Pith. sign in

REVIEW 3 major objections 7 minor 1 cited by

Classifier-Free Guidance: From High-Dimensional Analysis to Generalized Guidance Forms

T0 review · 3 major / 7 minor · reviewed 2026-08-08 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read In high and infinite dimensions, classifier-free guidance accurately reproduces the target conditional distribution, and the same property holds for a broad family of non-linear guidances.

desk verdict Important and useful paper, but the proof of the central blessing-of-dimensionality claim has a real gap near speciation; still deserves a serious referee. read the letter →

arxiv 2502.07849 v2 pith:UMMKF6OE submitted 2025-02-11 cs.LG cs.AIstat.ML

Krunoslav Lehman Pavasovic , Jakob Verbeek , Giulio Biroli , Marc Mezard This is my paper · ORCID
classification cs.LGcs.AIstat.ML
keywords classifier-freeguidancediffusionmodelsflowmatchinghigh-dimensionalstatisticsGaussianmixturespeciationtimepower-lawblessingofdimensionality
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

This paper sets out to determine what distribution classifier-free guidance (CFG) actually samples from when the data live in very high dimension. It claims that the distortions that prior work identified in one and few dimensions—the mean overshoot toward the class boundary and the shrinkage of variance—vanish as the dimension grows, and that in the infinite-dimensional limit CFG exactly reproduces the target conditional distribution. The mechanism is timing: CFG only exerts force during the early, pre-speciation regime of the backward diffusion, and just before the trajectory commits to a class, the guided path realigns with the unguided conditional path. The paper further claims that any guidance whose extra term is a function of the conditional minus unconditional score vanishes in the late regime, so a whole family of non-linear guidances, including a proposed power-law version, inherits the same blessing of dimensionality while improving robustness, fidelity, and diversity in practice.

What carries the argument

The central object is the speciation time $t_s=\tfrac12\log d$ of the backward diffusion in a high-dimensional two-Gaussian mixture. It separates Regime I, where the noise-dominated trajectory has not yet committed to a class, from Regime II, where it has. CFG's added score term is active only in Regime I; in Regime II it vanishes as $d\to\infty$, so all effects of guidance on the final distribution must enter through the pre-speciation dynamics. The proof then uses the explicit backward SDE for the projection $q=\vec x\cdot \vec m/|\vec m|$, whose solution in late Regime I loses memory of its initial condition exponentially fast, producing the realignment statement. This machinery does the work of converting the presence of CFG into a harmless speed-up.

What would settle it

Run the exact-score two-Gaussian backward process with CFG at increasing dimensions such as $d=10,100,1000$ and measure the mean and variance of $q=\vec x\cdot \vec m/|\vec m|$ at $t=0$ against the target; if the relative overshoot or variance gap stops shrinking or plateaus, path realignment fails. Alternatively, measure the CFG score difference $|\vec S_t^{\text{CFG}}(\vec x,c)-\vec S_t(\vec x,c)|$ along typical trajectories after speciation: the theory says it is exponentially small in $d$, so a direct simulation showing it remains of order one for large $d$ would refute Result III and with it the blessing-of-dimensionality claim.

Watch

Extended reading notes

Core claim

The paper claims that, for diffusion on a two-Gaussian mixture with exact scores, the distribution sampled by CFG converges to the exact conditional target distribution as $d\to\infty$. The argument has three steps, stated as Results I–III. Before the speciation time $t_s=\tfrac12\log d$, CFG adds a potential that pushes trajectories toward the target class, accelerating class selection; in the late part of this first regime the CFG force becomes exponentially small, and the backward SDE forgets its earlier dependence on the guidance, so guided and unguided paths realign; after speciation the class is locked in, the conditional and unconditional scores coincide, and the CFG correction $c-\tanh(\vec x\cdot \vec m e^{-t}/\Gamma_t)$ vanishes. Thus CFG changes the speed of class selection but not the terminal distribution. Finite-dimensional corrections are computed: mean overshoot of relative order $1/\sqrt{d}$ and variance shrinkage caused by the more confining effective potential. The same Regime I/Regime II logic is then used to exhibit a family of guidance functions $\phi_t(s)$ with $\lim_{s\to0} s\phi_t(s)=0$, including power-law CFG $\phi_t(s)=\omega s^\alpha$, that share the asymptotic correctness and show improved fidelity and diversity on class-conditional and text-to-image models.

Load-bearing premise

The whole high-dimensional result rests on the assumption that the extra push CFG applies in the early dynamical regime is entirely forgotten before the trajectory commits to a class; if even a trace of that push survives into the class-forming regime, the generated distribution stays shifted and narrowed no matter how large the dimension is.

Editorial extensions

If this is right

  • In the $d\to\infty$ limit with exact scores, CFG sampling is asymptotically unbiased: observed overshoot and variance shrinkage are finite-dimensional effects, not intrinsic to the guidance rule.
  • CFG's only role is to accelerate class selection before speciation; after speciation it is inert, so its strength $\omega$ can be raised without moving the asymptotic distribution.
  • Any guidance of the form $\vec S_t^{\text{CFG-NL}}=\vec S_t(\vec x,c)+[\vec S_t(\vec x,c)-\vec S_t(\vec x)]\phi_t(|\vec S_t(\vec x,c)-\vec S_t(\vec x)|)$ with $\lim_{s\to0}s\phi_t(s)=0$ inherits asymptotic correctness, unifying limited-interval CFG, weight schedulers, and other linear variants as members of one family.
  • The finite-$d$ mean overshoot has relative amplitude of order $1/\sqrt{d}$, so in real image dimensions the residual bias should be small relative to the target scale.
  • Power-law CFG with positive $\alpha$ improves FID, precision, and recall over standard CFG and over the strongest competing variants across class-conditional and text-to-image models, with increased robustness to the guidance strength $\omega$.

Reading between the lines

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

  • The theory uses exact scores and the authors explicitly leave open why CFG helps in practice; I infer that the same Regime-I analysis could be re-run with biased score estimates to predict which non-linearities compensate for estimator errors, a testable extension.
  • The proof is for Gaussian mixtures, but the regime structure is expected on manifolds and hierarchical data; I infer that the blessing of dimensionality should hold for any data model with a sharp speciation transition, so measuring real-model score differences in Regime II and checking whether they decay with data scale is a natural test.
  • The power-law exponent $\alpha$ is treated as a constant hyperparameter; I infer that a time-dependent $\alpha(t)$ or a learned $\phi_t$ could outperform the constant-exponent version by shaping the Regime-I push more precisely, since the framework permits arbitrary non-linearities.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 7 minor

Summary. This paper studies classifier-free guidance (CFG) for diffusion models in a high-dimensional two-Gaussian mixture setting with exact scores. The central claim is a "blessing-of-dimensionality" result: the mean overshoot and variance shrinkage induced by CFG vanish as the ambient dimension d grows, so that in the infinite-dimensional limit CFG generates exactly the target conditional distribution. The argument is built on a dynamical-regime analysis borrowed from Biroli et al. (2024), distinguishing a pre-speciation regime (Regime I) in which CFG acts and a post-speciation regime (Regime II) in which CFG is claimed to be inert. The paper further proposes a family of non-linear guidance forms, notably power-law CFG, and reports experiments on class-conditional ImageNet models and text-to-image models showing improved fidelity and robustness relative to standard CFG.

Significance. If rigorously established, the blessing-of-dimensionality result would be conceptually important: it would reconcile the well-documented finite-dimensional distortions of CFG with its practical success in high-dimensional image generation, and it would justify a broad family of guidance schemes. The paper is also valuable for its explicit score formulas and for the interrupted-guidance calculation in Appendix D, which provides a quantitative finite-d estimate of the mean shift. The experimental campaign is extensive, covering several large-scale diffusion and flow-matching models. However, the central theoretical claim is not fully proven: the paper does not establish distributional convergence of the CFG-guided process to the target law, and the mechanism invoked for path realignment is quantitatively incorrect for typical trajectories. This gap is load-bearing for the abstract's claim that CFG 'accurately reproduces the target distribution' as d grows.

major comments (3)
  1. [Sec. 4.2 and App. B.2, Eq. (5)] The justification of Result II rests on the assertion that in late Regime I the CFG force gives 'exponentially small corrections'. This is not true along typical paths. At forward time t = ts + δ with δ = O(1), the unguided conditional path has q(t) = √d e^{-t}, so q e^{-(t-ts)} = e^{-2δ} = O(1). Hence 1 - tanh(q e^{-(t-ts)}) is O(1), not exponentially small, and the CFG force term ω e^{-(t-ts)}(1 - tanh(...)) in Eq. (5) is O(ω). The linear SDE dq = -q + 2e^{-(t-ts)} + dη therefore does not describe the actual dynamics in the O(1)-window around speciation where class commitment is made, and the claimed realignment of CFG paths with unguided conditional paths is not established by the argument given.
  2. [App. D, Eqs. (27) and (35)] The rigorous finite-dimension calculation in Appendix D controls only the mean of the guided process. Equation (27) shows that if CFG is switched off at t1 = ts, the final mean shift at t = 0 is O(d^{-1/2}), but no bound is provided for the variance or for the full distribution of q(0). Equation (35) shows that CFG contracts the variance in the always-on protocol, but it does not analyze the interrupted protocol or show that the variance perturbation decays as d→∞. Without such a distributional control, the paper does not prove that the CFG-induced law converges to the target law in the infinite-d limit.
  3. [Sec. 4.2, Result II and Sec. 5.2] The abstract and Section 1 state that CFG 'accurately reproduces the target distribution' in infinite dimensions, but the results proven in the body are substantially weaker: a mean-level statement in App. D and an exponential-smallness claim in Regime II that holds only for typical paths already committed to the correct class. The non-linear guidance family in Section 5.2 inherits this gap, since its high-dimensional correctness is justified by the same realignment argument. The paper should either supply a rigorous distributional convergence proof (e.g., via coupling or a Wasserstein bound on the interrupted-guidance protocol) or clearly state the blessing-of-dimensionality conclusion as a conjecture supported by numerics and a proven mean-shift bound.
minor comments (7)
  1. [Sec. 1] Typo: 'Orstein-Uhlenbeck' should be 'Ornstein-Uhlenbeck'.
  2. [Sec. 5.3] Typo: 'hyerparameter' should be 'hyperparameter'.
  3. [App. G] Typo: 'theis non-linear scheme' should be 'this non-linear scheme'.
  4. [App. F] Typo: 'experimenet' should be 'experiment'.
  5. [Sec. 4.2 and App. B] The notation t is used both for forward time and, after the sentence 'we omit the dependency t(τ) for backward time and use t hereafter', for backward time. This makes Eqs. (5)-(6) confusing; consider using a distinct symbol such as s for backward time throughout.
  6. [Table 1] The caption says arrows indicate improvement, but it is not specified whether the comparison for rows like 'Power-law CFG (Ours)' is against standard CFG or against the corresponding baseline (e.g., CADS for the last row). Please state the reference method explicitly.
  7. [App. F.2] The normalization of the CFG-added term by division with σ(t') + 1 is introduced without explanation in the main text; please provide a justification or move the rationale to the main text.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: the derivation is self-contained relative to the externally defined two-Gaussian model, and the self-cited speciation framework does not presuppose the CFG conclusion.

full rationale

The paper's target distribution is defined externally as a two-Gaussian mixture, and the CFG score is the algebraic combination of the exact conditional and unconditional scores (Eq. 3), with no fitted parameters; the high-dimensional claim is therefore not a renamed fit or a fitted input called a prediction. The derivation chain (Eqs. 4-6, App. B) uses the same authors' prior speciation framework (Biroli and Mezard 2023; Biroli et al. 2024) for the Regime I/II decomposition and for the assertion that q becomes O(sqrt d) in late Regime I. Although this citation is load-bearing, the cited results concern unguided diffusion of the same Gaussian mixture and do not include the CFG conclusion, so they are independent support rather than a circular premise. The non-linear guidance family in Eq. (7) is deliberately constructed so that the extra term vanishes when the score difference tends to zero; this is a design choice with a stated sufficient condition, not a prediction derived from the conclusion. The real reviewer concern is a correctness gap, not a circularity: App. B.2 asserts without proof that the CFG term is exponentially small in late Regime I, while along typical paths q e^{-(t-ts)} is O(1) near speciation, so the distributional realignment is not established. This omitted proof should be weighed as a correctness risk, but it does not make the paper's derivation equivalent to its inputs by definition.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The central derivation assumes a two-Gaussian mixture with exact scores and relies on the speciation framework of the authors' earlier work (Biroli et al. 2024). No free parameter is fitted in the theory; ω is an input and α is tuned only in the experiments. No new entities are introduced.

free parameters (2)
  • α (power-law exponent) = e.g., 0.75 (DiT/XL-2), 0.85 (EDM2-S), 0.6 (MMDiT)
    New hyperparameter of the proposed non-linear CFG; tuned on validation FID in (0.3, 0.95). The theoretical claims hold for any α > -1, but the experimental improvements depend on the chosen value.
  • ω (guidance strength) = tuned per model, e.g., 4.85 (DiT/XL-2), 11.4 (EDM2-S), 7.0 (MMDiT)
    Standard CFG hyperparameter, selected by grid search. It is an input to the theory, not a fitted constant, but it is tuned in the experiments.
assumptions (5)
  • domain assumption The data distribution is a two-Gaussian mixture with equal weights, means ±m, isotropic variance σ², and |m|² = d μ̃² with μ̃, σ of order one.
    Sec. 4.1. The entire derivation is carried out for this model.
  • domain assumption Dynamical regimes I and II with a sharp speciation time ts = (1/2) log d, as established by Biroli et al. (2024).
    Sec. 3.2 and App. A. The CFG analysis relies on this regime decomposition.
  • domain assumption Exact score functions are available for the theoretical analysis.
    Sec. 4.1. The paper assumes no score estimation error, which it acknowledges in the limitations.
  • standard math Standard diffusion/backward-SDE theory: the reverse process with the exact score generates the target distribution.
    Eq. (1)-(2) and background.
  • domain assumption Real-world data and learned scores exhibit the same two-regime structure as the GMM.
    Sec. 4.1 and Sec. 5. Used to transfer the GMM result to ImageNet/text-to-image models; not proven for learned scores.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Classifier-Free Guidance: From High-Dimensional Analysis to Generalized Guidance Forms." pith.science (2026). https://pith.science/paper/UMMKF6OE

@misc{pith2026250207849,
  author       = {Pith},
  title        = {Pith review of: Classifier-Free Guidance: From High-Dimensional Analysis to Generalized Guidance Forms},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UMMKF6OE}},
  note         = {Machine review of arXiv:2502.07849}
}
read the original abstract

Classifier-Free Guidance (CFG) is a widely adopted technique in diffusion and flow-based generative models, enabling high-quality conditional generation. A key theoretical challenge is characterizing the distribution induced by CFG, particularly in high-dimensional settings relevant to real-world data. Previous works have shown that CFG modifies the target distribution, steering it towards a distribution sharper than the target one, more shifted towards the boundary of the class. In this work, we provide a high-dimensional analysis of CFG, showing that these distortions vanish as the data dimension grows. We present a blessing-of-dimensionality result demonstrating that in sufficiently high and infinite dimensions, CFG accurately reproduces the target distribution. Using our high-dimensional theory, we show that there is a large family of guidances enjoying this property, in particular non-linear CFG generalizations. We study a simple non-linear power-law version, for which we demonstrate improved robustness, sample fidelity and diversity. Our findings are validated with experiments on class-conditional and text-to-image generation using state-of-the-art diffusion and flow-matching models.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Conditional Diffusion Models with Classifier-Free Gibbs-like Guidance

    cs.LG 2025-05 conditional novelty 7.0 of 10

    CFG is missing a Rényi divergence repulsion term, and the new CFG IG sampler uses iterative noising and denoising to preserve diversity while improving conditional generation quality.

Reference graph

Works this paper leans on

49 extracted references · 17 canonical work pages · cited by 1 Pith paper

  1. [1]

    Memorization and generalization in generative diffusion under the manifold hypothesis.arXiv preprint arXiv:2502.09578,

    Beatrice Achilli, Luca Ambrogioni, Carlo Lucibello, Marc Mézard, and Enrico Ventura. Memorization and generalization in generative diffusion under the manifold hypothesis.arXiv preprint arXiv:2502.09578,

    arXiv

  2. [4]

    Consistency-diversity-realism Pareto fronts of conditional image generative models.arXiv preprint, 2406.10429,

    Pietro Astolfi, Marlene Careil, Melissa Hall, Oscar Mañas, Matthew Muckley, Jakob Verbeek, Adriana Romero Soriano, and Michal Drozdzal. Consistency-diversity-realism Pareto fronts of conditional image generative models.arXiv preprint, 2406.10429,

    arXiv

  3. [6]

    An expectation-maximization algorithm for training clean diffusion models from corrupted observations.arXiv preprint arXiv:2407.01014,

    Weimin Bai, Yifei Wang, Wenzheng Chen, and He Sun. An expectation-maximization algorithm for training clean diffusion models from corrupted observations.arXiv preprint arXiv:2407.01014,

    arXiv

  4. [7]

    Generative diffusion in very large dimensions.Journal of Statistical Mechanics: Theory and Experiment, 2023(9):093402,

    Giulio Biroli and Marc Mézard. Generative diffusion in very large dimensions.Journal of Statistical Mechanics: Theory and Experiment, 2023(9):093402,

    work page 2023

  5. [8]

    Dynamical regimes of diffusion models.arXiv preprint arXiv:2402.18491,

    Giulio Biroli, Tony Bonnaire, Valentin De Bortoli, and Marc Mézard. Dynamical regimes of diffusion models.arXiv preprint arXiv:2402.18491,

    arXiv

  6. [9]

    Classifier-free guidance is a predictor-corrector.arXiv preprint arXiv:2408.09000,

    Arwen Bradley and Preetum Nakkiran. Classifier-free guidance is a predictor-corrector.arXiv preprint arXiv:2408.09000,

    arXiv

  7. [10]

    As each framework uses a separate time reparameterization, the x-axis needs to be recalculated accordingly. For the EDM2 framework (Karras et al., 2022), this can be done as follows: given a noise scheduleσ(t), the reparameterization can be calculated ast′(t) = (1/2) log ( 1 +σ2(t) ) , assuming thats(t) =

    work page 2022

  8. [11]

    Cfg++: Manifold-constrained classifier free guidance for diffusion models.arXiv preprint arXiv:2406.08070,

    Hyungjin Chung, Jeongsol Kim, Geon Yeong Park, Hyelin Nam, and Jong Chul Ye. Cfg++: Manifold-constrained classifier free guidance for diffusion models.arXiv preprint arXiv:2406.08070,

    arXiv

Show all 49 references
  1. [12]

    Analysis of learning a flow-based generative model from limited sample complexity.arXiv preprint arXiv:2310.03575,

    Hugo Cui, Florent Krzakala, Eric Vanden-Eijnden, and Lenka Zdeborová. Analysis of learning a flow-based generative model from limited sample complexity.arXiv preprint arXiv:2310.03575,

    arXiv

  2. [13]

    Imagenet: A large-scale hierarchical image database

    Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei. Imagenet: A large-scale hierarchical image database. In 2009 IEEE conference on computer vision and pattern recognition, pages 248–255. Ieee,

    2009

  3. [14]

    Analysis of diffusion models for manifold data.arXiv preprint arXiv:2502.04339,

    Anand Jerry George, Rodrigo Veiga, and Nicolas Macris. Analysis of diffusion models for manifold data.arXiv preprint arXiv:2502.04339,

  4. [15]

    Evalgim: A library for evaluating generative image models.arXiv preprint arXiv:2412.10604,

    11 Melissa Hall, Oscar Mañas, Reyhane Askari, Mark Ibrahim, Candace Ross, Pietro Astolfi, Tariq Berrada Ifriqi, Marton Havasi, Yohann Benchetrit, Karen Ullrich, et al. Evalgim: A library for evaluating generative image models.arXiv preprint arXiv:2412.10604,

    arXiv

  5. [18]

    Guiding a diffusion model with a bad version of itself.arXiv preprint arXiv:2406.02507, 2024a

    Tero Karras, Miika Aittala, Tuomas Kynkäänniemi, Jaakko Lehtinen, Timo Aila, and Samuli Laine. Guiding a diffusion model with a bad version of itself.arXiv preprint arXiv:2406.02507, 2024a. Tero Karras, Miika Aittala, Jaakko Lehtinen, Janne Hellsten, Timo Aila, and Samuli Lain...

    arXiv

  6. [19]

    Critical windows: non-asymptotic theory for feature emergence in diffusion models.arXiv preprint arXiv:2403.01633,

    Marvin Li and Sitan Chen. Critical windows: non-asymptotic theory for feature emergence in diffusion models.arXiv preprint arXiv:2403.01633,

    arXiv

  7. [20]

    Unraveling the smoothness properties of diffusion models: A gaussian mixture perspective.arXiv preprint arXiv:2405.16418,

    Yingyu Liang, Zhenmei Shi, Zhao Song, and Yufa Zhou. Unraveling the smoothness properties of diffusion models: A gaussian mixture perspective.arXiv preprint arXiv:2405.16418,

    arXiv

  8. [21]

    Microsoft coco: Common objects in context

    Tsung-Yi Lin, Michael Maire, Serge Belongie, James Hays, Pietro Perona, Deva Ramanan, Piotr Dollár, and C Lawrence Zitnick. Microsoft coco: Common objects in context. InComputer Vision–ECCV 2014: 13th European Conference, Zurich, Switzerland, September 6-12, 2014, Proceedings,...

    2014

  9. [23]

    Flow matching guide and code.arXiv preprint arXiv:2412.06264,

    Yaron Lipman, Marton Havasi, Peter Holderrieth, Neta Shaul, Matt Le, Brian Karrer, Ricky TQ Chen, David Lopez-Paz, Heli Ben-Hamu, and Itai Gat. Flow matching guide and code.arXiv preprint arXiv:2412.06264,

    arXiv

  10. [24]

    Flow straight and fast: Learning to generate and transfer data with rectified flow.arXiv preprint arXiv:2209.03003,

    Xingchao Liu, Chengyue Gong, and Qiang Liu. Flow straight and fast: Learning to generate and transfer data with rectified flow.arXiv preprint arXiv:2209.03003,

    arXiv

  11. [25]

    Glide: Towards photorealistic image generation and editing with text-guided diffusion models.arXiv preprint arXiv:2112.10741,

    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,

    arXiv

  12. [26]

    Cads: Unleashing the diversity of diffusion models through condition-annealed sampling.arXiv preprint arXiv:2310.17347,

    Seyedmorteza Sadat, Jakob Buhmann, Derek Bradley, Otmar Hilliges, and Romann M Weber. Cads: Unleashing the diversity of diffusion models through condition-annealed sampling.arXiv preprint arXiv:2310.17347,

    arXiv

  13. [29]

    Manifolds, random matrices and spectral gaps: The geometric phases of generative diffusion.arXiv preprint arXiv:2410.05898,

    Enrico Ventura, Beatrice Achilli, Gianluigi Silvestri, Carlo Lucibello, and Luca Ambrogioni. Manifolds, random matrices and spectral gaps: The geometric phases of generative diffusion.arXiv preprint arXiv:2410.05898,

    arXiv

  14. [31]

    Theoretical insights for diffusion guidance: A case study for gaussian mixture models.arXiv preprint arXiv:2403.01639,

    Yuchen Wu, Minshuo Chen, Zihao Li, Mengdi Wang, and Yuting Wei. Theoretical insights for diffusion guidance: A case study for gaussian mixture models.arXiv preprint arXiv:2403.01639,

    arXiv

  15. [32]

    Rectified diffusion guidance for conditional generation

    Mengfei Xia, Nan Xue, Yujun Shen, Ran Yi, Tieliang Gong, and Yong-Jin Liu. Rectified diffusion guidance for conditional generation. arXiv preprint arXiv:2410.18737,

  16. [33]

    Florence- 2: Advancing a unified representation for a variety of vision tasks (2023).URL https://arxiv

    Bin Xiao, Haiping Wu, Weijian Xu, Xiyang Dai, Houdong Hu, Yumao Lu, Michael Zeng, Ce Liu, and Lu Yuan. Florence- 2: Advancing a unified representation for a variety of vision tasks (2023).URL https://arxiv. org/abs/2311.06242,

    2023 arXiv

  17. [34]

    Nonequilbrium physics of generative diffusion models

    Zhendong Yu and Haiping Huang. Nonequilbrium physics of generative diffusion models. arXiv preprint arXiv:2405.11932,

    arXiv

  18. [35]

    Characteristic guidance: Non-linear correction for DDPM at large guidance scale.arXiv preprint arXiv:2312.07586,

    Candi Zheng and Yuan Lan. Characteristic guidance: Non-linear correction for DDPM at large guidance scale.arXiv preprint arXiv:2312.07586,

    arXiv

  19. [36]

    13 Appendix The supplementary material is structured as follows: • In Section A, we give a brief introduction to related work, focusing on Biroli et al. (2024). • In Section B, we give proofs for two equidistant, symmetric Gaussian mixtures. • In Section C, we present argument...

    2024

  20. [37]

    transverse

    As the process evolves, the emergence of speciation resembles symmetry breaking observed during thermody- namic phase transitions. A common approach to analyzing this phenomenon is to construct a perturbative expansion of the free energy as a function of the field. Therefore, ...

    2024

  21. [38]

    transverse

    In consequence, in Regime I at large times, the SDE just reads: dq =−q + 2e−(tf−ts−τ) +dη(τ), The effect of CFG is to lead to different values ofq when entering this late regime of Regime I. We call these valuesq(τi) and denoteτi the fixed time at which the CFG contribution ca...

    2022

  22. [39]

    Table 2 Assets used for our work

    F Experimental details: Real-world analyses F.1 Assets In Table 2 we list the datasets and models used in our work along with their licensing. Table 2 Assets used for our work. Name License/Link COCO’14 https://www.cocodataset.org ImageNet https://www.image-net.org CC12M https...

    2023

  23. [41]

    The last two plots correspond to the actual trajectories projected onto the target mean +⃗ mfor values ofω∈{ 0., 5., 10., 15., 20.}

    In Figure 2, the first two plots correspond to the histograms of the samples generated using the backward process with dimensionsd∈{ 2, 200} and guidance parameterω∈{ 0, 0.2, 15}, withσ2 = 1, averaged over 10, 000 trajectories. The last two plots correspond to the actual traje...

    2024

  24. [42]

    In Figure 10, we use DiT/XL-2 model trained on 2, 500 and 1000 classes

    at times t1 = 0.69, 1.38, 3.19. In Figure 10, we use DiT/XL-2 model trained on 2, 500 and 1000 classes. For 2 classes, we have selected the same classes as in Biroli et al. (2024), and for the 500 classes we selected the first 500 classes in ImageNet-1K. The x-axis represents ...

    2024

  25. [43]

    The evaluation code relied on EvalGIM library by Hall et al. (2024). 28 Table 3 Hyperparameter configurations used throughout the experiments. (α,ω) DiT/XL-2 EDM2-S Diff. MMDiT CC12m Diff. MDTv2 IMN-1K FM MMDiT COCO FM MMDiT CC12M Standard (0.,1.5) (0 .,1.4) (0 .,1.55) (0 .,1,...

    2024

  26. [44]

    In Table 4 present additional quantitative evaluations of our method, focusing on diversity and coverage metrics (as described in Hall et al

    • Ablation studies showing that Power-Law CFG outperforms standard linear CFG when changing the number of steps (see Tables 5-10) • Sensitivity analysis showing the FID benefit for increasing value ofα (see Section F.4.1, Figures 11-13) • Further qualitative analyses of power-...

    2024

  27. [45]

    As demonstrated in the main manuscript, power-law CFG generally outperforms standard CFG (indicated by arrows in the table)

    and limited-guidance (Kynkäänniemi et al., 2024), which proved to be the most competitive approaches. As demonstrated in the main manuscript, power-law CFG generally outperforms standard CFG (indicated by arrows in the table). Moreover, when combined with CADS and limited-inte...

    2024

  28. [47]

    steps α ω FID (↓) IS (↑) Precision (↑) Recall (↑) sFID (↓) Stand

    0.850 0.771 1.112 0.833 1.091 0.855 0.903 0.783CFG++ (Chung et al., 2024)N/A N/A N/A N/A 1.265 0.859 0.919 0.784 Power-law CFG (Ours) 0.845 (↓) 0.760 (↑) 0.986 (↑) 0.844 (↑) 1.128 (↑) 0.850 (↑) 0.918 (↑) 0.778 (↑)Power-law CFG + Limited (Ours)0.850 (↑) 0.778 (↑) 1.115 (↓) 0.83...

    2024

  29. [48]

    trained on ImageNet-1000 (Deng et al., 2009): randomly selected class withω = 4, using DDPM (Ho et al.,

    2009

  30. [256]

    Diff. MMDiT (T2IM, CC12m) FM MMDiT (T2IM, COCO)Density Coverage Density Coverage Density Coverage Density Coverage Standard (Ho and Salimans, 2022)0.850 0.764 0.951 0.801 1.091 0.840 0.902 0.772Scheduler (Wang et al., 2024)0.867 0.780 1.117 0.790 1.266 0.860 0.908 0.795Limited...

    2022

  31. [2009]

    Analysis of classifier-free guidance weight schedulers.arXiv preprint, 2404.13040,

    Xi Wang, Nicolas Dufour, Nefeli Andreou, Marie-Paule Cani, Victoria Fernández Abrevaya, David Picard, and Vicky Kalogeiton. Analysis of classifier-free guidance weight schedulers.arXiv preprint, 2404.13040,

    arXiv

  32. [2014]

    Flow matching for generative modeling

    Yaron Lipman, Ricky TQ Chen, Heli Ben-Hamu, Maximilian Nickel, and Matt Le. Flow matching for generative modeling. arXiv preprint arXiv:2210.02747,

    arXiv

  33. [2015]

    Yang Song and Stefano Ermon

    https://arxiv.org/abs/1503.03585. Yang Song and Stefano Ermon. Generative modeling by estimating gradients of the data distribution, 2020.https: //arxiv.org/abs/1907.05600. Yang Song, Jascha Sohl-Dickstein, Diederik P Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole. Score...

    2020 arXiv

  34. [2016]

    A phase transition in diffusion models reveals the hierarchical nature of data.arXiv preprint arXiv:2402.16991,

    Antonio Sclocchi, Alessandro Favero, and Matthieu Wyart. A phase transition in diffusion models reveals the hierarchical nature of data.arXiv preprint arXiv:2402.16991,

    arXiv

  35. [2017]

    Classifier-free diffusion guidance.arXiv preprint arXiv:2207.12598,

    Jonathan Ho and Tim Salimans. Classifier-free diffusion guidance.arXiv preprint arXiv:2207.12598,

    arXiv

  36. [2020]

    with250 sampling steps, averaged over 25 samples. First column: Power-Law CFG.Second column: Rescaled Power-Law CFG (38).Left column: Jensen- Shannon Divergence between the embedded data points corresponding to randomly selected class and the generated samples as a function of...

    2009

  37. [2021]

    What does guidance do? a fine-grained analysis in a simple setting.arXiv preprint, 2409.13074,

    Muthu Chidambaram, Khashayar Gatmiry, Sitan Chen, Holden Lee, and Jianfeng Lu. What does guidance do? a fine-grained analysis in a simple setting.arXiv preprint, 2409.13074,

    arXiv

  38. [2022]

    Denoising diffusion probabilistic models, 2020.https://arxiv.org/abs/ 2006.11239

    Jonathan Ho, Ajay Jain, and Pieter Abbeel. Denoising diffusion probabilistic models, 2020.https://arxiv.org/abs/ 2006.11239. Zahra Kadkhodaie, Stéphane Mallat, and Eero P Simoncelli. Feature-guided score diffusion for sampling conditional densities. arXiv preprint arXiv:2410.11646,

    2020 arXiv

  39. [2023]

    Optimizing noise schedules of generative models in high dimensionss.arXiv preprint arXiv:2501.00988,

    Santiago Aranguri, Giulio Biroli, Marc Mezard, and Eric Vanden-Eijnden. Optimizing noise schedules of generative models in high dimensionss.arXiv preprint arXiv:2501.00988,

    arXiv

  40. [2024]

    A very effective and simple diffusion reconstruction for the diluted ising model.arXiv preprint arXiv:2407.07266,

    Stefano Bae, Enzo Marinari, and Federico Ricci-Tersenghi. A very effective and simple diffusion reconstruction for the diluted ising model.arXiv preprint arXiv:2407.07266,

    arXiv

  41. [2025]

    Stochastic interpolants: A unifying framework for flows and diffusions.arXiv preprint arXiv:2303.08797,

    Michael S Albergo, Nicholas M Boffi, and Eric Vanden-Eijnden. Stochastic interpolants: A unifying framework for flows and diffusions.arXiv preprint arXiv:2303.08797,

    arXiv

Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.