 62G0768T07
keywords semi-supervised learningconditional diffusion modelslabel augmentationdenoising score matchingtotal variation distanceWasserstein-1 distanceshared baselinemissing data
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper proposes label-augmented conditional diffusion (LACD): give every unlabeled example a trivial label ∅ and train a conditional diffusion model on the augmented dataset, so the marginal score and the conditional scores are learned in one objective. The central claim is that under a shared-baseline model family — each conditional density equals p(x; b0 + Φ0 e_y) for a common baseline b0 — the unlabeled samples improve estimation of the shared component and therefore of every conditional. The main theorem gives finite-sample bounds: in total variation distance LACD achieves Õ(N_ℓ^{-1/2} + N_u^{-β_x/(2β_x+d_x)}) against Õ(N_ℓ^{-β_x/(2β_x+d_x)}) for supervised-only training, and when N_ℓ/N_u → 0 the unlabeled term is strictly smaller. The paper reads this as unlabeled data becoming the rate-limiting resource, and supports it with experiments on synthetic, image, and tabular benchmarks where added unlabeled samples consistently lower generative error.

Core claim

The paper establishes that attaching a designated label ∅ to unlabeled X and performing joint denoising score matching over the augmented label space Ỹ = Y ∪ {∅} identifies and estimates the target conditionals PX|Y. Identifiability follows from missing-completely-at-random label dropout: conditional on ∅ the augmented distribution is the marginal PX, conditional on y it is PX|Y=y. Under the model specification p(x; b0 + Φ0 e_y) with shared baseline, the total-variation convergence rate of the generated distribution is Õ(N_ℓ^{-1/2} + N_u^{-β_x/(2β_x+d_x)}), strictly better than the supervised-only rate Õ(N_ℓ^{-β_x/(2β_x+d_x)}) when unlabeled samples dominate; in Wasserstein-1 the rate is at

What carries the argument

The load-bearing object is the augmented embedding h(ỹ) = b + Φ e_y · 1{ỹ = y ∈ Y}, where b is a shared baseline and Φ e_y is a class-specific offset. Unlabeled data train b through the marginal score while labeled pairs train Φ through the conditional score. The proof runs through an error decomposition into embedding, shared-parameter, and approximation terms; Assumption 3 (structural consistency) says conditional error is bounded by marginal error, which is the mechanism that lets N_u replace N_ℓ in the rate.

Load-bearing premise

The load-bearing premise is Assumption 3 (structural consistency — conditional score error is controlled by marginal score error), which is exactly the benefit unlabeled data are claimed to provide, is never verified empirically, and has no realistic sufficient conditions; the SDE error-propagation step of the proof is additionally deferred to a supplementary file not included in this version.

What would settle it

Fit LACD and a supervised-only model on data where each class is a distinct low-dimensional manifold embedded in high-dimensional space, so the marginal score carries no class-specific information, and measure TV error against N_u; if TV does not improve as N_u grows, the structural-consistency condition fails. Alternatively, directly estimate |Δc − Δc*| and |Δm − Δm*| for a trained network; a ratio that grows with N or with model capacity would falsify Assumption 3.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • When unlabeled data vastly outnumber labeled data, the TV sampling-error rate is governed by N_u, not N_ℓ, so cheap unlabeled data substitutes for expensive labels up to the limit of the shared-baseline assumption.
  • In Wasserstein-1 distance, LACD is never slower than supervised-only training, and is strictly faster when the covariate dimension exceeds 2 and N_ℓ/N_u → 0.
  • Population-level identifiability of PX|Y holds under MCAR label dropout, so the augmented space preserves both the marginal and the conditionals exactly.
  • On CIFAR-10, 1,000 labels plus 10,000 unlabeled images match 5,000 labels alone, and class-averaged FID falls by up to about 50% as unlabeled data are added, indicating that unlabeled data can partially replace labels in practice.

Where Pith is reading between the lines

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

  • If the structural-consistency assumption holds, the same label-augmentation trick should transfer to other generative estimators with a shared baseline, such as normalizing flows or GANs, though the paper proves the rate only for diffusion models.
  • The strict-improvement result is an upper-bound comparison; a minimax lower-bound analysis could reveal whether the true TV rate is actually N_u-dominated or whether supervised and semi-supervised rates coincide in the worst case.
  • When the shared-baseline model is wrong — for instance, each class lives on a different manifold — unlabeled data could distort the shared baseline; a diagnostic is to measure conditional versus marginal score error on real data before trusting the rate gain.
  • Because MCAR is assumed, any label-missingness mechanism that depends on X or Y would break the identification of PX|Y through ∅; extending the method to missing-not-at-random settings would require weighting or imputation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper introduces label-augmented conditional diffusion (LACD): unlabeled covariates X are assigned a trivial label ∅, and a score-based diffusion model is trained by denoising score matching over the augmented pairs (X, eY). The target conditional P_{X|Y} is recovered because P_{X|eY=y}=P_{X|Y=y} and P_{X|eY=∅}=P_X. Under a shared-baseline model specification p(x; b0+Φ0 e_y·1{y∈Y}) and Assumptions 1–4, Theorem 3.1 gives W1 and TV upper bounds for the reverse-process output whose dominant terms involve N_u instead of N_l; Table 1 compares these with the supervised counterpart. Experiments on synthetic, CIFAR-10, Intel Scenes, and EEG data show improved FID/W1 as N_u increases. The paper claims strict improvement in TV from unlabeled data, but this rests on a transfer assumption and on proofs placed in a missing supplementary file.

Significance. If the assumptions are accepted, the paper provides a clean shared-parameter framework and the first finite-sample rates for semi-supervised conditional diffusion with MCAR labels. The identification calculation in Lemma 2.1 is correct, the rate arithmetic in Table 1 is internally consistent, and the empirical evaluation is broad and generally supports the qualitative message. However, the central improvement is carried by Assumption 3, a transfer inequality that is close in content to the conclusion and is neither derived nor empirically validated; moreover, all proofs of the main theorem are in a missing supplementary file. The result is best read as a conditional statement: given a shared-baseline structure strong enough to satisfy Assumption 3, unlabeled data provably enter the upper bound. That is a potentially useful contribution, but the current manuscript does not yet establish the headline 'strictly faster' claim.

major comments (3)
  1. [§3.1, Assumption 3] Assumption 3 is load-bearing: through Lemma 3.2 it converts marginal-score error into the E_shared term that replaces N_l by N_u in the TV bound of Theorem 3.1 and Table 1. The objective is L = π_N L_c + (1−π_N)L_m with π_N→0, so without Assumption 3 the conditional loss at the full-data minimizer need not decrease with N_u and only N_l terms remain. Assumption 3 asserts |Δ_c(θ,b)−Δ_c(θ̄,b̄)| ≤ c_1|Δ_m(θ,b)−Δ_m(θ̄,b̄)|, which is qualitatively the transfer property the paper claims to prove. The §2.4 examples verify model (2), not Assumption 3; no sufficient condition in terms of the model primitives or an empirical diagnostic is provided. Please derive Assumption 3 for a concrete family or add a direct check, and state the theorem explicitly as conditional on this transfer assumption.
  2. [§3.1–§3.3, proofs] The SDE error-propagation inequalities and the proofs of Lemmas 3.1–3.3 and Theorem 3.1 are all deferred to 'SM', which is not included in v1. The central statistical guarantees therefore cannot be verified from the submitted manuscript. In particular, Lemma 3.1 uses the marginal-loss gap |L_{m,i}(θ̂,b̂)−L_{m,i}(θ̄,b̄)|, but no stated lemma bounds this gap; the path from equations (10)–(11) to Theorem 3.1 requires an additional empirical-process argument that is not shown. The supplementary file must be supplied and these steps presented.
  3. [Abstract and §5] The claim that LACD 'converges strictly faster' than the supervised estimator is stronger than what is proven. Theorem 3.1 and Corollary 3.1 are upper bounds; no lower bounds are given. Table 1 compares dominant terms of these upper bounds. The abstract and conclusion should say that the derived upper bound is strictly smaller (or 'the rate bound improves'), and the paper's own §5 correctly notes that lower bounds are missing. The current wording overstates the result.
minor comments (5)
  1. [§2.1, Lemma 2.1] The product-space construction is correct but more elaborate than needed: P_{X|eY=y}=P_{X|Y=y} and P_{X|eY=∅}=P_X follow directly from D⊥(X,Y) and Bayes' rule. The lemma is not used elsewhere and could be replaced by a short argument.
  2. [§3, Theorem 3.1] The statement 'there exists ŝ∈Γ...' is misleading. The bounds are intended for the empirical DSM minimizer over Γ; as written, existence of some network achieving the bound is an approximation statement, not a guarantee for the LACD estimator. Please restate the theorem for (θ̂,b̂,Φ̂) minimizing the empirical loss.
  3. [Notation] The augmented label is denoted inconsistently as ̃Y, eY, and ̃y across sections. Please unify notation. Also, the section header 'CIF AR-10' and the phrase 'CIF AR-101' should be 'CIFAR-10'.
  4. [Table 1] The heading 'Dominant convergence rates' should specify 'dominant terms in the upper bounds', to avoid implying lower-bound optimality.
  5. [§4.1 and §4.3] Reporting the best FID/TV attained during training can be optimistic. Please also report final-iteration metrics or a validation-based selection rule for the main empirical claims.

Circularity Check

0 steps flagged

No significant circularity: Theorem 3.1 is a genuine conditional result under the explicitly stated Assumption 3, with no fitted-input-as-prediction or load-bearing self-citation chain.

full rationale

The paper's central claim—that unlabeled samples improve conditional generation—is derived as a theorem conditional on Assumptions 1–4. Assumption 3 (Structural Consistency) is an explicit premise, not a hidden restatement of the conclusion. It postulates that the conditional score-matching gap Δc is controlled by the marginal gap Δm; this is a transfer condition that, together with standard statistical-complexity bounds, yields the N_u-dependent rates in Theorem 3.1. The derivation is not circular in the sense of Eq. X = Eq. Y by construction: the assumption is not defined from the theorem's TV/W1 rates, and the paper does not claim to prove it from model (2). It is a strong, unverified sufficient condition, and the paper's own examples only illustrate model (2), not Assumption 3; this is a limitation of evidence, not a circular derivation. The authors also explicitly state in Section 5 that 'establishing minimax lower bounds to complement the upper bounds' remains future work, conceding that the 'strictly faster' claim is only a comparison of upper bounds—again a correctness/risk concern rather than circularity. Self-citations appear (Gao et al. 2022; Song et al. 2024; Song et al. 2025) but only for dataset conventions or SSL background, not as load-bearing uniqueness theorems. The SDE error-propagation bounds are deferred to a supplementary file absent from v1; this is an omitted-proof issue, not a circular step. No fitted parameter is renamed as a prediction, and the identification Lemma 2.1 is a direct consequence of MCAR and the definition of the augmented label. Therefore, despite Assumption 3 being the load-bearing weak point, the paper does not exhibit a specific reduction of its output to its input by construction.

Axiom & Free-Parameter Ledger

3 free parameters · 8 axioms · 1 invented entities

The central claim rests on three families of premises: (i) the data model — MCAR missingness and the exact shared-baseline specification (2) that makes the marginal a member of the same parametric family as the conditionals (§2.2); (ii) Assumption 3, the transferability condition that converts marginal score error into conditional score error — the qualitative content of the headline result; (iii) the standard diffusion-analysis toolkit (time reversal, DSM equivalence, SDE error propagation, ReLU approximation), the last two deferred to a missing SM. No numbers are fitted to data in the rate derivation; T and τ are balancing choices. The only 'invented entity' is the ∅ label, which is a coding device already conceptually present in classifier-free guidance.

free parameters (3)
  • c₁ (Assumption 3 alignment constant)
    Strength of the structural-consistency inequality |Δ_c − Δ_c̄| ≤ c₁|Δ_m − Δ_m̄|. Never estimated or verified; the magnitude and validity of all unlabeled-data gains scale through it.
  • Terminal time T = Θ(log N)
    Chosen to balance the e^{−T} initialization error in the SDE propagation bounds, not fitted to data; a standard theory-balancing choice.
  • Early-stopping time τ = N_u^{−2(1+1/β_x)/(2+d_x/β_x)}
    Chosen to balance √τ with the score-error terms in Theorem 3.1; a proof-balancing device rather than a fitted quantity.
axioms (8)
  • domain assumption MCAR: D ⊥ (X,Y) with observation probability π_N, allowing π_N → 0 but N π_N → ∞
    Required for Lemma 2.1 identification P_{X|Ỹ=y} = P_{X|Y=y}; if labels are missing depending on X or Y, the ∅-conditioned distribution is not P_X. Authors flag relaxation as future work in §5.
  • domain assumption Model specification (2): p_{X|Ỹ=ỹ} = p(x; h(ỹ)) with h(y) = b₀+Φ₀e_y and h(∅) = b₀; the true marginal P_X equals p(x; b₀)
    The shared-baseline structure that lets unlabeled data inform the conditionals through the common parameter b₀; a correct-specification assumption for both theory and the parametric examples in §2.4.
  • domain assumption Assumption 3 (Structural Consistency): |Δ_c(θ,b) − Δ_c(θ̄,b̄)| ≤ c₁|Δ_m(θ,b) − Δ_m(θ̄,b̄)|
    Load-bearing transferability condition: reduces conditional score error to marginal score error. This is the mathematical content of 'unlabeled data help conditionals'; never empirically verified.
  • domain assumption Assumptions 1–2: compact support; Hölder smoothness β_x; bounded densities
    Standard regularity for rate analysis; fixes the exponents β_x/(2β_x+d_x) in TV and (1+β_x)/(2β_x+d_x) in W1.
  • standard math Assumption 4: diffusion schedule β_t continuous, non-decreasing, bounded
    Standard in diffusion-rate analysis; satisfied by constant/linear/cosine schedules.
  • standard math Vincent (2011) DSM–Fisher equivalence; Anderson (1982) time reversal
    Used to equate the DSM objective with the Fisher divergence (8) and to justify the reverse-process sampler.
  • standard math SDE error-propagation bounds used in Theorem 3.1 (deferred to SM)
    The e^{−T}, √τ, and Σ√(t_i log N)√L_c,i inequalities in §3.1 are asserted with 'see SM'; the supplementary file is not present in v1, so this step is unverifiable from the preprint.
  • standard math ReLU approximation bounds (Lemma 3.3 network construction)
    Relies on neural-network approximation theory for Hölder score functions; the explicit network sizes are given in the lemma but its proof is in the absent SM.
invented entities (1)
  • Trivial label ∅ in the augmented conditioning space Ỹ = Y ∪ {∅} no independent evidence
    purpose: Folds the marginal distribution P_X into the conditional score network as the condition 'unlabeled', enabling joint denoising score matching over labeled and unlabeled data.
    A modeling device, not a physical entity; its only evidence is the paper's own experiments (FID/W1 gains). It is analogous to the null/dropped condition in classifier-free guidance (Ho & Salimans 2022), which the paper does not cite for this mechanism.

pith-pipeline@v1.3.0-alltime-deepseek · 19605 in / 39465 out tokens · 348867 ms · 2026-08-01T20:16:46.445312+00:00 · methodology

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read the original abstract

Conditional diffusion models have become a powerful and flexible framework for learning complex conditional distributions from labeled data. In practice, however, acquiring high-quality labels is costly and time-consuming, leaving large volumes of unlabeled data unused. To address this, we introduce label-augmented conditional diffusion (LACD), a simple and effective approach that incorporates unlabeled examples by assigning them a designated trivial label and performing joint denoising score matching over the augmented dataset. We provide sufficient conditions guaranteeing population-level identifiability of the target conditional distribution under this scheme. Moreover, we establish rigorous statistical guarantees: when sufficiently many unlabeled samples are available, the sampling distribution produced by LACD converges strictly faster than the purely supervised estimator in total variation distance, and at least as fast in Wasserstein-1 distance. Extensive experiments on synthetic, image, and tabular benchmarks corroborate our theory and show substantial gains in sample efficiency and generative performance compared with the purely supervised estimator.

Figures

Figures reproduced from arXiv: 2607.16685 by Jian Huang, Jin Su, Yong Zhou, Yuan Gao.

Figure 1
Figure 1. Figure 1: Target distributions and generated samples for [PITH_FULL_IMAGE:figures/full_fig_p021_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Class-averaged TV, MMD, and W1 distances on large 4gaussians, rings, and 2spirals versus Nu. For each example, Nℓ = 200 with varying Nu ∈ {0, 200, . . . , 1,000, 2,000}. 4.3 CIFAR-10 Dataset CIFAR-101 (Krizhevsky and Hinton, 2009) comprises nr = 60,000 color images (x ∈ R 32×32×3 ) across K = 10 classes with nr,y = 6,000 images per class. We consider Nℓ ∈ {1,000, 2,000, 5,000} labeled samples, with labels … view at source ↗
Figure 3
Figure 3. Figure 3: CIFAR-10: class-averaged FID (left) and overall FID (right) versus [PITH_FULL_IMAGE:figures/full_fig_p023_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: CIFAR-10 generated samples conditioned on the class “bird” under [PITH_FULL_IMAGE:figures/full_fig_p024_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Intel Scenes: class-averaged FID (left) and overall FID (right) versus [PITH_FULL_IMAGE:figures/full_fig_p025_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Intel Scenes: CLIP-based nearest-neighbor analysis for generated images. Gen [PITH_FULL_IMAGE:figures/full_fig_p026_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: BEED results with Nℓ = 800. Curves and error bars show mean ± standard deviation over five random seeds. Grey dashed lines indicate the reference obtained by using all training samples as labeled data. Arrows in the axis labels indicate the favorable direction. better agreement in the marginal feature distributions and a reduced tendency to generate implausible feature values, respectively. More specifical… view at source ↗

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Works this paper leans on

127 extracted references · 1 canonical work pages

  1. [1]

    Brian D. O. Anderson , title =. Stochastic Processes and their Applications , year =. doi:10.1016/0304-4149(82)90051-5 , url =

    doi:10.1016/0304-4149(82)90051-5

  2. [2]

    S. M. Nikolskii , title =. 1975 , address =

    1975

  3. [3]

    1983 , address =

    Hans Triebel , title =. 1983 , address =

    1983

  4. [4]

    Journal of Machine Learning Research , volume=

    The correlation-assisted missing data estimator , author=. Journal of Machine Learning Research , volume=

  5. [5]

    arXiv preprint arXiv:2405.05512 , year=

    Characteristic learning for provable one step generation , author=. arXiv preprint arXiv:2405.05512 , year=

    arXiv

  6. [6]

    Biometrika , volume =

    Wen, Mengtao and Jia, Yinxu and Ren, Haojie and Wang, Zhaojun and Zou, Changliang , title =. Biometrika , volume =. 2024 , month =. doi:10.1093/biomet/asae056 , url =

    work page doi:10.1093/biomet/asae056 2024

  7. [7]

    Advances in Neural Information Processing Systems , pages=

    Statistical analysis of semi-supervised regression , author=. Advances in Neural Information Processing Systems , pages=

  8. [8]

    International Conference on Machine Learning , publisher=

    Understanding and Mitigating Memorization in Generative Models via Sharpness of Probability Landscapes , author=. International Conference on Machine Learning , publisher=. 2025 , url=

    2025

  9. [9]

    Extracting training data from diffusion models , year =

    Carlini, Nicholas and Hayes, Jamie and Nasr, Milad and Jagielski, Matthew and Sehwag, Vikash and Tram\`. Extracting training data from diffusion models , year =. Proceedings of the 32nd USENIX Conference on Security Symposium , articleno =

  10. [10]

    arXiv preprint arXiv:2211.03264 , year=

    Few-shot image generation with diffusion models , author=. arXiv preprint arXiv:2211.03264 , year=

    Pith/arXiv arXiv

  11. [11]

    arXiv preprint arXiv:2205.15463 , year=

    Few-shot diffusion models , author=. arXiv preprint arXiv:2205.15463 , year=

    Pith/arXiv arXiv

  12. [12]

    Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV) , pages=

    Adding conditional control to text-to-image diffusion models , author=. Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV) , pages=

  13. [13]

    2022 , publisher=

    Nichol, Alexander Quinn and Dhariwal, Prafulla and Ramesh, Aditya and Shyam, Pranav and Mishkin, Pamela and McGrew, Bob and Sutskever, Ilya and Chen, Mark , booktitle=. 2022 , publisher=

    2022

  14. [14]

    Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops , publisher=

    Universal Guidance for Diffusion Models , author=. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops , publisher=

  15. [15]

    Wu, Dongze and Inouye, David I and Xie, Yao , journal=

  16. [16]

    Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition , pages=

    Diffusion autoencoders: Toward a meaningful and decodable representation , author=. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition , pages=

  17. [17]

    Learning Structured Output Representation using Deep Conditional Generative Models , pages =

    Sohn, Kihyuk and Lee, Honglak and Yan, Xinchen , booktitle =. Learning Structured Output Representation using Deep Conditional Generative Models , pages =

  18. [18]

    Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics , pages =

    Variational Autoencoders and Nonlinear ICA: A Unifying Framework , author =. Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics , pages =. 2020 , publisher =

    2020

  19. [19]

    2025 , journal=

    Enhancing Causal Effect Estimation with Diffusion-Generated Data , author=. 2025 , journal=

    2025

  20. [20]

    arXiv preprint arXiv:2207.12598 , year=

    Classifier-free diffusion guidance , author=. arXiv preprint arXiv:2207.12598 , year=

    Pith/arXiv arXiv

  21. [21]

    arXiv preprint arXiv:2002.03938 , year=

    Distribution approximation and statistical estimation guarantees of generative adversarial networks , author=. arXiv preprint arXiv:2002.03938 , year=

    Pith/arXiv arXiv 2002

  22. [22]

    International Conference on Machine Learning , pages=

    Score approximation, estimation and distribution recovery of diffusion models on low-dimensional data , author=. International Conference on Machine Learning , pages=. 2023 , organization=

    2023

  23. [23]

    International Conference on Learning Representations , publisher =

    Suzuki, Taiji , title =. International Conference on Learning Representations , publisher =

  24. [24]

    Estimation of Non-Normalized Statistical Models by Score Matching , volume =

    Hyv. Estimation of Non-Normalized Statistical Models by Score Matching , volume =. Journal of Machine Learning Research , number =

  25. [25]

    Semi-Supervised Deep Sobolev Regression: Estimation and Variable Selection by ReQU Neural Network , year=

    Ding, Zhao and Duan, Chenguang and Jiao, Yuling and Yang, Jerry Zhijian , journal=. Semi-Supervised Deep Sobolev Regression: Estimation and Variable Selection by ReQU Neural Network , year=

  26. [26]

    High-Resolution Image Synthesis With Latent Diffusion Models , publisher=

    Rombach, Robin and Blattmann, Andreas and Lorenz, Dominik and Esser, Patrick and Ommer, Bj. High-Resolution Image Synthesis With Latent Diffusion Models , publisher=. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition , pages =

  27. [27]

    Diffusion Models Beat

    Dhariwal, Prafulla and Nichol, Alexander Quinn , booktitle =. Diffusion Models Beat

  28. [28]

    Smooth regression analysis , year =

    Watson, Geoffrey S , journal =. Smooth regression analysis , year =

  29. [29]

    On estimating regression , volume =

    Nadaraya, Elizbar A , journal =. On estimating regression , volume =

  30. [30]

    Multivariate kernel smoothing and its applications , publisher =

    Chac. Multivariate kernel smoothing and its applications , publisher =

  31. [31]

    All of nonparametric statistics , year =

    Wasserman, Larry , publisher =. All of nonparametric statistics , year =

  32. [32]

    Finite mixture models , volume =

    McLachlan, Geoffrey J and Lee, Sharon X and Rathnayake, Suren I , journal =. Finite mixture models , volume =

  33. [33]

    Minimax rate of distribution estimation on unknown submanifolds under adversarial losses , volume =

    Tang, Rong and Yang, Yun , journal =. Minimax rate of distribution estimation on unknown submanifolds under adversarial losses , volume =

  34. [34]

    Manifold regularization: A geometric framework for learning from labeled and unlabeled examples

    Belkin, Mikhail and Niyogi, Partha and Sindhwani, Vikas , journal =. Manifold regularization: A geometric framework for learning from labeled and unlabeled examples. , volume =

  35. [35]

    Manifold regularization and semi-supervised learning: Some theoretical analyses , volume =

    Niyogi, Partha , journal =. Manifold regularization and semi-supervised learning: Some theoretical analyses , volume =

  36. [36]

    Semi-supervised learning on Riemannian manifolds , volume =

    Belkin, Mikhail and Niyogi, Partha , journal =. Semi-supervised learning on Riemannian manifolds , volume =

  37. [37]

    arXiv preprint arXiv:2506.07504 , year =

    Tang, Rong and Yang, Yun , title =. arXiv preprint arXiv:2506.07504 , year =

    Pith/arXiv arXiv

  38. [38]

    International Conference on Learning Representations , publisher =

    Pope, Phil and Zhu, Chen and Abdelkader, Ahmed and Goldblum, Micah and Goldstein, Tom , title =. International Conference on Learning Representations , publisher =

  39. [39]

    Deep learning , year =

    Goodfellow, Ian and Courville, Aaron and Bengio, Yoshua , publisher =. Deep learning , year =

  40. [40]

    Testing the manifold hypothesis , volume =

    Fefferman, Charles and Mitter, Sanjoy and Narayanan, Hariharan , journal =. Testing the manifold hypothesis , volume =

  41. [41]

    arXiv preprint arXiv:2402.01460 , year =

    Chang, Jinyuan and Ding, Zhao and Jiao, Yuling and Li, Ruoxuan and Yang, Jerry Zhijian , title =. arXiv preprint arXiv:2402.01460 , year =

    arXiv

  42. [42]

    International Conference on Learning Representations , publisher =

    Miyato, Takeru and Kataoka, Toshiki and Koyama, Masanori and Yoshida, Yuichi , title =. International Conference on Learning Representations , publisher =

  43. [43]

    K., Nizar Banu , title =

    Najmusseher and P. K., Nizar Banu , title =

  44. [44]

    Learning Transferable Visual Models From Natural Language Supervision , pages =

    Radford, Alec and Kim, Jong Wook and Hallacy, Chris and Ramesh, Aditya and Goh, Gabriel and Agarwal, Sandhini and Sastry, Girish and Askell, Amanda and Mishkin, Pamela and Clark, Jack and Krueger, Gretchen and Sutskever, Ilya , booktitle =. Learning Transferable Visual Models From Natural Language Supervision , pages =

  45. [45]

    Wasserstein barycenter and its application to texture mixing , year =

    Rabin, Julien and Peyr. Wasserstein barycenter and its application to texture mixing , year =. Scale Space and Variational Methods in Computer Vision , pages =

  46. [46]

    Grathwohl, Will and Chen, Ricky T. Q. and Bettencourt, Jesse and Duvenaud, David , title =. International Conference on Learning Representations , publisher =

  47. [47]

    On the role of surrogates in the efficient estimation of treatment effects with limited outcome data , volume =

    Kallus, Nathan and Mao, Xiaojie , journal =. On the role of surrogates in the efficient estimation of treatment effects with limited outcome data , volume =

  48. [48]

    Statistical analysis with missing data , volume =

    Little, Roderick JA and Rubin, Donald B , publisher =. Statistical analysis with missing data , volume =

  49. [49]

    Score-based generative modeling through stochastic differential equations , year =

    Song, Yang and Sohl-Dickstein, Jascha and Kingma, Diederik P and Kumar, Abhishek and Ermon, Stefano and Poole, Ben , journal =. Score-based generative modeling through stochastic differential equations , year =

  50. [50]

    On unifying deep generative models , year =

    Hu, Zhiting and Yang, Zichao and Salakhutdinov, Ruslan and Xing, Eric P , journal =. On unifying deep generative models , year =

  51. [51]

    Exchangeable random measures , volume =

    Austin, Tim , journal =. Exchangeable random measures , volume =

  52. [52]

    A deep generative approach to conditional sampling , volume =

    Zhou, Xingyu and Jiao, Yuling and Liu, Jin and Huang, Jian , journal =. A deep generative approach to conditional sampling , volume =

  53. [53]

    Learning Manifold Dimensions with Conditional Variational Autoencoders , year =

    Zheng, Yijia and He, Tong and Qiu, Yixuan and Wipf, David P , booktitle =. Learning Manifold Dimensions with Conditional Variational Autoencoders , year =

  54. [54]

    Conditional variational autoencoder with adversarial learning for end-to-end text-to-speech , year =

    Kim, Jaehyeon and Kong, Jungil and Son, Juhee , booktitle =. Conditional variational autoencoder with adversarial learning for end-to-end text-to-speech , year =

  55. [55]

    Generative adversarial network: An overview of theory and applications , volume =

    Aggarwal, Alankrita and Mittal, Mamta and Battineni, Gopi , journal =. Generative adversarial network: An overview of theory and applications , volume =

  56. [56]

    Maximum likelihood training of score-based diffusion models , volume =

    Song, Yang and Durkan, Conor and Murray, Iain and Ermon, Stefano , journal =. Maximum likelihood training of score-based diffusion models , volume =

  57. [57]

    Transactions on Machine Learning Research , issn =

    De Bortoli, Valentin , title =. Transactions on Machine Learning Research , issn =

  58. [58]

    Improved denoising diffusion probabilistic models , year =

    Nichol, Alexander Quinn and Dhariwal, Prafulla , booktitle =. Improved denoising diffusion probabilistic models , year =

  59. [59]

    Unveil conditional diffusion models with classifier-free guidance: A sharp statistical theory , year =

    Fu, Hengyu and Yang, Zhuoran and Wang, Mengdi and Chen, Minshuo , journal =. Unveil conditional diffusion models with classifier-free guidance: A sharp statistical theory , year =

  60. [60]

    Gaussian Interpolation Flows , volume =

    Gao, Yuan and Huang, Jian and Jiao, Yuling , journal =. Gaussian Interpolation Flows , volume =

  61. [61]

    Conditional stochastic interpolation for generative learning , year =

    Huang, Ding and Huang, Jian and Li, Ting and Shen, Guohao , journal =. Conditional stochastic interpolation for generative learning , year =

  62. [62]

    Deep conditional generative learning: Model and error analysis , year =

    Chang, Jinyuan and Ding, Zhao and Jiao, Yuling and Li, Ruoxuan and Zhijian Yang, Jerry , journal =. Deep conditional generative learning: Model and error analysis , year =

  63. [63]

    Rethinking Open-World Semi-Supervised Learning: Distribution Mismatch and Inductive Inference , year =

    Park, Seongheon and Kwon, Hyuk and Sohn, Kwanghoon and Lee, Kibok , journal =. Rethinking Open-World Semi-Supervised Learning: Distribution Mismatch and Inductive Inference , year =

  64. [64]

    Generalized category discovery , year =

    Vaze, Sagar and Han, Kai and Vedaldi, Andrea and Zisserman, Andrew , booktitle =. Generalized category discovery , year =

  65. [65]

    Convergence of Continuous Normalizing Flows for Learning Probability Distributions , year =

    Gao, Yuan and Huang, Jian and Jiao, Yuling and Zheng, Shurong , journal =. Convergence of Continuous Normalizing Flows for Learning Probability Distributions , year =

  66. [66]

    A connection between score matching and denoising autoencoders , volume =

    Vincent, Pascal , journal =. A connection between score matching and denoising autoencoders , volume =

  67. [67]

    A general class of coefficients of divergence of one distribution from another , volume =

    Ali, Syed Mumtaz and Silvey, Samuel D , journal =. A general class of coefficients of divergence of one distribution from another , volume =

  68. [68]

    Local polynomial regression on unknown manifolds , year =

    Bickel, Peter J and Li, Bo , journal =. Local polynomial regression on unknown manifolds , year =

  69. [69]

    Angelopoulos, Anastasios N and Duchi, John C and Zrnic, Tijana , journal =

  70. [70]

    Cross-prediction-powered inference , volume =

    Zrnic, Tijana and Cand. Cross-prediction-powered inference , volume =. Proceedings of the National Academy of Sciences , number =

  71. [71]

    Virtual Adversarial Training: A Regularization Method for Supervised and Semi-Supervised Learning , volume =

    Miyato, Takeru and Maeda, Shin-Ichi and Koyama, Masanori and Ishii, Shin , journal =. Virtual Adversarial Training: A Regularization Method for Supervised and Semi-Supervised Learning , volume =

  72. [72]

    Deep nonparametric regression on approximate manifolds: Nonasymptotic error bounds with polynomial prefactors , volume =

    Jiao, Yuling and Shen, Guohao and Lin, Yuanyuan and Huang, Jian , journal =. Deep nonparametric regression on approximate manifolds: Nonasymptotic error bounds with polynomial prefactors , volume =

  73. [73]

    Deep Dimension Reduction for Supervised Representation Learning , volume =

    Huang, Jian and Jiao, Yuling and Liao, Xu and Liu, Jin and Yu, Zhou , journal =. Deep Dimension Reduction for Supervised Representation Learning , volume =

  74. [74]

    arXiv preprint arXiv:1511.01844 , title =

    Theis, Lucas and Oord, A. arXiv preprint arXiv:1511.01844 , title =

    Pith/arXiv arXiv

  75. [75]

    Generative modeling: A review , year =

    Nareklishvili, Maria and Polson, Nick and Sokolov, Vadim , journal =. Generative modeling: A review , year =

  76. [76]

    Generative adversarial nets , pages =

    Goodfellow, Ian J and Pouget-Abadie, Jean and Mirza, Mehdi and Xu, Bing and Warde-Farley, David and Ozair, Sherjil and Courville, Aaron and Bengio, Yoshua , booktitle =. Generative adversarial nets , pages =

  77. [77]

    Generative adversarial networks , volume =

    Goodfellow, Ian and Pouget-Abadie, Jean and Mirza, Mehdi and Xu, Bing and Warde-Farley, David and Ozair, Sherjil and Courville, Aaron and Bengio, Yoshua , journal =. Generative adversarial networks , volume =

  78. [78]

    An introduction to variational autoencoders , volume =

    Kingma, Diederik P and Welling, Max , journal =. An introduction to variational autoencoders , volume =

  79. [79]

    Tutorial on variational autoencoders , year =

    Doersch, Carl , journal =. Tutorial on variational autoencoders , year =

  80. [80]

    Transformers are

    Katharopoulos, Angelos and Vyas, Apoorv and Pappas, Nikolaos and Fleuret, Fran. Transformers are. International Conference on Machine Learning , publisher =

Showing first 80 references.