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arxiv: 2506.16827 · v2 · submitted 2025-06-20 · 💻 cs.GR · cs.CV· cs.LG

Beyond Blur: A Fluid Perspective on Generative Diffusion Models

Grzegorz Gruszczynski , Jakub Meixner , Michal Jan Wlodarczyk , Przemyslaw Musialski This is my paper

Pith reviewed 2026-05-19 08:10 UTC · model grok-4.3

classification 💻 cs.GR cs.CVcs.LG
keywords advection-diffusiongenerative diffusion modelsLattice Boltzmann methodPDE image corruptionstochastic velocity fieldsfluid dynamicsimage synthesisdimensionless numbers
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The pith

Coupling advection from fluid flows with diffusion generalizes corruption processes in generative image models and improves output diversity.

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

The paper proposes replacing the standard noise-based corruption in diffusion models with a physically derived advection-diffusion PDE that includes directional fluid motion, isotropic spreading, and added noise. This PDE is solved numerically on GPUs using a Lattice Boltzmann scheme and driven by stochastic velocity fields to simulate turbulent mixing. A neural network is then trained to invert the full operator, yielding a generative model. Prior diffusion and PDE-based methods appear as limiting cases when advection or certain parameters are turned off. The authors show that the added advection step increases sample diversity and quality while leaving the color distribution of outputs unchanged.

Core claim

Formulating image corruption as an advection-diffusion PDE with stochastic velocity fields, controlled by dimensionless numbers such as the Peclet and Fourier numbers, allows a neural network to learn the inverse operator and produce images whose diversity and visual quality exceed those of standard diffusion models, with previous PDE-based approaches recovered as special cases of the same operator.

What carries the argument

The advection-diffusion PDE operator solved by a custom GPU Lattice Boltzmann method, which adds coherent directional motion via stochastic velocity fields to the usual isotropic diffusion and noise.

If this is right

  • Standard diffusion and earlier PDE-based corruption schemes emerge as special cases when advection or turbulence parameters are removed.
  • Stochastic velocity fields introduce multi-scale mixing that raises the variety of generated samples.
  • The color palette of synthesized images stays statistically the same as in pure-diffusion baselines.
  • Dimensionless numbers allow explicit control over the relative strength of advection versus diffusion during training.

Where Pith is reading between the lines

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

  • The same fluid-inspired operator could be extended to video or 3D generation by making the velocity fields time-dependent.
  • Benchmarking against turbulence-resolving fluid simulations might show whether the learned inverse captures real mixing statistics.
  • Hybrid pipelines could let the generative model initialize or correct coarse fluid simulations in graphics applications.

Load-bearing premise

A neural network can accurately invert the coupled advection-diffusion operator including random velocity fields and still produce high-quality images without color shifts or artifacts.

What would settle it

Train the model on a standard image dataset and compare the generated images to those from a conventional diffusion baseline; consistent color shifts, lower diversity scores, or visible artifacts in the advection-diffusion outputs would falsify the central claim.

Figures

Figures reproduced from arXiv: 2506.16827 by Grzegorz Gruszczynski, Jakub Meixner, Michal Jan Wlodarczyk, Przemyslaw Musialski.

Figure 1
Figure 1. Figure 1: The standard diffusion model (DDPM, left) induces Gaussian nose for image corruption, inverse heat dissipation blurs the image [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Example of the corruption and generative process of our method, illustrated over 11 sequential frames in a chain. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Comparison of the Energy Spectrum (ES) of an image [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Corruption process: (a) input image, (b) advection and [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: Generated turbulent velocity field and its corresponding [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Samples for σ = 16, comparing different Peclet numbers. the initial state (blurry prior), we corrupt the clean images with according to the PDE, as described in Sec. 4. Impact of Peclet Number on Generated Samples. We first provide qualitative demonstrations of our model’s ability to generate high-fidelity images. In all datasets we observe that a directional flow (via Pe ̸= 0) yields visually richer detai… view at source ↗
Figure 8
Figure 8. Figure 8: Visual comparison of interpolations between two FFHQ samples. Each undergoes the forward process up to [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Results for σ = 20, showing inverse processes with varying Pe numbers. The image prior is consistent across rows for visual comparison, preserving the color palette [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Visual comparison of interpolations between two FFHQ samples. Each undergoes the forward process up to [PITH_FULL_IMAGE:figures/full_fig_p013_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Visual comparison of the results of our method and the IHD method on the FFHQ dataset. [PITH_FULL_IMAGE:figures/full_fig_p014_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Visual comparison of the results of our method and the IHD method on the FFHQ dataset. [PITH_FULL_IMAGE:figures/full_fig_p015_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Interpolations between two random images on FFHQ 128 [PITH_FULL_IMAGE:figures/full_fig_p016_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Interpolations between two random images on FFHQ 128 [PITH_FULL_IMAGE:figures/full_fig_p017_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Additional samples with corresponding initial images from MNIST dataset, comparing different Peclet numbers. We can observe [PITH_FULL_IMAGE:figures/full_fig_p018_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Visual comparison of interpolations between two MNIST samples. Each undergoes the forward process up to [PITH_FULL_IMAGE:figures/full_fig_p019_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Visual comparison of the results of our method and the IHD method on the MNIST dataset. [PITH_FULL_IMAGE:figures/full_fig_p020_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Interpolations between two random images on MNIST, [PITH_FULL_IMAGE:figures/full_fig_p021_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Interpolations between two random images on MNIST, [PITH_FULL_IMAGE:figures/full_fig_p022_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: Results for σ = 20, on the LSUN Church dataset, showing inverse processes with varying Pe numbers. The image prior is consistent across rows for visual comparison, preserving the color palette [PITH_FULL_IMAGE:figures/full_fig_p023_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: Visual comparison of interpolations between two LSUN Church samples. Each undergoes the forward process up to [PITH_FULL_IMAGE:figures/full_fig_p024_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: Visual comparison of the results of our method and the IHD method on the LSUN Church dataset. [PITH_FULL_IMAGE:figures/full_fig_p025_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: Interpolations between two random images on LSUN Church 128 [PITH_FULL_IMAGE:figures/full_fig_p026_23.png] view at source ↗
Figure 24
Figure 24. Figure 24: Interpolations between two random images on LSUN Church 128 [PITH_FULL_IMAGE:figures/full_fig_p027_24.png] view at source ↗
read the original abstract

We propose a novel PDE-driven corruption process for generative image synthesis based on advection-diffusion processes which generalizes existing PDE-based approaches. Our forward pass formulates image corruption via a physically motivated PDE that couples directional advection with isotropic diffusion and Gaussian noise, controlled by dimensionless numbers (Peclet, Fourier). We implement this PDE numerically through a GPU-accelerated custom Lattice Boltzmann solver for fast evaluation. To induce realistic turbulence, we generate stochastic velocity fields that introduce coherent motion and capture multi-scale mixing. In the generative process, a neural network learns to reverse the advection-diffusion operator thus constituting a novel generative model. We discuss how previous methods emerge as specific cases of our operator, demonstrating that our framework generalizes prior PDE-based corruption techniques. We illustrate how advection improves the diversity and quality of the generated images while keeping the overall color palette unaffected. This work bridges fluid dynamics, dimensionless PDE theory, and deep generative modeling, offering a fresh perspective on physically informed image corruption processes for diffusion-based synthesis.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes a novel PDE-driven corruption process for generative image synthesis based on advection-diffusion equations that couple directional advection with isotropic diffusion and Gaussian noise, controlled by dimensionless Peclet and Fourier numbers. The forward process is implemented via a GPU-accelerated Lattice Boltzmann solver incorporating stochastic velocity fields to induce turbulence and multi-scale mixing. A neural network learns to reverse this operator, generalizing prior PDE-based diffusion approaches as special cases, with the claim that advection improves generated image diversity and quality without affecting the overall color palette.

Significance. If validated, the work bridges fluid dynamics and deep generative modeling by providing a physically motivated generalization of diffusion corruption processes, potentially enabling better control over coherent motion and mixing effects. The use of dimensionless numbers and a custom Lattice Boltzmann implementation offers a reproducible numerical foundation that could inspire further cross-disciplinary methods.

major comments (2)
  1. [§4 (Generative Process)] §4 (Generative Process): The reverse step is presented as a neural network learning to invert the coupled advection-diffusion operator, but no explicit reverse PDE is derived and the loss does not appear to incorporate the stochastic velocity field or advective transport terms. This is load-bearing for the central claim, as standard U-Net denoisers may approximate the inversion in a biased manner that fails to undo coherent motion, risking artifacts or reduced diversity as highlighted by the stress-test concern.
  2. [Results section] Results section: The illustrations of improved diversity and quality from advection lack any quantitative metrics, ablation studies (with vs. without advection), error bars, or baseline comparisons to standard diffusion models. Without such evidence the claim that advection enhances outcomes while preserving color fidelity remains unsubstantiated and cannot be assessed for load-bearing impact.
minor comments (2)
  1. [§3 (Forward Process)] Clarify the exact form of the stochastic velocity field generation and how it is sampled during training versus inference to ensure reproducibility.
  2. Add a table or figure caption explicitly listing the Peclet and Fourier number ranges used in experiments.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed feedback on our manuscript. We have carefully reviewed each major comment and provide point-by-point responses below. Where revisions are warranted, we outline the specific changes planned for the next version of the paper.

read point-by-point responses

  1. Referee: [§4 (Generative Process)] The reverse step is presented as a neural network learning to invert the coupled advection-diffusion operator, but no explicit reverse PDE is derived and the loss does not appear to incorporate the stochastic velocity field or advective transport terms. This is load-bearing for the central claim, as standard U-Net denoisers may approximate the inversion in a biased manner that fails to undo coherent motion, risking artifacts or reduced diversity as highlighted by the stress-test concern.

    Authors: We thank the referee for this observation. The current manuscript trains the network via a denoising objective on pairs generated by the full forward advection-diffusion process (including stochastic velocities), so the learned mapping implicitly inverts both transport and diffusion. An explicit reverse PDE is not derived because the stochastic velocity fields preclude a simple closed-form adjoint; the network instead learns the inversion empirically while being conditioned on the velocity field. We agree that additional clarification would strengthen the presentation and will revise §4 to (i) provide a brief derivation of the deterministic reverse advection-diffusion equation for intuition and (ii) explicitly state how the training loss accounts for advective terms through velocity conditioning. This addresses the potential for biased inversion without altering the core method. revision: partial

  2. Referee: [Results section] The illustrations of improved diversity and quality from advection lack any quantitative metrics, ablation studies (with vs. without advection), error bars, or baseline comparisons to standard diffusion models. Without such evidence the claim that advection enhances outcomes while preserving color fidelity remains unsubstantiated and cannot be assessed for load-bearing impact.

    Authors: We agree that the current results rely on qualitative illustrations and that quantitative support is required to substantiate the claims. In the revised manuscript we will expand the Results section to include: FID and perceptual quality metrics, diversity measures (e.g., average pairwise LPIPS), color-fidelity metrics (histogram intersection and palette variance), ablation studies with and without the advection term, error bars from multiple independent runs, and direct comparisons against DDPM and prior PDE-based baselines. These additions will allow readers to evaluate the load-bearing impact of advection on diversity, quality, and color preservation. revision: yes

Circularity Check

0 steps flagged

No significant circularity; novel PDE generalization with independent forward process and empirical reverse

full rationale

The paper proposes a new forward corruption operator based on coupled advection-diffusion PDE with stochastic velocity fields, implemented numerically via a custom Lattice Boltzmann solver. It positions this as a generalization where prior diffusion methods emerge as special cases (e.g., by setting advection to zero). The generative step trains a neural network to invert the operator, which is presented as an empirical learning task rather than a derived prediction or self-referential fit. No load-bearing step reduces by construction to fitted inputs or self-citations; the central claim rests on the physical motivation of the new PDE and the NN's ability to learn the inverse, which is externally verifiable through image quality metrics. This is self-contained against external benchmarks like standard diffusion models.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard PDE theory for advection-diffusion, the numerical accuracy of the Lattice Boltzmann method for image data, and the assumption that fluid-like corruption benefits generative reversal.

free parameters (1)
  • Peclet and Fourier numbers
    Dimensionless control parameters that set the relative strength of advection versus diffusion in the corruption process.
axioms (1)
  • domain assumption The advection-diffusion PDE with added Gaussian noise and stochastic velocity fields provides a physically motivated and numerically tractable model of image corruption.
    Invoked when stating that the forward pass formulates corruption via this PDE and that previous methods emerge as special cases.

pith-pipeline@v0.9.0 · 5716 in / 1335 out tokens · 46959 ms · 2026-05-19T08:10:11.672750+00:00 · methodology

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Reference graph

Works this paper leans on

40 extracted references · 40 canonical work pages · 8 internal anchors

  1. [1]

    Xlb: A differentiable massively parallel lattice boltzmann library in python

    Mohammadmehdi Ataei and Hesam Salehipour. Xlb: A differentiable massively parallel lattice boltzmann library in python. Comput. Phys. Commun., 300:109187, 2023. 2

    work page 2023

  2. [2]

    Cold diffusion: Inverting arbitrary image transforms without noise

    Arpit Bansal, Eitan Borgnia, Hong-Min Chu, Jie Li, Hamid Kazemi, Furong Huang, Micah Goldblum, Jonas Geiping, and Tom Goldstein. Cold diffusion: Inverting arbitrary image transforms without noise. In Advances in Neural Information Processing Systems, pages 41259–41282. Curran Associates, Inc., 2023. 1, 2

    work page 2023

  3. [3]

    Klie- mank, Dirk Reith, Holger Foysi, and Andreas Krämer

    Mario Christopher Bedrunka, Dominik Wilde, Martin L. Klie- mank, Dirk Reith, Holger Foysi, and Andreas Krämer. Let- tuce: Pytorch-based lattice boltzmann framework. In ISC Workshops, 2021. 2

    work page 2021

  4. [4]

    Hanqun Cao, Cheng Tan, Zhangyang Gao, Yilun Xu, Guangy- ong Chen, Pheng-Ann Heng, and Stan Z. Li. A survey on generative diffusion models. IEEE Transactions on Knowl- edge and Data Engineering, 36:2814–2830, 2022. 2

    work page 2022

  5. [5]

    On the importance of noise scheduling for diffusion models.arXiv preprint arXiv:2301.10972, 2023

    Ting Chen. On the importance of noise scheduling for diffu- sion models. arXiv preprint arXiv:2301.10972, 2023. 2

    work page arXiv 2023

  6. [6]

    Dimakis, and Peyman Milanfar

    Giannis Daras, Mauricio Delbracio, Hossein Talebi, Alexan- dros G. Dimakis, and Peyman Milanfar. Soft diffusion: Score matching for general corruptions, 2022. 1, 2, 4

    work page 2022

  7. [7]

    Diffusion Models Beat GANs on Image Synthesis

    Prafulla Dhariwal and Alex Nichol. Diffusion models beat gans on image synthesis. ArXiv, abs/2105.05233, 2021. 1, 2

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  8. [8]

    J. C. H. Fung, J. C. R. Hunt, N. A. Malik, and R. J. Perkins. Kinematic simulation of homogeneous turbulence by un- steady random fourier modes. Journal of Fluid Mechanics, 236:281–318, 1992. 4

    work page 1992

  9. [9]

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

    Martin Heusel, Hubert Ramsauer, Thomas Unterthiner, Bern- hard Nessler, and Sepp Hochreiter. GANs trained by a two time-scale update rule converge to a local nash equilibrium. In Advances in Neural Information Processing Systems, 2017. 7

    work page 2017

  10. [10]

    Classifier-Free Diffusion Guidance

    Jonathan Ho. Classifier-free diffusion guidance. ArXiv, abs/2207.12598, 2022. 2

    work page internal anchor Pith review Pith/arXiv arXiv 2022

  11. [11]

    Jonathan Ho, Ajay Jain, and P. Abbeel. Denoising diffusion probabilistic models. ArXiv, abs/2006.11239, 2020. 1, 2

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  12. [12]

    Blurring diffusion models

    Emiel Hoogeboom and Tim Salimans. Blurring diffusion models. arXiv preprint arXiv:2209.05557, 2022. 1, 2, 3, 4, 7, 8

    work page arXiv 2022

  13. [13]

    Taichi: a language for high- performance computation on spatially sparse data structures

    Yuanming Hu, Tzu-Mao Li, Luke Anderson, Jonathan Ragan- Kelley, and Frédo Durand. Taichi: a language for high- performance computation on spatially sparse data structures. ACM Transactions on Graphics (TOG), 38(6):201, 2019. 5

    work page 2019

  14. [14]

    Blue noise for diffusion models

    Xingchang Huang, Corentin Salaun, Cristina Vasconcelos, Christian Theobalt, Cengiz Oztireli, and Gurprit Singh. Blue noise for diffusion models. In ACM SIGGRAPH 2024 Con- ference Papers, New York, NY , USA, 2024. Association for Computing Machinery. 2

    work page 2024

  15. [15]

    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. ArXiv, abs/2206.00364, 2022. 2

    work page internal anchor Pith review Pith/arXiv arXiv 2022

  16. [16]

    Analyzing and

    Tero Karras, Miika Aittala, Jaakko Lehtinen, Janne Hellsten, Timo Aila, and Samuli Laine. Analyzing and improving the training dynamics of diffusion models. arXiv preprint arXiv:2312.02696, 2023. 2

    work page arXiv 2023

  17. [17]

    Kingma, Tim Salimans, Ben Poole, Prafulla Dhari- wal, Xi Chen, and Tim Chen

    Diederik P. Kingma, Tim Salimans, Ben Poole, Prafulla Dhari- wal, Xi Chen, and Tim Chen. Variational diffusion models. In Advances in Neural Information Processing Systems, 2021. 2

    work page 2021

  18. [18]

    Smith, Ayya Alieva, Qing Wang, Michael P

    Dmitrii Kochkov, Jamie A. Smith, Ayya Alieva, Qing Wang, Michael P. Brenner, and Stephan Hoyer. Machine learn- ing–accelerated computational fluid dynamics. Proceedings of the National Academy of Sciences of the United States of America, 118, 2021. 2

    work page 2021

  19. [19]

    The Lattice Boltzmann Method

    Timm Krüger, Halim Kusumaatmaja, Alexandr Kuzmin, Or- est Shardt, Goncalo Silva, and Erlend Magnus Viggen. The Lattice Boltzmann Method . Springer, Cham, first edition,

    work page

  20. [20]

    Adjoint lattice boltzmann for topology optimization on multi-gpu architecture

    Łaniewski-Wołłk and Rokicki. Adjoint lattice boltzmann for topology optimization on multi-gpu architecture. Comput- ers and Mathematics with and Applications, 71(3):833–848,

    work page

  21. [21]

    Accuracy and per- formance of the lattice boltzmann method with 64-bit, 32-bit, and customized 16-bit number formats

    Moritz Lehmann, Mathias J Krause, Giorgio Amati, Marcello Sega, Jens Harting, and Stephan Gekle. Accuracy and per- formance of the lattice boltzmann method with 64-bit, 32-bit, and customized 16-bit number formats. Physical Review E, 106(1):015308, 2022. 2

    work page 2022

  22. [22]

    Fourier Neural Operator for Parametric Partial Differential Equations

    Zong-Yi Li, Nikola B. Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew M. Stuart, and Anima Anandkumar. Fourier neural operator for parametric partial differential equations. ArXiv, abs/2010.08895, 2020. 2

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  23. [23]

    Yaron Lipman, Ricky T. Q. Chen, Heli Ben-Hamu, Maxi- milian Nickel, and Matt Le. Flow matching for generative modeling, 2023. 8

    work page 2023

  24. [24]

    Reliable fidelity and diversity metrics for generative models

    Muhammad Ferjad Naeem, Seong Joon Oh, Youngjung Uh, Yunjey Choi, and Jaejun Yoo. Reliable fidelity and diversity metrics for generative models. In International conference on machine learning, pages 7176–7185. PMLR, 2020. 7

    work page 2020

  25. [25]

    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,

    work page

  26. [26]

    Convolutional neural operators for robust and accurate learning of pdes, 2023

    Bogdan Raoni ´c, Roberto Molinaro, Tim De Ryck, Tobias Rohner, Francesca Bartolucci, Rima Alaifari, Siddhartha Mishra, and Emmanuel de Bézenac. Convolutional neural operators for robust and accurate learning of pdes, 2023. 2

    work page 2023

  27. [27]

    Severi Rissanen, Markus Heinonen, and A. Solin. Gen- erative modelling with inverse heat dissipation. ArXiv, abs/2206.13397, 2022. 1, 2, 3, 5, 6, 8

    work page arXiv 2022

  28. [28]

    High-resolution image synthesis with latent diffusion models

    Robin Rombach, Andreas Blattmann, Dominik Lorenz, Patrick Esser, and Björn Ommer. High-resolution image synthesis with latent diffusion models. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2022. 2

    work page 2022

  29. [29]

    U-net: Convolutional networks for biomedical image segmentation

    Olaf Ronneberger, Philipp Fischer, and Thomas Brox. U-net: Convolutional networks for biomedical image segmentation. In Medical Image Computing and Computer-Assisted Inter- vention (MICCAI), pages 234–241. Springer, 2015. 6

    work page 2015

  30. [30]

    Fleet, and Mohammad Norouzi

    Chitwan Saharia, Jonathan Ho, William Chan, Tim Sali- mans, David J. Fleet, and Mohammad Norouzi. Image super- resolution via iterative refinement. IEEE Transactions on Pattern Analysis and Machine Intelligence, 45:4713–4726,

    work page

  31. [31]

    Progressive distillation for fast sampling of diffusion models

    Tim Salimans and Jonathan Ho. Progressive distillation for fast sampling of diffusion models. In International Confer- ence on Learning Representations (ICLR), 2022. 2

    work page 2022

  32. [32]

    Animating rotation with quaternion curves

    Ken Shoemake. Animating rotation with quaternion curves. SIGGRAPH Comput. Graph., 19(3):245–254, 1985. 7

    work page 1985

  33. [33]

    Deep Unsupervised Learning using Nonequilibrium Thermodynamics

    Jascha Narain Sohl-Dickstein, Eric A. Weiss, Niru Ma- heswaranathan, and Surya Ganguli. Deep unsupervised learning using nonequilibrium thermodynamics. ArXiv, abs/1503.03585, 2015. 1, 2

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  34. [34]

    Denoising Diffusion Implicit Models

    Jiaming Song, Chenlin Meng, and Stefano Ermon. Denoising diffusion implicit models. ArXiv, abs/2010.02502, 2020. 2

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  35. [35]

    Generative modeling by estimating gradients of the data distribution

    Yang Song and Stefano Ermon. Generative modeling by estimating gradients of the data distribution. In Advances in Neural Information Processing Systems, 2019. 2

    work page 2019

  36. [36]

    Score-Based Generative Modeling through Stochastic Differential Equations

    Yang Song, Jascha Narain Sohl-Dickstein, Diederik P. Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole. Score-based generative modeling through stochastic differen- tial equations. ArXiv, abs/2011.13456, 2020. 1, 2, 3

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  37. [37]

    Csdi: Conditional score-based diffusion models for probabilistic time series imputation

    Yusuke Tashiro, Jiaming Song, Yang Song, and Stefano Er- mon. Csdi: Conditional score-based diffusion models for probabilistic time series imputation. In Neural Information Processing Systems, 2021. 2

    work page 2021

  38. [38]

    D.C. Wilcox. Turbulence Modeling for CFD. Number v. 1 in Turbulence Modeling for CFD. DCW Industries, 2006. 4

    work page 2006

  39. [39]

    Diffusion models: A comprehensive survey of methods and applications

    Ling Yang, Zhilong Zhang, Shenda Hong, Runsheng Xu, Yue Zhao, Yingxia Shao, Wentao Zhang, Ming-Hsuan Yang, and Bin Cui. Diffusion models: A comprehensive survey of methods and applications. ACM Computing Surveys, 56:1 – 39, 2022. 2

    work page 2022

  40. [40]

    Efros, Eli Shechtman, and Oliver Wang

    Richard Zhang, Phillip Isola, Alexei A. Efros, Eli Shechtman, and Oliver Wang. The unreasonable effectiveness of deep features as a perceptual metric, 2018. 7 Appendix In this appendix, §A contains hyperparameters and experiment setup. §B contains additional samples and interpolations for FFHQ-128, MNIST and LSUN Church datasets. §C contains solver implem...

    work page 2018