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Bootstrapping Diffusion: Diffusion Model Training Leveraging Partial and Corrupted Data

T0 review · 4 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Bootstrapping diffusion lets partial views—low-res images, short clips, crops—substitute for most full-resolution training data: train a residual denoiser on a small clean set, with clean-sample needs scaling like the signal views miss.

desk verdict Novel two-stage training idea with plausible small-scale results, but the claimed optimality is asserted rather than proved; the residual-case bound is a restatement and the small-variance premise conflicts with the paper's own motivating regime. read the letter →

arxiv 2505.11825 v1 pith:SIOTHIFQ submitted 2025-05-17 cs.CV cs.AI

Xudong Ma This is my paper · ORCID
classification cs.CVcs.AI MSC 68T0768T45
keywords diffusionmodelspartialdataviewscorruptedresidualdenoiservarianceregularizationgeneralizationboundsscorefunctionefficiency
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper attacks the data bottleneck of diffusion training: full-resolution images and long videos are scarce, while low-resolution images, short clips, and watermarked or cropped footage are abundant. It claims these partial views can be exploited by a two-stage scheme: train one diffusion denoiser per view, combine their predictions, then train a residual denoiser on a small full-resolution set to learn only the missing gap. The theoretical core is a pair of generalization bounds showing this residual approach need not be worse than training on the full-resolution set alone, and that variance regularization on the residual shrinks the complexity terms. The data-efficiency payoff is stated sharply: the amount of full-resolution data required scales with the signal correlation the views fail to capture, which the paper calls near first-order optimal efficiency. If correct, the result makes large diffusion training sets less expensive to assemble and lets corrupted or partial collections become first-class training data.

What carries the argument

The load-bearing object is the residual denoiser $f_0$ trained on $r(x_t)=\mathbb{E}[X_0\mid X_t]-\sum_i B_i f_i(A_i x_t)$, together with the variance regularization that controls its output norm. The mechanism runs through Theorem 5's decomposition $\mathbb{E}[\lVert X_0-\mathbb{E}[X_0\mid \sum_i B_i A_i X_t]\rVert^2] = \text{MMSE} + \mathbb{E}[\lVert \mathbb{E}[X_0\mid X_t]-\mathbb{E}[X_0\mid \sum_i B_i A_i X_t]\rVert^2]$: when the combined view denoiser is close to the conditional expectation, the residual target has small variance, so a low-Lipschitz, low-capacity network suffices. Covering-number and Rademacher-complexity machinery then converts that capacity reduction into a tighter generalization bound. Tweedie's formula is what lets the whole argument run on conditional-expectation denoisers rather than raw score functions.

What would settle it

Compute, on a fixed dataset with known view projections (for example, AFHQv2-Cat latents with 8-by-8 patches and low-resolution views), the residual variance $\mathbb{E}[\lVert \mathbb{E}[X_0\mid X_t]-\mathbb{E}[X_0\mid \{A_i X_t\}]\rVert^2]$ for many noise levels; if it does not shrink relative to the full MMSE term, the complexity-reduction premise is violated. Then run the two-stage training with and without variance regularization for a range of full-resolution set sizes $N$ and compare generalization loss: bootstrapping should beat single-stage training at matching $N$ exactly in the regime where the residual variance is small, and the gap should vanish where it is not.

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Extended reading notes

Core claim

The paper's central discovery is that the score function of a full-resolution diffusion model can be decomposed into a combined partial-view estimate plus a residual, and the residual is the right thing to learn from the scarce clean data. Formally, with clean sample $x_0$, noisy observation $x_t$, and view projections $A_i$, one trains view denoisers $f_i(A_i x_t; \theta_i) \approx \mathbb{E}[A_i X_0 \mid A_i X_t]$, forms a combined estimate $\sum_i B_i f_i(A_i x_t)$, and then trains $f_0(x_t;\theta_0)$ on the residual target $r(x_t)=\mathbb{E}[X_0 \mid X_t]-\sum_i B_i f_i(A_i x_t)$. The generalization bound for this residual denoiser (Theorem 4) is proved in the same form as the bound for training on the full-resolution set alone (Theorem 3), but variance regularization—penalizing $\lVert f_0\rVert^2$ or scaling it with a time-dependent range adapter—reduces the Lipschitz constant, hence the covering number and Rademacher complexity that dominate the bound. The paper also proves an orthogonal decomposition (Theorem 5) showing that the combined denoiser's mean squared error equals the MMSE plus the variance of the residual target, so the residual variance is exactly the information the views fail to capture; the residual's training difficulty scales with that variance. Experiments on AFHQv2-Cat with 8-by-8 patches and low-resolution views as partial data, and only 64 full-resolution latents for the residual stage, generate coherent full-resolution images where each view alone fails in a complementary way.

Load-bearing premise

The proof relies on the residual training target having small variance because the combined view denoisers already approximate the true conditional expectation, and if the views genuinely lack the global information the full model needs, this is exactly the premise that may fail.

Editorial extensions

If this is right

  • A small full-resolution set plus large view sets can yield lower generalization error than the same small set alone; in the paper's experiments 64 full-resolution latents plus patch and low-resolution views produce coherent output.
  • Data requirements for the residual stage scale with uncaptured signal correlation; the more complementary the views (for example, local patches plus a global low-resolution view), the less clean data are needed.
  • Variance regularization is not a minor detail: without it, the residual denoiser's complexity would scale with the full-resolution problem and the data-efficiency gain would disappear.
  • Because view projections include downsampling, cropping, and clipping, the same recipe applies to low-resolution images, short videos, and subtitle- or watermark-affected footage, for any linear view of the data.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial inference — if the combined view models are weak, the residual target's variance is large by Theorem 5 itself, so the theoretical mechanism predicts little or no gain; a practical check is to measure that residual variance on validation data before training the residual stage, treating the small-residual premise as an empirical condition rather than an automatic property of views.
  • Editorial inference — the paper keeps view denoisers fixed during residual training; an alternating procedure that fine-tunes the view denoisers while fitting the residual could reduce the residual variance further and improve the data-efficiency constant, a natural extension not analyzed here.
  • Editorial inference — the bounds suggest a scaling rule for practitioners: add more full-resolution data only until the residual variance stops decreasing, since beyond that point the residual is no longer the bottleneck, which directly operationalizes near first-order data efficiency.
  • Editorial inference — the view models plus residual can be distilled into a single network (the paper lists this as future work), which would turn the method's cost from several models into one at inference while preserving the data-collection savings.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. The paper proposes 'bootstrapping diffusion,' a two-stage training scheme in which separate diffusion denoisers are first trained on partial or corrupted views (e.g., low-resolution images, image patches, short clips), and then a residual denoiser is trained on a small full-resolution dataset to correct the combined view-based prediction, with variance regularization on the residual output. The main claimed contributions are generalization-error bounds: Theorem 3 for standard full-resolution-only training and Theorem 4 for the bootstrapped residual training, which the paper says show lower generalization errors and 'near first-order optimal data efficiency.' Experiments on AFHQv2-Cat are presented qualitatively.

Significance. If the theoretical claims were established, this would be a practically valuable result: it would provide a principled guarantee that abundant partial or corrupted data can be used to reduce the amount of full-resolution data required for diffusion model training. The paper correctly identifies a meaningful problem and uses standard martingale and covering-number machinery. Some components, such as the orthogonal decomposition in Theorem 5, are correct and potentially useful. However, the central claims are not established by the presented proofs: the two main bounds are identical in form and no comparison is derived, and the load-bearing small-variance assumption on the residual target is asserted rather than proven and is in tension with the paper's own experimental observations.

major comments (4)
  1. [Sections 5.2 and 5.4; Appendix J] Theorems 3 and 4 have exactly the same algebraic form. The residual-case bound uses redefined quantities V(S0), R_L(F,S0), and Delta_b, but no inequality is derived between these and the baseline quantities. In fact, the definition of V(S) in Appendix J includes the view denoisers' outputs added inside the squared norm, so it is not even shown that the residual-case V(S0) is no larger than the baseline V(S0). Without a comparison of the redefined terms, the central claim that bootstrapping diffusion achieves lower generalization error than full-resolution-only training is not proven.
  2. [Section 5.3; Appendix A; Theorem 5] The small-variance property of the residual target r(Xt) is asserted in Section 5.3 ('should have small variances') and Appendix A ('if the error variance of combined denoiser approaches the MMSE'), but it is not proven. Theorem 5 shows that the variance of r(Xt) equals the excess conditional MSE of the combined denoiser over the MMSE. In the paper's own motivating and experimental regime, 8x8 patches and low-resolution views of 32x32 latents, the combined denoiser lacks global structure: Appendix B states that linear combinations 'fail to produce accurate global structures.' Hence the residual variance is expected to be large precisely where the method needs it to be small. No theorem bounds the residual variance in terms of the uncaptured signal correlation.
  3. [Section 5.5; Equations (6) and (7)] The paper claims that variance regularization reduces the Lipschitz constant of the residual denoiser and thereby reduces the covering number and Rademacher complexity in Theorem 4. However, no theorem or lemma connects the constraint in Equation (6) or the penalty in Equation (7) to a quantitative bound on any of these complexity measures. The claim that variance regularization lowers generalization error is therefore not established by the presented analysis.
  4. [Abstract; Section 5.5] The claim of 'near first-order optimal data efficiency' is not defined and is not derived from any of the theorems. The paper does not state a formal notion of first-order optimality, does not extract a sample-complexity rate from the bounds, and does not provide a lower bound. The statement that 'the data required for training the residual denoiser is proportional to this uncaptured information' is qualitative and does not follow from the displayed bounds.
minor comments (4)
  1. [Appendix B; Section 6] The experimental evaluation reports no quantitative metrics such as FID or a comparison against a baseline diffusion model trained only on the same number of full-resolution images. The claim that bootstrapping diffusion 'effectively compensates for missing data' is based solely on visual inspection of generated images.
  2. [Section 5.2] The notation V(S) is used both for the empirical quantity in Equation (12) and for its expectation E[V(S0)] in the theorems; the distinction between the random empirical quantity and its expectation should be made explicit.
  3. [Section 5.4; Appendix J] Theorem 4 is stated in the main text without redefining F, R_L(F,S0), R_R(F,S0), and Delta_b for the residual case; the statement is incomplete without the definitions in Appendix J, which should be moved to or summarized at the point of the theorem.
  4. [Throughout] There are several typos, including 'Radamacher' for 'Rademacher' in Sections 5.2 and 5.4, 'Liptschiz' in Assumption 1, 'propositional' for 'proportional' in Section 5.5, and a reference to 'Algorithm 4' where the algorithm is labeled Algorithm 1.

Circularity Check

1 steps flagged · score 6.0 of 10

The data-efficiency claim reduces by construction to the assertion that the residual target has small variance, which the paper derives only by restating the assumption that the combined denoiser already approximates the true score.

  1. self definitional [Section 5.3, paragraph after Eq. (23); load-bearing for Section 5.5 and Theorem 4.]
    "Given that st(θ1,...,θ I) is trained from partial data views to approximate the true score function sµA t , KL(µA∥µ(θ1,...,θ I)) should take small values and thus the training goal r(Xt) should have small variances."

    By Eq. (8), KL(µA∥µ(θ1,...,θI)) equals E[∫ (g(t)^2/2) ||s_t^{µA} − s_t(θ1,...,θI)||^2 dt]. By Eq. (23), that score difference is (E[X0|Xt] − Σ_i B_i f_i(A_i Xt))/σ_t^2 = r(Xt)/σ_t^2, where r(Xt) is exactly the residual target that f0 is trained to predict. Therefore 'KL is small' and 'r has small variance' are the same statement, not a consequence of one another. The paper supplies no independent bound on the combined denoiser's approximation error; it merely asserts that training on partial views makes it approximate the true score. The variance-regularization and near-first-order data-efficiency argument in Section 5.5 then uses this unproved equivalence as its load-bearing premise.

full rationale

The probability-theoretic generalization bounds (Theorems 1–4 and their appendices) are self-contained and not circular: they are standard martingale, Azuma, covering-number, and Rademacher arguments, and they do not fit parameters to data. There is no load-bearing self-citation chain; the external citations (Graf et al. for covering numbers, Franzese et al. for the KL identity, Karras et al. for architecture) are appropriate external support. The circularity is in the interpretation that converts these bounds into the paper's headline claim. Section 5.3 asserts that the residual training target r(Xt) has small variance because the combined denoiser 'should' approximate the true score; Appendix A repeats the same reasoning via the tower property. But by the paper's own Eq. (8) and Eq. (23), the KL divergence of the combined model from the true distribution is, up to the σ_t^2 scaling, exactly the squared norm of r(Xt)—the quantity the residual denoiser is trained to learn. So the premise and the conclusion are the same expression, and the 'difficulty scales with uncaptured correlation' statement in Section 5.5 is a restatement rather than a derived bound. The theorem comparison does not repair this: Theorem 4 has the same bound formula as Theorem 3, with V(S0), Rademacher, and covering terms redefined in Appendix J, so the claimed lower generalization error is not exhibited by comparing the two bounds; it is carried entirely by the assumed smallness of the redefined residual variance. The experiments do not contradict this reading but confirm the gap: Appendix B states that images from a straightforward linear combination 'fail to produce accurate global structures,' i.e., the residual variance is large in the motivating regime where the views lack global information. Overall, the derivation chain from the generalization bounds to the central data-efficiency conclusion contains one substantive circular step, so the score is 6 rather than 0.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The theory rests on imported concentration and covering-number assumptions; the distinctive load-bearing assumption is that the residual denoiser's task is low-variance, asserted in Section 5.3, plus the distributional match between partial-view and full-resolution data. In the experiment, the combination weights and range adapter are fitted on the same 64 full-resolution images used for residual training, which weakens the data-efficiency demonstration.

free parameters (3)
  • Combination matrices B_i = Estimated on the 64-image full-resolution set (Appendix B)
    The view denoiser outputs are linearly combined with weights B_i; in experiments these are estimated from 64 generated samples from the full-resolution latent model, so part of the small dataset is used for calibration.
  • Range adapter s(t) = Piecewise linear over 100 intervals, estimated on 64 images (Appendix B)
    Scales the residual denoiser output per diffusion step; fitted to the same 64-image set used for residual training.
  • Variance regularization strength (lambda or bound M) = Not specified
    Equation 7 introduces lambda but no value or selection procedure is given; the theory never ties lambda to the generalization bound.
assumptions (6)
  • standard math Assumption 1: covering number of the neural network class is bounded by log N(F,epsilon,d) <= L_bar W log(1 + C_bar N / epsilon)
    Imported from Graf et al. (2022); used in Theorems 2 through 4 to bound model complexity.
  • domain assumption Assumption 2: clean data and denoisers are element-wise bounded in [-U, U]
    Used in the Azuma-Hoeffding martingale bounds and in bounding Lipschitz constants.
  • domain assumption All datasets S0..SI share the same underlying distribution p0 and same dimension m
    Section 4 first paragraph; required for the view denoisers to estimate E[A_i X0 | A_i X_t] of the full-resolution target. Fails for genuinely out-of-domain partial data such as low-resolution web images of a different content domain.
  • domain assumption Views are linear projections A_i of full data
    Section 4; downsampling and cropping fit this, but subtitles, watermarks, and logos are additive corruptions, not projections.
  • standard math KL divergence between data distributions is dominated by the denoiser or score error via Equation 8 (Franzese et al. 2024)
    Imported result used to translate denoiser errors into KL; assumes terminal distributions match for large T.
  • ad hoc to paper The residual denoiser's target has small variance
    Section 5.3 asserts this from the supposed smallness of KL between the true distribution and the combined view models; it is not proved and conflicts with the paper's own motivation that views lack global information.

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Pith. "Pith review of Bootstrapping Diffusion: Diffusion Model Training Leveraging Partial and Corrupted Data." pith.science (2026). https://pith.science/paper/SIOTHIFQ

@misc{pith2026250511825,
  author       = {Pith},
  title        = {Pith review of: Bootstrapping Diffusion: Diffusion Model Training Leveraging Partial and Corrupted Data},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SIOTHIFQ}},
  note         = {Machine review of arXiv:2505.11825}
}
read the original abstract

Training diffusion models requires large datasets. However, acquiring large volumes of high-quality data can be challenging, for example, collecting large numbers of high-resolution images and long videos. On the other hand, there are many complementary data that are usually considered corrupted or partial, such as low-resolution images and short videos. Other examples of corrupted data include videos that contain subtitles, watermarks, and logos. In this study, we investigate the theoretical problem of whether the above partial data can be utilized to train conventional diffusion models. Motivated by our theoretical analysis in this study, we propose a straightforward approach of training diffusion models utilizing partial data views, where we consider each form of complementary data as a view of conventional data. Our proposed approach first trains one separate diffusion model for each individual view, and then trains a model for predicting the residual score function. We prove generalization error bounds, which show that the proposed diffusion model training approach can achieve lower generalization errors if proper regularizations are adopted in the residual score function training. In particular, we prove that the difficulty in training the residual score function scales proportionally with the signal correlations not captured by partial data views. Consequently, the proposed approach achieves near first-order optimal data efficiency.

Figures

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Figure 1
Figure 1. Randomly generated images. The first row of images are generated using the low-resolution [PITH_FULL_IMAGE:figures/full_fig_p014_1.png] view at source ↗

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Works this paper leans on

38 extracted references · 15 canonical work pages

  1. [1]

    Anderson, B. D. O. Reverse-time diffusion equation models. Stochastic Processes and their Applications, 12 0 (3): 0 313--326, May 1982. doi:10.1016/0304-4149(82)90058-0

    work page doi:10.1016/0304-4149(82)90058-0 1982

  2. [2]

    Weighted sums of certain dependent random variables

    Azuma, K. Weighted sums of certain dependent random variables. Tohoku Mathematical Journal, 19 0 (3): 0 357--367, 1967. doi:10.2748/tmj/1178243286

    arXiv 1967

  3. [3]

    An expectation-maximization algorithm for training clean diffusion models from corrupted observations

    Bai, W., Wang, Y., Chen, W., and Sun, H. An expectation-maximization algorithm for training clean diffusion models from corrupted observations. In Advances in Neural Information Processing Systems, 2024. URL https://arxiv.org/abs/2407.01014

    arXiv 2024

  4. [4]

    Webvid-10m: A large-scale video-text dataset

    Bain, M. Webvid-10m: A large-scale video-text dataset. https://github.com/m-bain/webvid, 2021. Accessed: 2025-04-02

    work page 2021

  5. [5]

    Bartlett, P. L. and Mendelson, S. Rademacher and gaussian complexities: Risk bounds and structural results. Journal of Machine Learning Research, 3: 0 463--482, 2002

    work page 2002

  6. [6]

    Probability and Measure

    Billingsley, P. Probability and Measure. Wiley Series in Probability and Statistics. Wiley-Interscience, 3rd edition, 1995. ISBN 9780471007104

    work page 1995

  7. [7]

    Coyo-700m: Image-text dataset for better text-to-image generation

    Brain, K. Coyo-700m: Image-text dataset for better text-to-image generation. Dataset Release, 2023. URL https://github.com/kakaobrain/coyo-dataset

    work page 2023

  8. [8]

    C., Yu, J., et al

    Chen, Z., Liu, L., Zhu, X., He, Z., Dai, B., Loy, C. C., Yu, J., et al. Fantasia3d: Text-to-3d content creation with holistic understanding. arXiv preprint arXiv:2303.13873, 2023. URL https://arxiv.org/abs/2303.13873

    arXiv 2023

Show all 38 references
  1. [9]

    G., and Gui, L.-Y

    Cheng, Y.-C., Lee, H.-Y., Tulyakov, S., Schwing, A. G., and Gui, L.-Y. SDFusion : Multimodal 3d shape completion, reconstruction, and generation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp.\ 4456--4465, 2023. URL https://arx...

    2023 arXiv

  2. [10]

    Stargan v2: Diverse image synthesis for multiple domains

    Choi, Y., Uh, Y., Yoo, J., and Ha, J.-W. Stargan v2: Diverse image synthesis for multiple domains. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp.\ 8188--8197, 2020

    2020

  3. [11]

    Modelscope text-to-video synthesis

    DAMO Academy, Alibaba Group . Modelscope text-to-video synthesis. https://huggingface.co/spaces/damo-vilab/modelscope-text-to-video-synthesis, 2023. Open-source demo

    2023

  4. [12]

    G., and Klivans, A

    Daras, G., Shah, K., Dagan, Y., Gollakota, A., Dimakis, A. G., and Klivans, A. Ambient diffusion: Learning clean distributions from corrupted data. In Advances in Neural Information Processing Systems (NeurIPS), 2023. URL https://arxiv.org/abs/2305.19256

    2023 arXiv

  5. [13]

    G., and Daskalakis, C

    Daras, G., Dimakis, A. G., and Daskalakis, C. Consistent diffusion meets tweedie: Training exact ambient diffusion models with noisy data. In Proceedings of the 41st International Conference on Machine Learning (ICML), 2024. URL https://arxiv.org/abs/2404.10177

    2024 arXiv

  6. [14]

    and Nichol, A

    Dhariwal, P. and Nichol, A. Q. Diffusion models beat gans on image synthesis. In Advances in Neural Information Processing Systems (NeurIPS), 2021. URL https://arxiv.org/abs/2105.05233. arXiv:2105.05233

    2021 arXiv

  7. [15]

    Doob, J. L. Stochastic Processes. Wiley, 1953. ISBN 9780471218135

    1953

  8. [16]

    Tweedie’s formula and selection bias

    Efron, B. Tweedie’s formula and selection bias. Journal of the American Statistical Association, 106 0 (496): 0 1602--1614, 2012. doi:10.1198/jasa.2011.tm11181

    2012 doi

  9. [17]

    MINDE : Mutual information neural diffusion estimation

    Franzese, G., Bounoua, M., and Michiardi, P. MINDE : Mutual information neural diffusion estimation. In The Twelfth International Conference on Learning Representations, 2024. URL https://openreview.net/forum?id=0kWd8SJq8d

    2024

  10. [18]

    On measuring excess capacity in neural networks

    Graf, F., Zeng, S., Rieck, B., Niethammer, M., and Kwitt, R. On measuring excess capacity in neural networks. In Advances in Neural Information Processing Systems (NeurIPS), 2022. URL https://openreview.net/forum?id=l2CVt1ySC2Q

    2022

  11. [19]

    Animatediff: Animate your personalized text-to-image diffusion model without tuning

    Gu, Y., Lin, J., He, T., Zhu, Z., Qiao, Y., and Dai, Q. Animatediff: Animate your personalized text-to-image diffusion model without tuning. arXiv preprint arXiv:2307.04725, 2023 a . URL https://arxiv.org/abs/2307.04725

    2023 arXiv

  12. [20]

    Gu, Z., Xu, S., Wang, X., Zhao, L., Zheng, L., Zhao, H., Ren, Z., and Zhao, W. X. Pixart- alpha : High-resolution text-to-image diffusion with pixel-level semantics. arXiv preprint arXiv:2310.00426, 2023 b . URL https://arxiv.org/abs/2310.00426

    2023 arXiv

  13. [21]

    Denoising diffusion probabilistic models

    Ho, J., Jain, A., and Abbeel, P. Denoising diffusion probabilistic models. In Advances in Neural Information Processing Systems (NeurIPS), volume 33, pp.\ 6840--6851, 2020. URL https://arxiv.org/abs/2006.11239

    2020 arXiv

  14. [22]

    Ho, J., Salimans, T., Norouzi, M., Chan, W., and Fleet, D. J. Video diffusion models. arXiv preprint arXiv:2204.03458, 2022. URL https://arxiv.org/abs/2204.03458

    2022 arXiv

  15. [23]

    Elucidating the design space of diffusion-based generative models

    Karras, T., Aittala, M., Aila, T., and Laine, S. Elucidating the design space of diffusion-based generative models. arXiv preprint arXiv:2206.00364, 2022

    2022 arXiv

  16. [24]

    Gsure-based diffusion model training with corrupted data

    Kawar, B., Elata, N., Michaeli, T., and Elad, M. Gsure-based diffusion model training with corrupted data. arXiv preprint arXiv:2305.13128, 2023

    2023 arXiv

  17. [25]

    Scaling laws for diffusion transformers

    Liang, Z., He, H., Yang, C., and Dai, B. Scaling laws for diffusion transformers. arXiv preprint arXiv:2410.08184, 2024. URL https://arxiv.org/abs/2410.08184

    2024

  18. [26]

    Magic3d: High-resolution text-to-3d content creation

    Lin, C.-H., Gao, M., Rajeswaran, A., Tan, M.-Y., Ho, J., Salimans, T., Chan, W., and Norouzi, M. Magic3d: High-resolution text-to-3d content creation. arXiv preprint arXiv:2211.10440, 2022. URL https://arxiv.org/abs/2211.10440

    2022 arXiv

  19. [27]

    and Upfal, E

    Mitzenmacher, M. and Upfal, E. Probability and Computing: Randomization and Probabilistic Techniques in Algorithms and Data Analysis. Cambridge University Press, Cambridge, UK, 2nd edition, 2017. ISBN 9781107154889

    2017

  20. [28]

    Sora: World-modeling text-to-video generation

    OpenAI. Sora: World-modeling text-to-video generation. https://openai.com/sora, 2025. Preview demo, not peer-reviewed

    2025

  21. [29]

    T., Mildenhall, B., Duan, Y., Nichol, A., Dhariwal, P., Abbeel, P., Dinh, L., and Chan, E

    Poole, B., Jain, A., Barron, J. T., Mildenhall, B., Duan, Y., Nichol, A., Dhariwal, P., Abbeel, P., Dinh, L., and Chan, E. Dreamfusion: Text-to-3d using 2d diffusion. arXiv preprint arXiv:2209.14988, 2022. URL https://arxiv.org/abs/2209.14988

    2022 arXiv

  22. [30]

    High-resolution image synthesis with latent diffusion models

    Rombach, R., Blattmann, A., Lorenz, D., Esser, P., and Ommer, B. High-resolution image synthesis with latent diffusion models. arXiv preprint arXiv:2112.10752, 2022. URL https://arxiv.org/abs/2112.10752

    2022 arXiv

  23. [31]

    Laion-5b: An open large-scale dataset for training next generation image-text models

    Schuhmann, C., Beaumont, R., Vencu, R., Gordon, C., Wightman, R., Cherti, M., Coombes, T., Luc, P., Mill, J., Kiyono, S., et al. Laion-5b: An open large-scale dataset for training next generation image-text models. arXiv preprint arXiv:2210.08402, 2022. URL https://arxiv.org/a...

    arXiv

  24. [32]

    A., Maheswaranathan, N., and Ganguli, S

    Sohl-Dickstein, J., Weiss, E. A., Maheswaranathan, N., and Ganguli, S. Deep unsupervised learning using nonequilibrium thermodynamics. In International Conference on Machine Learning (ICML), pp.\ 2256--2265. PMLR, 2015. URL https://arxiv.org/abs/1503.03585

    2015 arXiv

  25. [33]

    P., Kumar, A., Ermon, S., and Poole, B

    Song, Y., Sohl-Dickstein, J., Kingma, D. P., Kumar, A., Ermon, S., and Poole, B. Score-based generative modeling through stochastic differential equations. In International Conference on Learning Representations (ICLR), 2021. URL https://arxiv.org/abs/2011.13456

    2021 arXiv

  26. [34]

    Versatile diffusion: Text, images, and variations all in one diffusion model

    Song, Y., Meng, C., Tan, R., He, Y., Ermon, S., et al. Versatile diffusion: Text, images, and variations all in one diffusion model. arXiv preprint arXiv:2211.08332, 2022. URL https://arxiv.org/abs/2211.08332

    2022 arXiv

  27. [35]

    A Little Book of Martingales, volume 78 of Texts and Readings in Mathematics

    Welsh, D. A Little Book of Martingales, volume 78 of Texts and Readings in Mathematics. Hindustan Book Agency, 2023. ISBN 9789819744716

    2023

  28. [36]

    Xue, H. et al. Hd-vila-100m: A large-scale high-definition video-language dataset. https://github.com/microsoft/XPretrain/blob/main/hd-vila-100m/README.md, 2022. Accessed: 2025-04-02

    2022

  29. [37]

    3d shape generation and completion through point-voxel diffusion

    Zhou, L., Du, Y., and Wu, J. 3d shape generation and completion through point-voxel diffusion. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), pp.\ 5826--5835, 2021. URL https://arxiv.org/abs/2104.03670

    2021 arXiv

  30. [38]

    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 gl...

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.