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This paper sets out to establish that deterministic ODE-based samplers for diffusion models introduce collapse errors—generated samples become overly concentrated in local data space—and that a see-saw effect in score learning is the cause.

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Deterministic diffusion samplers induce collapse errors, where samples overly concentrate locally, caused by low-noise score learning degrading high-noise score accuracy.

T0 review reviewed 2026-08-05 challenge →

load-bearing objection Collapse errors from deterministic samplers is a plausible and important claim, but with only the abstract and one appendix in hand, the TID metric is unvalidated; the paper deserves a careful referee, not a desk reject. the 3 major comments →

arxiv 2508.16154 v1 pith:SP7CFS72 submitted 2025-08-22 cs.LG cs.AI

On the Collapse Errors Induced by the Deterministic Sampler for Diffusion Models

Yi Zhang , Zhenyu Liao , Jingfeng Wu , Difan Zou This is my paper
classification cs.LG cs.AI
keywords diffusion modelsdeterministic samplersODE-based samplingcollapse errorsscore learningsee-saw effectsample diversitylocal over-concentration
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 reading

This paper sets out to establish that deterministic samplers for diffusion models—the widely used ODE-based fast generation route—have a failure mode that previous evaluations missed: they over-concentrate sampled data in local regions of data space, silently reducing diversity even for a well-trained model. To make this measurable, the authors introduce a metric (called TID in the paper) that detects local over-concentration, and report that collapse errors appear across model sizes, dataset sizes, data dimensions, and training durations. They trace the cause to a see-saw effect in score learning, in which better score fit at low noise comes at the cost of worse score fit at high noise; deterministic ODE dynamics then carry that high-noise misfit into the final samples. If the paper is right, standard practice for fast diffusion sampling should be re-examined, because global image-quality scores can look fine while output diversity is narrowing.

Core claim

The central claim is the identification of collapse errors in ODE-based diffusion sampling. The paper argues that deterministic samplers, as opposed to stochastic ones, systematically drive generated samples into small local neighborhoods of data space, even when the trained score function is good by standard measures. This is quantified by the authors' metric, and the evidence shows collapse grows with model width and training epochs and shrinks with dataset size. The proposed mechanism is the see-saw effect: score learning in low-noise regimes harms score learning in high-noise regimes, so the learned score field is misfit where deterministic sampling starts; the ODE's lack of randomness p

What carries the argument

The central mechanism is the combination of a deterministic ODE sampler (e.g., DDIM or DPM-Solver, which integrates the learned score field without injected noise) and the see-saw effect in score learning, where improvements in low-noise score fit degrade the high-noise score fit. The paper's named instrument is TID, a metric intended to measure how much generated samples cluster locally; it is what turns the qualitative 'collapse' claim into a quantitative one.

Load-bearing premise

The load-bearing premise is that the paper's new metric truly captures local over-concentration and is not distorted by output scale or by harmless low-frequency structure; if the metric is miscalibrated, the collapse-error phenomenon may be a measurement artifact.

What would settle it

Take a single trained diffusion model, sample with a deterministic ODE sampler and with a stochastic SDE sampler, and compare local clustering under the paper's metric. If deterministic samples are not more locally concentrated than stochastic ones on the same model, the claim that deterministic dynamics cause collapse errors is falsified; additionally, a synthetic control set of exact training-set duplicates versus diverse low-frequency variants could test the metric itself.

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

If this is right

  • A global image-quality score is not enough to judge a diffusion model; local concentration must be checked separately.
  • Deterministic fast samplers such as DDIM and DPM-Solver may be the specific culprits, so stochastic correction or hybrid samplers could be needed to preserve diversity.
  • Training recipes that improve low-noise score accuracy, such as more epochs or wider models, can inadvertently worsen collapse on small datasets, so capacity and dataset size interact with sampler choice.
  • Existing interventions in sampling, training, and architecture that reduce collapse provide a practical toolkit, but the see-saw explanation says these fixes should be understood as repairing high-noise score misfit.

Where Pith is reading between the lines

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

  • If the see-saw mechanism is right, then reweighting or decoupling noise-level losses during training—protecting high-noise score fit—should reduce collapse without changing dataset size.
  • The TID lens may connect to memorization: since both intensify with smaller datasets and larger models, collapse errors and training-set memorization could share a high-noise score-fitting root cause, a hypothesis the paper does not explore.
  • A practical implication for deployment is that deterministic sampling is the riskier choice for small or high-dimensional data; a stochastic sampler may be safer even if slower, unless a collapse-repairing correction is added.
  • The metric itself could be repurposed as a diversity regularizer during training or as an acceptance criterion during sampling.
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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 / 4 minor

Summary. The paper claims that ODE-based deterministic samplers for diffusion models introduce a previously unrecognized failure mode, 'collapse errors', in which generated samples are overly concentrated in local regions of data space. It introduces a new metric (referred to as TID) to quantify this effect and reports, from experiments on CelebA, that TID is positive across almost all training settings and varies with model width, dataset size, data dimension, and training epochs. The paper further proposes a 'see-saw effect' in score learning—misfitting in high-noise regimes caused by low-noise learning—and claims this, combined with deterministic sampler dynamics, causes collapse errors. Existing sampling, training, and architecture techniques are then adapted to support the explanation. The provided text contains only the abstract, introduction, references, and Appendix C; the definition of TID, the main experiments, and the supporting analyses are not visible in the submitted excerpt.

Significance. If the collapse-error phenomenon is real, this is a significant result: deterministic ODE samplers are widely used in practice, and the suggestion that they systematically reduce output diversity even for well-trained diffusion models would merit substantial follow-up. A validated TID metric could be a useful diagnostic for the community. The see-saw mechanism, if properly supported, would connect across-noise-regime score learning to sampler dynamics. However, the current contribution rests entirely on an unvalidated metric and on qualitative trends; the visible portion of the manuscript does not provide the necessary calibration, null controls, or statistical evidence to establish the central claim.

major comments (3)
  1. [Appendix C / TID definition] The TID metric is never defined in the visible text. Appendix C reports only that 'TID values evaluated on almost all training settings are larger than 0' and describes directional trends. Without a formal definition, a calibration procedure, a null distribution, or a decision threshold, a positive TID cannot be interpreted as collapse. The observation that larger datasets yield 'near-zero' but not exactly zero TID is consistent with an unnormalized discrepancy that has a nonzero baseline under a perfect sampler. A null-data control—TID computed on samples drawn from the true distribution or on training-set samples from a perfect model—is essential and is absent.
  2. [Appendix C / experimental claims] The trends in Fig. 12 are reported qualitatively: 'TID values increase as the model width grows', 'TID values decrease as dataset size increases', etc. No error bars, repeated seeds, or statistical tests are shown in the visible excerpt. Since the paper's abstract claims collapse errors occur 'across a variety of settings', the lack of quantitative uncertainty measures makes it impossible to assess whether the observed differences are significant or whether TID conflates collapse with overfitting, memorization, or simple finite-sample fluctuations.
  3. [Abstract / see-saw effect] The see-saw effect is introduced as an observed cause after the fact: the paper 'observe[s] a see-saw effect' and then 'applies existing techniques ... to empirically support' the explanation. This ordering is vulnerable to post-hoc rationalization. No independent, pre-registered prediction or counterfactual experiment is reported that distinguishes the see-saw mechanism from alternative explanations, such as memorization or overfitting in high-noise regimes. As a result, the abstract's causal statement that the see-saw effect 'ultimately causes collapse errors' overreaches the evidence provided.
minor comments (4)
  1. [Appendix C] The phrase 'indicating the university of collapse errors' appears to be a typo for 'universality of collapse errors'.
  2. [Throughout] The acronym TID is never expanded in the visible text; the full name of the metric should be given at first use.
  3. [References] Reference [31] contains the placeholder '[Insert Date Accessed]' and should be completed.
  4. [Appendix C] The appendix refers to 'Fig. 4' and 'Fig. 12', but these figures are not included in the provided text; figure captions and the main-text discussion are needed for reproducibility.

Circularity Check

0 steps flagged

No significant circularity found in the excerpted manuscript.

full rationale

The paper's central claim—that deterministic ODE samplers induce 'collapse errors'—is supported by a novel TID metric, whose definition is not provided in the excerpt. However, nothing in the quoted text indicates that TID is defined in terms of the collapse phenomenon it purports to measure, nor that the see-saw effect is an input rather than an observed regularity. The abstract states that the authors observe the see-saw effect after investigating causes, then apply existing techniques guided by that insight; this is a post-hoc explanation, but the rules for circularity require a quote showing a specific reduction (e.g., Eq. X = Eq. Y by construction), which is not present. Self-citations in the introduction are background references to the authors' prior work on feature learning and hidden rules in diffusion models; they are not load-bearing assumptions. No fitted parameter is renamed as a prediction, no uniqueness theorem is imported from self-cited work, and no known result is merely renamed. The excerpt is self-contained in the sense that the empirical evidence is presented as measurements under varied settings, and any concerns about metric validity or post-hoc reasoning are correctness/risk issues, not circularity.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The provided text does not include the definition of the novel metric or the experimental details, so the free-parameter audit is incomplete. The only identifiable potential free parameter is the unspecified TID metric hyperparameter.

free parameters (1)
  • TID metric kernel bandwidth / neighborhood radius (undetermined)
    The paper introduces a novel metric (TID) but its definition is not present in the provided excerpt. If the metric involves a distance threshold, kernel bandwidth, or neighborhood size, that quantity would be a free parameter. It cannot be audited from the available text.
axioms (2)
  • domain assumption ODE-based deterministic samplers faithfully approximate the probability-flow ODE, so observed output concentration reflects score misfit rather than discretization error.
    The paper's explanation of collapse errors relies on the sampler dynamics being accurate; otherwise, collapse could be a numerical artifact. Invoked implicitly in the abstract's coupling of misfitting with deterministic sampler dynamics.
  • standard math Denoising score matching provides valid per-noise-level score estimates, so the see-saw effect is a property of the learned model rather than a failure of the training objective itself.
    The paper treats score learning in low and high noise regimes as comparable quantities. This relies on standard score-matching theory (Vincent 2011, Song et al. 2020).

reviewed 2026-08-05 · how reviews work

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Cite this review

Pith. "Pith review of On the Collapse Errors Induced by the Deterministic Sampler for Diffusion Models." pith.science (2026). https://pith.science/paper/SP7CFS72

@misc{pith2026250816154,
  author       = {Pith},
  title        = {Pith review of: On the Collapse Errors Induced by the Deterministic Sampler for Diffusion Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SP7CFS72}},
  note         = {Machine review of arXiv:2508.16154}
}
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read the original abstract

Despite the widespread adoption of deterministic samplers in diffusion models (DMs), their potential limitations remain largely unexplored. In this paper, we identify collapse errors, a previously unrecognized phenomenon in ODE-based diffusion sampling, where the sampled data is overly concentrated in local data space. To quantify this effect, we introduce a novel metric and demonstrate that collapse errors occur across a variety of settings. When investigating its underlying causes, we observe a see-saw effect, where score learning in low noise regimes adversely impacts the one in high noise regimes. This misfitting in high noise regimes, coupled with the dynamics of deterministic samplers, ultimately causes collapse errors. Guided by these insights, we apply existing techniques from sampling, training, and architecture to empirically support our explanation of collapse errors. This work provides intensive empirical evidence of collapse errors in ODE-based diffusion sampling, emphasizing the need for further research into the interplay between score learning and deterministic sampling, an overlooked yet fundamental aspect of diffusion models.

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Reference graph

Works this paper leans on

57 extracted references · 49 canonical work pages · cited by 1 Pith paper · 1 internal anchor

  1. [11]

    Investigating data memorization in 3d latent diffusion models for medical image synthesis

    Salman Ul Hassan Dar, Arman Ghanaat, Jannik Kahmann, Isabelle Ayx, Theano Papavassiliu, Stefan O Schoenberg, and Sandy Engelhardt. Investigating data memorization in 3d latent diffusion models for medical image synthesis. In International Conference on Medical Image Computing and Computer-Assisted Intervention , pages 56–65. Springer, 2023. 2, 3

    work page 2023

  2. [12]

    Diffusion models beat gans on image synthesis

    Prafulla Dhariwal and Alexander Nichol. Diffusion models beat gans on image synthesis. Advances in neural information processing systems , 34:8780–8794, 2021. 1

    work page 2021

  3. [13]

    Scaling rectified flow transformers for high-resolution image synthesis

    Patrick Esser, Sumith Kulal, Andreas Blattmann, Rahim Entezari, Jonas M¨ uller, Harry Saini, Yam Levi, Dominik Lorenz, Axel Sauer, Frederic Boesel, et al. Scaling rectified flow transformers for high-resolution image synthesis. In Forty-first International Conference on Machine Learning, 2024. 3

    work page 2024

  4. [14]

    Sur la distance de deux lois de probabilit´ e

    Maurice Fr´ echet. Sur la distance de deux lois de probabilit´ e. InAnnales de l’ISUP , volume 6, pages 183–198, 1957. 12, 35

    work page 1957

  5. [15]

    Generative adversarial nets

    Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio. Generative adversarial nets. Advances in neural information processing systems, 27, 2014. 1, 2

    2014

  6. [16]

    On memorization in diffusion models

    Xiangming Gu, Chao Du, Tianyu Pang, Chongxuan Li, Min Lin, and Ye Wang. On memorization in diffusion models. arXiv preprint arXiv:2310.02664 , 2023. 1, 2, 3

    Pith/arXiv arXiv 2023

  7. [17]

    Improved training of wasserstein gans

    Ishaan Gulrajani, Faruk Ahmed, Martin Arjovsky, Vincent Dumoulin, and Aaron C Courville. Improved training of wasserstein gans. Advances in neural information processing systems , 30,

    work page

  8. [18]

    On the feature learning in diffusion models

    Andi Han, Wei Huang, Yuan Cao, and Difan Zou. On the feature learning in diffusion models. In The Thirteenth International Conference on Learning Representations , 2025. 3

    work page 2025

  9. [19]

    Can diffusion models learn hidden inter-feature rules behind images? In Forty-second International Conference on Machine Learning, 2025

    Yujin Han, Andi Han, Wei Huang, Chaochao Lu, and Difan Zou. Can diffusion models learn hidden inter-feature rules behind images? In Forty-second International Conference on Machine Learning, 2025. 3

    work page 2025

  10. [20]

    Gans trained by a two time-scale update rule converge to a local nash equilibrium

    Martin Heusel, Hubert Ramsauer, Thomas Unterthiner, Bernhard Nessler, and Sepp Hochreiter. Gans trained by a two time-scale update rule converge to a local nash equilibrium. In I. Guyon, U. Von Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett, editors, Advances in Neural Information Processing Systems , volume 30. Curran Associat...

    work page 2017

  11. [21]

    A simple general approach to inference about the tail of a distribution

    Bruce M Hill. A simple general approach to inference about the tail of a distribution. The annals of statistics , pages 1163–1174, 1975. 7

    work page 1975

  12. [22]

    Denoising diffusion probabilistic models

    Jonathan Ho, Ajay Jain, and Pieter Abbeel. Denoising diffusion probabilistic models. Advances in neural information processing systems , 33:6840–6851, 2020. 1, 2, 4

    work page 2020

  13. [23]

    Video diffusion models

    Jonathan Ho, Tim Salimans, Alexey Gritsenko, William Chan, Mohammad Norouzi, and David J Fleet. Video diffusion models. Advances in Neural Information Processing Systems , 35:8633–8646, 2022. 1

    work page 2022

  14. [24]

    Reverse transition kernel: A flexible framework to accelerate diffusion inference

    Xunpeng Huang, Difan Zou, Hanze Dong, Zhang Zhang, Yian Ma, and Tong Zhang. Reverse transition kernel: A flexible framework to accelerate diffusion inference. Advances in Neural Information Processing Systems, 37:95515–95578, 2024. 3 14

    work page 2024

  15. [25]

    Generalization in diffusion models arises from geometry-adaptive harmonic representations

    Zahra Kadkhodaie, Florentin Guth, Eero P Simoncelli, and St´ ephane Mallat. Generalization in diffusion models arises from geometry-adaptive harmonic representations. In The Twelfth International Conference on Learning Representations , 2024. 2, 3

    work page 2024

  16. [26]

    Progressive growing of GANs for improved quality, stability, and variation

    Tero Karras, Timo Aila, Samuli Laine, and Jaakko Lehtinen. Progressive growing of GANs for improved quality, stability, and variation. In International Conference on Learning Representa- tions, 2018. 3

    work page 2018

  17. [27]

    Elucidating the design space of diffusion-based generative models

    Tero Karras, Miika Aittala, Timo Aila, and Samuli Laine. Elucidating the design space of diffusion-based generative models. Advances in neural information processing systems , 35:26565–26577, 2022. 3, 4, 5, 12

    work page 2022

  18. [28]

    Tackling structural hallucination in image translation with local diffusion

    Seunghoi Kim, Chen Jin, Tom Diethe, Matteo Figini, Henry FJ Tregidgo, Asher Mullokandov, Philip Teare, and Daniel C Alexander. Tackling structural hallucination in image translation with local diffusion. In European Conference on Computer Vision , pages 87–103. Springer,

    work page

  19. [29]

    Kingma and Jimmy Ba

    Diederik P. Kingma and Jimmy Ba. Adam: A method for stochastic optimization. In Yoshua Bengio and Yann LeCun, editors, 3rd International Conference on Learning Representations, ICLR 2015, San Diego, CA, USA, May 7-9, 2015, Conference Track Proceedings , 2015. 19, 21, 23, 24, 29

    work page 2015

  20. [30]

    Learning multiple layers of features from tiny images

    Alex Krizhevsky, Geoffrey Hinton, et al. Learning multiple layers of features from tiny images

  21. [31]

    Yann LeCun, Corinna Cortes, and Christopher J.C. Burges. The mnist database of handwritten digits. http://yann.lecun.com/exdb/mnist/, 1998. Accessed: [Insert Date Accessed]. 19

    work page 1998

  22. [32]

    Srdiff: Single image super-resolution with diffusion probabilistic models

    Haoying Li, Yifan Yang, Meng Chang, Shiqi Chen, Huajun Feng, Zhihai Xu, Qi Li, and Yueting Chen. Srdiff: Single image super-resolution with diffusion probabilistic models. Neurocomputing, 479:47–59, 2022. 1

    work page 2022

  23. [33]

    On the generalization properties of diffusion models

    Puheng Li, Zhong Li, Huishuai Zhang, and Jiang Bian. On the generalization properties of diffusion models. Advances in Neural Information Processing Systems , 36:2097–2127, 2023. 2, 3

    work page 2097

  24. [34]

    Understanding generalizability of diffusion models requires rethinking the hidden gaussian structure

    Xiang Li, Yixiang Dai, and Qing Qu. Understanding generalizability of diffusion models requires rethinking the hidden gaussian structure. Advances in neural information processing systems , 37:57499–57538, 2024. 3

    work page 2024

  25. [35]

    Evaluating Image Hallucination in Text-to-Image Generation with Question-Answering

    Youngsun Lim, Hojun Choi, Pin-Yu Chen, and Hyunjung Shim. Evaluating image hallucination in text-to-image generation with question-answering. CoRR, abs/2409.12784, 2024. 2

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  26. [36]

    Pacgan: The power of two samples in generative adversarial networks

    Zinan Lin, Ashish Khetan, Giulia Fanti, and Sewoong Oh. Pacgan: The power of two samples in generative adversarial networks. Advances in neural information processing systems , 31,

    work page

  27. [37]

    Yaron Lipman, Ricky T. Q. Chen, Heli Ben-Hamu, Maximilian Nickel, and Matthew Le. Flow matching for generative modeling. In The Eleventh International Conference on Learning Representations, 2023. 3, 35

    work page 2023

  28. [38]

    Flow straight and fast: Learning to generate and transfer data with rectified flow

    Xingchao Liu, Chengyue Gong, and qiang liu. Flow straight and fast: Learning to generate and transfer data with rectified flow. In The Eleventh International Conference on Learning Representations, 2023. 1, 3, 35 15

    work page 2023

  29. [39]

    Deep learning face attributes in the wild

    Ziwei Liu, Ping Luo, Xiaogang Wang, and Xiaoou Tang. Deep learning face attributes in the wild. In Proceedings of the IEEE international conference on computer vision , pages 3730–3738,

    work page

  30. [40]

    Dpm-solver: A fast ode solver for diffusion probabilistic model sampling in around 10 steps

    Cheng Lu, Yuhao Zhou, Fan Bao, Jianfei Chen, Chongxuan Li, and Jun Zhu. Dpm-solver: A fast ode solver for diffusion probabilistic model sampling in around 10 steps. Advances in Neural Information Processing Systems , 35:5775–5787, 2022. 3, 5, 36

    work page 2022

  31. [41]

    Dpm- solver++: Fast solver for guided sampling of diffusion probabilistic models

    Cheng Lu, Yuhao Zhou, Fan Bao, Jianfei Chen, Chongxuan Li, and Jun Zhu. Dpm- solver++: Fast solver for guided sampling of diffusion probabilistic models. arXiv preprint arXiv:2211.01095, 2022. 3, 5

    Pith/arXiv arXiv 2022

  32. [42]

    Interacting particle solutions of fokker–planck equations through gradient–log–density estimation

    Dimitra Maoutsa, Sebastian Reich, and Manfred Opper. Interacting particle solutions of fokker–planck equations through gradient–log–density estimation. Entropy, 22(8):802, 2020. 3

    work page 2020

  33. [43]

    Unrolled generative adversarial networks

    Luke Metz, Ben Poole, David Pfau, and Jascha Sohl-Dickstein. Unrolled generative adversarial networks. arXiv preprint arXiv:1611.02163 , 2016. 2

    Pith/arXiv arXiv 2016

  34. [44]

    Deep double descent: Where bigger models and more data hurt

    Preetum Nakkiran, Gal Kaplun, Yamini Bansal, Tristan Yang, Boaz Barak, and Ilya Sutskever. Deep double descent: Where bigger models and more data hurt. In International Conference on Learning Representations, 2020. 13

    work page 2020

  35. [45]

    Deep double descent: Where bigger models and more data hurt

    Preetum Nakkiran, Gal Kaplun, Yamini Bansal, Tristan Yang, Boaz Barak, and Ilya Sutskever. Deep double descent: Where bigger models and more data hurt. Journal of Statistical Mechanics: Theory and Experiment , 2021(12):124003, 2021. 3

    work page 2021

  36. [46]

    Glide: Towards photorealistic image generation and editing with text-guided diffusion models

    Alex Nichol, Prafulla Dhariwal, Aditya Ramesh, Pranav Shyam, Pamela Mishkin, Bob McGrew, Ilya Sutskever, and Mark Chen. Glide: Towards photorealistic image generation and editing with text-guided diffusion models. arXiv preprint arXiv:2112.10741 , 2021. 1

    Pith/arXiv arXiv 2021

  37. [47]

    Improved denoising diffusion probabilistic models

    Alexander Quinn Nichol and Prafulla Dhariwal. Improved denoising diffusion probabilistic models. In International conference on machine learning , pages 8162–8171. PMLR, 2021. 3, 4

    work page 2021

  38. [48]

    Hierarchical text-conditional image generation with clip latents

    Aditya Ramesh, Prafulla Dhariwal, Alex Nichol, Casey Chu, and Mark Chen. Hierarchical text-conditional image generation with clip latents. arXiv preprint arXiv:2204.06125 , 1(2):3,

    Pith/arXiv arXiv

  39. [49]

    High-resolution image synthesis with latent diffusion models

    Robin Rombach, Andreas Blattmann, Dominik Lorenz, Patrick Esser, and Bj¨ orn Ommer. High-resolution image synthesis with latent diffusion models. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , pages 10684–10695, 2022. 1, 35

    work page 2022

  40. [50]

    U-net: Convolutional networks for biomedical image segmentation

    Olaf Ronneberger, Philipp Fischer, and Thomas Brox. U-net: Convolutional networks for biomedical image segmentation. In Nassir Navab, Joachim Hornegger, William M. Wells, and Alejandro F. Frangi, editors, Medical Image Computing and Computer-Assisted Intervention – MICCAI 2015 , pages 234–241, Cham, 2015. Springer International Publishing. 19

    work page 2015

  41. [51]

    Principles of Mathematical Analysis , volume 3 of International Series in Pure and Applied Mathematics

    Walter Rudin. Principles of Mathematical Analysis , volume 3 of International Series in Pure and Applied Mathematics . McGraw-Hill Education, 3 edition, 1964. 32

    work page 1964

  42. [52]

    Photorealistic text-to-image diffusion models with deep language understanding

    Chitwan Saharia, William Chan, Saurabh Saxena, Lala Li, Jay Whang, Emily L Denton, Kamyar Ghasemipour, Raphael Gontijo Lopes, Burcu Karagol Ayan, Tim Salimans, et al. Photorealistic text-to-image diffusion models with deep language understanding. Advances in neural information processing systems , 35:36479–36494, 2022. 1 16

    work page 2022

  43. [53]

    Image super-resolution via iterative refinement

    Chitwan Saharia, Jonathan Ho, William Chan, Tim Salimans, David J Fleet, and Mohammad Norouzi. Image super-resolution via iterative refinement. IEEE transactions on pattern analysis and machine intelligence , 45(4):4713–4726, 2022. 1, 5

    work page 2022

  44. [55]

    Improved techniques for training gans

    Tim Salimans, Ian Goodfellow, Wojciech Zaremba, Vicki Cheung, Alec Radford, and Xi Chen. Improved techniques for training gans. Advances in neural information processing systems , 29,

    work page

  45. [56]

    Progressive distillation for fast sampling of diffusion models

    Tim Salimans and Jonathan Ho. Progressive distillation for fast sampling of diffusion models. In International Conference on Learning Representations , 2022. 3

    work page 2022

  46. [57]

    Learning mixtures of gaussians using the ddpm objective

    Kulin Shah, Sitan Chen, and Adam Klivans. Learning mixtures of gaussians using the ddpm objective. Advances in Neural Information Processing Systems , 36:19636–19649, 2023. 32

    work page 2023

  47. [58]

    Parallel sampling of diffusion models

    Andy Shih, Suneel Belkhale, Stefano Ermon, Dorsa Sadigh, and Nima Anari. Parallel sampling of diffusion models. Advances in Neural Information Processing Systems , 36, 2024. 3

    work page 2024

  48. [59]

    Diffusion art or digital forgery? investigating data replication in diffusion models

    Gowthami Somepalli, Vasu Singla, Micah Goldblum, Jonas Geiping, and Tom Goldstein. Diffusion art or digital forgery? investigating data replication in diffusion models. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition , pages 6048–6058,

    work page

  49. [60]

    Denoising diffusion implicit models

    Jiaming Song, Chenlin Meng, and Stefano Ermon. Denoising diffusion implicit models. In International Conference on Learning Representations , 2021. 2, 3, 5, 8, 36

    work page 2021

  50. [61]

    Generative modeling by estimating gradients of the data distribution

    Yang Song and Stefano Ermon. Generative modeling by estimating gradients of the data distribution. Advances in neural information processing systems , 32, 2019. 1, 3, 8, 12

    work page 2019

  51. [62]

    Score-based generative modeling through stochastic differential equations

    Yang Song, Jascha Sohl-Dickstein, Diederik P Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole. Score-based generative modeling through stochastic differential equations. In International Conference on Learning Representations , 2020. 1, 3, 5, 7, 8, 19, 20, 24, 25, 34, 35

    work page 2020

  52. [63]

    Veegan: Reducing mode collapse in gans using implicit variational learning

    Akash Srivastava, Lazar Valkov, Chris Russell, Michael U Gutmann, and Charles Sutton. Veegan: Reducing mode collapse in gans using implicit variational learning. Advances in neural information processing systems, 30, 2017. 2

    work page 2017

  53. [64]

    Rethink- ing the inception architecture for computer vision

    Christian Szegedy, Vincent Vanhoucke, Sergey Ioffe, Jon Shlens, and Zbigniew Wojna. Rethink- ing the inception architecture for computer vision. In Proceedings of the IEEE conference on computer vision and pattern recognition , pages 2818–2826, 2016. 35

    work page 2016

  54. [65]

    Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N

    Ashish Vaswani, Noam M. Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N. Gomez, Lukasz Kaiser, and Illia Polosukhin. Attention is all you need. In Neural Information Processing Systems, 2017. 25

    work page 2017

  55. [66]

    A connection between score matching and denoising autoencoders

    Pascal Vincent. A connection between score matching and denoising autoencoders. Neural computation, 23(7):1661–1674, 2011. 10

    work page 2011

  56. [67]

    Diffusion models learn low-dimensional distributions via subspace clustering

    Peng Wang, Huijie Zhang, Zekai Zhang, Siyi Chen, Yi Ma, and Qing Qu. Diffusion models learn low-dimensional distributions via subspace clustering. arXiv preprint arXiv:2409.02426 ,

    Pith/arXiv arXiv

  57. [2024]

    4, we evaluate the TID on CelebA on various experimental settings, as shown in Fig

    3 17 C TID on CelebA To supplement Fig. 4, we evaluate the TID on CelebA on various experimental settings, as shown in Fig. 12. The details of experimental settings can be found in Appendix. A.1. We observe that the TID values evaluated on almost all training settings are larger than 0, indicating the university of collapse errors. Observations from Fig. ...

    work page

This paper was first reviewed by deepseek-v4-flash on August 5, 2026.