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Diffusion Models, Denoiser Architecture and Creativity

T0 review · 1 major / 0 minor · reviewed 2026-06-30 · grok-4.3

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Pith's one-line read Creativity in diffusion models arises because denoiser architectures impose inductive biases that interact with the target distribution to yield samples outside the training set.

desk verdict The paper derives closed forms showing how linear, polynomial, and bottleneck denoisers produce different output distributions from a target, but the step from idealized architecture to trained finite-data behavior is not clearly bridged. read the letter →

arxiv 2605.16415 v3 pith:THCZLJGY submitted 2026-05-13 cs.CV cs.LG

Itamar Levine , Yair Weiss This is my paper
classification cs.CVcs.LG
keywords diffusionmodelsdenoiserarchitecturegenerativemodelinginductivebiasUNettargetdistributioncreativityBayesoptimal
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 establishes that if a denoiser were the Bayes optimal estimator for the training data, diffusion models would simply reproduce the training samples. Instead, the authors derive explicit closed-form distributions of generated samples for linear, polynomial, and bottleneck denoisers, showing how each architecture produces systematic deviations from the target. Experiments with small modifications to the standard UNet confirm that architectural choices alter the form of generated images, often yielding nonrealistic outputs. The central conclusion is that diffusion models succeed only when the denoiser's built-in biases align closely with the structure of the true data distribution. This framing shifts attention from training procedures to the match between architecture and data.

What carries the argument

Explicit closed-form expressions for the distribution of generated samples as a function of the target distribution and the denoiser architecture (linear, polynomial, bottleneck).

What would settle it

Train a linear or polynomial denoiser on a simple known distribution such as a mixture of Gaussians and check whether the empirical histogram of generated samples matches the predicted scaled or moment-adjusted form.

Watch

Extended reading notes

Core claim

For linear denoisers the generated distribution is a scaled version of the target; for polynomial denoisers it incorporates higher-order moments; for bottleneck denoisers it is a low-rank projection. These explicit forms deviate from the target distribution in ways that produce creative yet sometimes unrealistic samples. The same interaction appears in practice when minor changes to the UNet architecture produce qualitatively different generative behavior, supporting the claim that success requires strong alignment between the denoiser's inductive bias and the true target distribution.

Load-bearing premise

The closed-form distributions derived for the three idealized denoisers accurately describe the outputs of models trained on finite real data.

Editorial extensions

If this is right

  • Linear denoisers produce scaled copies of the target distribution.
  • Polynomial denoisers generate samples whose statistics reflect higher-order moments of the target.
  • Bottleneck denoisers yield low-dimensional projections of the target.
  • Minor architectural changes in UNet-style networks can shift outputs from realistic to nonrealistic.
  • Diffusion models require denoiser inductive bias to match the structure of the data distribution.

Reading between the lines

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

  • Architectures could be selected or designed by matching their known bias properties to statistical features of the target domain.
  • The same analysis framework might extend to other score-based or flow-based generative models that rely on learned denoisers.
  • On datasets with known low-rank or polynomial structure, the derived forms predict which architectures will produce the most faithful samples.
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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

1 major / 0 minor

Summary. The paper claims that creativity in diffusion models (generating realistic but non-training-set samples) arises from an interaction between denoiser architecture inductive bias and the target distribution. It derives explicit closed-form distributions of generated samples as a function of the target for linear, polynomial, and bottleneck denoisers; empirically shows that small modifications to the UNet architecture produce qualitatively different creativity outcomes, frequently yielding highly non-realistic samples; and concludes that diffusion models succeed only when the denoiser architecture's inductive bias is in strong alignment with the true target distribution.

Significance. If the closed-form results apply to trained finite-data models, the work supplies a concrete theoretical mechanism linking architecture bias to sample distribution, which is a strength given the explicit derivations. The empirical sensitivity of UNet variants to small changes is useful for practitioners. The central claim is interesting and could inform architecture design, but its validity hinges on the idealized-to-trained mapping.

major comments (1)
  1. [theoretical results on denoiser architectures (closed-form derivations)] The central theoretical results derive explicit generated-sample distributions for linear, polynomial, and bottleneck denoisers as functions of the target. These derivations treat the denoiser as exactly realizing the architectural constraint (e.g., exactly linear or exactly low-rank bottleneck). In actual diffusion training the denoiser parameters are optimized on finite data, so the learned function is the result of gradient descent within the architecture class rather than an exact closed-form projection. If finite-sample effects, optimization trajectory, or the score-matching objective cause the trained denoiser to deviate from the assumed functional form, the predicted distributions no longer describe the deployed model. Because the paper uses these closed-forms to explain why architecture bias produces creativity (and why UNET variants produce unrealistic samples), this assumption

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive report and the opportunity to clarify our work. The main concern is the applicability of the closed-form derivations to trained models; we address this directly below and outline revisions to improve clarity on the scope of the theoretical results.

read point-by-point responses

  1. Referee: The central theoretical results derive explicit generated-sample distributions for linear, polynomial, and bottleneck denoisers as functions of the target. These derivations treat the denoiser as exactly realizing the architectural constraint (e.g., exactly linear or exactly low-rank bottleneck). In actual diffusion training the denoiser parameters are optimized on finite data, so the learned function is the result of gradient descent within the architecture class rather than an exact closed-form projection. If finite-sample effects, optimization trajectory, or the score-matching objective cause the trained denoiser to deviate from the assumed functional form, the predicted distributions no longer describe the deployed model. Because the paper uses these closed-forms to explain why architecture bias produces creativity (and why UNET variants produce unrealistic samples), this assumption

    Authors: We agree that the derivations assume the denoiser exactly realizes the architectural constraint, which is an idealization not guaranteed in finite-data training. The closed-forms are presented to characterize the inductive bias of each architecture class and to derive the resulting generated distribution under that constraint; they are not claimed to be exact for any particular trained network. The manuscript's central argument is that creativity arises from the interaction of architecture bias and target distribution, with the closed-forms serving as an explicit illustration of one direction of that interaction. The empirical section then shows that small UNet modifications produce qualitatively different (and often unrealistic) samples even after training, indicating that architectural biases remain influential in practice. We will revise the manuscript to add an explicit discussion of this idealization, including a new paragraph noting that the theoretical results describe the effect of the constraint while the empirical results provide supporting evidence that such biases affect trained models. This revision will also clarify the mapping between the two without changing the derivations themselves. revision: partial

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: closed-form derivations are independent of fitted parameters

full rationale

The paper derives explicit generated-sample distributions for idealized linear, polynomial, and bottleneck denoisers directly from the architectural constraints and target distribution. These are mathematical reductions under stated assumptions rather than any parameter fitted to data and then renamed as a prediction. No self-citation chain, self-definitional loop, or ansatz smuggled via prior work is present in the provided text. The empirical section on UNET variants is observational and does not rely on the closed-forms for its claims. The central result (architecture-target alignment determines creativity) therefore rests on independent theoretical and empirical content, not on any reduction to its own inputs by construction.

Assumptions & free parameters 0 free parameters · 1 assumptions · 0 invented entities

Based solely on the abstract, no free parameters, invented entities, or non-standard axioms are identifiable; the work relies on standard diffusion model assumptions.

assumptions (1)
  • domain assumption The denoiser is trained to approximate the optimal denoiser for the given training set but is constrained by its architecture.
    This is the starting point for both the theoretical derivations and the explanation of creativity.

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Cite this review

Pith. "Pith review of Diffusion Models, Denoiser Architecture and Creativity." pith.science (2026). https://pith.science/paper/THCZLJGY

@misc{pith2026260516415,
  author       = {Pith},
  title        = {Pith review of: Diffusion Models, Denoiser Architecture and Creativity},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/THCZLJGY}},
  note         = {Machine review of arXiv:2605.16415}
}
read the original abstract

The creativity of diffusion models refers to their ability to generate highly realistic images that are different from their training data. Creativity is somewhat surprising since it is known that if the denoiser used in the diffusion model is the Bayes optimal denoiser for a given training set, then the model will simply copy the training samples. In this paper we present empirical and theoretical results that suggest that creativity in diffusion models is due to an interaction between the denoiser architecture and the target distribution. Theoretically, we give explicit forms for the distribution of generated samples as a function of the target distribution and the denoiser architecture for three different denoiser architectures (linear, polynomial, bottleneck). Empirically, we show that small changes in the popular UNET denoiser architecture leads to very different forms of creativity, and these small changes often yield samples that are highly nonrealistic. Taken together, our results show that diffusion models will only be successful if the inductive bias of the denoiser architecture is in strong alignment with the true target distribution.

Figures

Figures reproduced from arXiv: 2605.16415 by the authors.

Figure 1
Figure 1. The impact of minor U-Net architectural variations on diffusion model outputs. All models [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Two different data sets with the same mean and covariance (most left and right) and data [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. A dataset sampled from a mixture of three Gaussians, and the data sampled from [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: A 3 GMM data set, and the data sampled from [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: Samples from Pgenerated learn by linear denoiser with bottle neck of size 10 (top row), 100 (second row) and no bottle neck (bottom row). each column have generated with the same starting noise. even after the bias of a linear denoiser, the bottle neck size have big in…
Figure 6
Figure 6. Figure 6: First row: samples from Pgenerated learn by linear denoiser over CelebA. second row: samples from Pgenerated learn by linear denoiser over samlped data set from Pgenerated learn by linear denoiser over CelebA. data, y denotes the noisy input data, R is the fixed random…
Figure 7
Figure 7. Figure 7: Samples from Pgenerated learn by a polynomial denoiser over CelebA. we used different degree (from up: 3, 9, 27). the last row is the nearest neighbor of the 27-degree polynomial result. When using high degree, the polynomial denoiser create both creativity images and …
Figure 8
Figure 8. Figure 8: Samples from Pgenerated learn by a patch polynomial denoiser over CelebA. Conversely, as we restricted the capacity in the networks with h = 500 and h = 100, the models avoided strict memorization and instead exhibited distinct forms of generative creativity. As illust…
Figure 9
Figure 9. Figure 9: Samples from Pgenerated learn by a bottle neck architecture with h=1000 (up), h=500 (middle) and h=100 (down). as expected, the top row is exact sample from train set. 8 [PITH_FULL_IMAGE:figures/full_fig_p008_9.png]

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Works this paper leans on

15 extracted references · 15 canonical work pages

  1. [1]

    Cambridge University Press, 2014

    Shai Shalev-Shwartz and Shai Ben-David.Understanding Machine Learning - From Theory to Algorithms. Cambridge University Press, 2014

    work page 2014

  2. [2]

    Denoising diffusion implicit models

    Jiaming Song, Chenlin Meng, and Stefano Ermon. Denoising diffusion implicit models. InInternational Conference on Learning Representations (ICLR), 2021

    work page 2021

  3. [3]

    U-net: Convolutional networks for biomedical image segmentation

    Olaf Ronneberger, Philipp Fischer, and Thomas Brox. U-net: Convolutional networks for biomedical image segmentation. InMedical Image Computing and Computer-Assisted Intervention – MICCAI 2015, pages 234–241. Springer International Publishing, 2015

    work page 2015

  4. [4]

    Weiss, Niru Maheswaranathan, and Surya Ganguli

    Jascha Sohl-Dickstein, Eric A. Weiss, Niru Maheswaranathan, and Surya Ganguli. Deep unsupervised learning using nonequilibrium thermodynamics. InProceedings of the 32nd International Conference on Machine Learning, pages 2256–2265, 2015

    work page 2015

  5. [5]

    Denoising diffusion probabilistic models

    Jonathan Ho, Ajay Jain, and Pieter Abbeel. Denoising diffusion probabilistic models. InProceedings of the 34th International Conference on Neural Information Processing Systems, 2020

    work page 2020

  6. [6]

    Elucidating the design space of diffusion-based generative models

    Tero Karras, Miika Aittala, Samuli Laine, and Timo Aila. Elucidating the design space of diffusion-based generative models. InProceedings of the 36th International Conference on Neural Information Processing Systems, 2022

    work page 2022

  7. [7]

    Generalization in diffusion models arises from geometry-adaptive harmonic representations

    Zahra Kadkhodaie, Florentin Guth, Eero P Simoncelli, and Stéphane Mallat. Generalization in diffusion models arises from geometry-adaptive harmonic representations. InThe Twelfth International Conference on Learning Representations, 2024

    work page 2024

  8. [8]

    Unconditional cnn denoisers contain sparse semantic representation of images.arXiv preprint arXiv:2506.01912, 2025

    Zahra Kadkhodaie, Stéphane Mallat, and Eero Simoncelli. Unconditional cnn denoisers contain sparse semantic representation of images.arXiv preprint arXiv:2506.01912, 2025

    work page arXiv 2025

Show all 15 references
  1. [9]

    An analytic theory of creativity in convolutional diffusion models

    Mason Kamb and Surya Ganguli. An analytic theory of creativity in convolutional diffusion models. In Forty-second International Conference on Machine Learning, 2025

    2025

  2. [10]

    S. M. Kay.Fundamentals of Statistical Signal Processing: Estimation Theory. Prentice Hall, 1997

    1997

  3. [11]

    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 International Conference on Computer Vision (ICCV), 2015

    2015

  4. [12]

    Locality in image diffusion models emerges from data statistics

    Artem Lukoianov, Chenyang Yuan, Justin Solomon, and Vincent Sitzmann. Locality in image diffusion models emerges from data statistics. InThe Thirty-ninth Annual Conference on Neural Information Processing Systems, 2026

    2026

  5. [13]

    Towards a mechanistic explanation of diffusion model generalization

    Matthew Niedoba, Berend Zwartsenberg, Kevin Patrick Murphy, and Frank Wood. Towards a mechanistic explanation of diffusion model generalization. InForty-second International Conference on Machine Learning, 2025

    2025

  6. [14]

    Binxu Wang and John J. Vastola. The hidden linear structure in score-based models and its application. arXiv preprint arXiv:2311.10892, 2023

    2023

  7. [15]

    When diffusion models memorize: Inductive biases in probability flow of minimum-norm shallow neural nets

    Chen Zeno, Hila Manor, Greg Ongie, Nir Weinberger, Tomer Michaeli, and Daniel Soudry. When diffusion models memorize: Inductive biases in probability flow of minimum-norm shallow neural nets. In Forty-second International Conference on Machine Learning, 2025. A Theoretical pro...

    2025

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