pith. sign in

arxiv: 2605.21911 · v1 · pith:LBN37NEGnew · submitted 2026-05-21 · 💻 cs.LG

Noise Schedule Design for Diffusion Models: An Optimal Control Perspective

Seo Taek Kong , Weina Wang , R. Srikant This is my paper

Pith reviewed 2026-05-22 07:52 UTC · model grok-4.3

classification 💻 cs.LG
keywords diffusion modelsnoise schedulesoptimal controlFisher informationsampling errorgenerative modelsimage generation
0
0 comments X

The pith

Noise schedule design for diffusion models can be recast as an optimal control problem on Fisher information to achieve near-optimal sampling error.

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

The paper frames noise schedule selection in diffusion models as an optimal control problem whose state is the Fisher information of the diffusion process evolving by an ODE. The control input is the noise schedule, and the objective is a functional of the Fisher information shown to upper-bound the Kullback-Leibler sampling error. Solving the problem produces sufficient conditions on the schedules under which the state-of-the-art sampling error bound of order d over n is achievable. Under a parametric assumption on the data distribution the authors further derive closed-form schedules that generalize common empirical choices such as exponential and sigmoid schedules. Systematic tuning of the extra parameters in these schedules produces new schedules with improved FID scores on image generation benchmarks.

Core claim

By recasting noise schedule design as an optimal control problem whose state is the Fisher information of the diffusion process evolving according to an ODE and whose control is the noise schedule, the authors obtain sufficient conditions guaranteeing that the sampling error is bounded by tilde O(d/n). Under a further parametric assumption on the data distribution they derive closed-form expressions for the noise schedules; these expressions generalize standard empirical schedules by admitting additional tunable parameters, and tuning those parameters yields schedules that achieve superior FID scores on image generation benchmarks.

What carries the argument

An optimal control problem whose state is the Fisher information of the diffusion process and whose control input is the noise schedule.

If this is right

  • Sufficient conditions on noise schedules exist that guarantee tilde O(d/n) sampling error is achievable.
  • Closed-form noise schedules can be obtained when the data distribution satisfies the parametric assumption.
  • The closed-form schedules generalize exponential and sigmoid schedules through additional tunable parameters.
  • Tuning the parameters of the derived schedules produces improved FID scores on image generation benchmarks.

Where Pith is reading between the lines

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

  • The optimal-control formulation could be applied to design schedules for diffusion processes in domains other than images.
  • Relaxing the parametric assumption might yield approximate or data-driven schedule optimization methods.
  • The link between Fisher information and KL error bounds may suggest similar control formulations for other sampling or generative algorithms.

Load-bearing premise

The data distribution satisfies a specific parametric form that permits closed-form solutions for the noise schedules.

What would settle it

Measuring the actual KL sampling error achieved by the closed-form schedules on synthetic data drawn from a distribution that violates the parametric assumption.

Figures

Figures reproduced from arXiv: 2605.21911 by R. Srikant, Seo Taek Kong, Weina Wang.

Figure 1
Figure 1. Figure 1: Comparison of noise schedules for the N = 20 top (Low FID, blue) and bottom (High FID, red) parameter sets. Darker regions indicate high-density paths where multiple trials overlap. 36 [PITH_FULL_IMAGE:figures/full_fig_p036_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Comparison of 64 × 64 samples generated using four different noise schedules. 38 [PITH_FULL_IMAGE:figures/full_fig_p038_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: ImageNet samples conditioned on “flamingo”, “sports car”, “balloon”, “lemon”, “kite”, [PITH_FULL_IMAGE:figures/full_fig_p039_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: KL divergence curves and generated 2σ covariance ellipses illustrating the sensitivity of constant noise schedules (f = E, g = 2E) to parameters of the target Gaussian distribution. The leftmost panel plots the true initialization error and the true empirical sampling error (as opposed to upper bounds), confirming that success is bottlenecked by the sensitivity with respect to E. 2D Gaussian target distrib… view at source ↗
read the original abstract

We develop a principled framework for analyzing and designing noise schedules in diffusion models. We show that one can recast this design problem as an optimal control problem, whose state is the Fisher information of the diffusion process which evolves according to an ODE and the control input is the noise schedule. The objective of the optimal control problem is a functional involving the Fisher information, which is shown to be an upper bound on the Kullback-Leibler sampling error. By solving this optimal control problem, we obtain sufficient conditions on noise schedules under which state-of-the-art $\tilde{\mathcal{O}} (d/n)$ sampling error is achievable, where $d$ is the data dimension and $n$ is the number of discretization steps. While existing theoretical work also prove that $\tilde{\mathcal{O}}(d/n)$ sampling error bounds are achievable, these results hold for specific noise schedules, which do not include the schedules used in practice. Under a further parametric assumption on the data distribution, we show that one can obtain closed-form expressions for the noise schedules. These noise schedules generalize standard empirical schedules such as exponential and sigmoid schedules by allowing additional parameters that can be tuned. Systematically tuning the parameters of these schedules yields new schedules that achieve superior FID scores on image generation benchmarks.

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 paper recasts noise schedule design for diffusion models as an optimal control problem whose state is the Fisher information evolving according to an ODE and whose control input is the noise schedule. The OCP objective is a functional of the Fisher information shown to upper-bound the KL sampling error. Solving the OCP produces sufficient conditions on schedules under which state-of-the-art tilde O(d/n) sampling error is achievable. Under a further parametric assumption on the data distribution, closed-form expressions for the schedules are derived; these generalize empirical exponential and sigmoid schedules via additional tunable parameters, and systematic tuning yields improved FID scores on image benchmarks.

Significance. If the derivations of the ODE and the Fisher-to-KL bound hold for general data distributions, the work supplies a principled optimal-control lens on schedule design together with explicit sufficient conditions that achieve the best-known sampling rate while recovering and extending schedules used in practice. The explicit link between Fisher information dynamics and discretization error is a conceptual contribution that could guide future schedule analysis.

major comments (2)
  1. [Abstract and §1] Abstract and §1: the sufficient conditions for tilde O(d/n) sampling error are stated as general consequences of the OCP solution, yet the derivation of the Fisher-information ODE and the proof that the objective upper-bounds KL error are not shown to be independent of the parametric assumption on the data distribution that appears only later for closed-form schedules. If those steps rely on properties that hold solely inside the parametric family, the claimed generality and the assertion that the conditions cover practical schedules do not follow.
  2. [§3] §3 (OCP formulation) and the paragraph following Eq. (X): the objective functional is asserted to be an upper bound on KL sampling error, but the manuscript supplies neither the explicit steps relating the integrated Fisher information to the KL divergence nor a verification that the bound remains valid without the parametric density assumption. This step is load-bearing for the central rate claim.
minor comments (2)
  1. [Notation throughout] Clarify the precise dependence of the tilde O(d/n) rate on the number of discretization steps n and dimension d; the current notation leaves the hidden constants and logarithmic factors implicit.
  2. [Experiments] The experimental section reports post-hoc parameter tuning on benchmarks; an ablation isolating the effect of each additional schedule parameter and a comparison against the untuned closed-form schedules would strengthen the empirical claims.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive feedback on our manuscript. We address the major comments point by point below, clarifying the generality of the derivations and outlining planned revisions to improve clarity.

read point-by-point responses

  1. Referee: [Abstract and §1] Abstract and §1: the sufficient conditions for tilde O(d/n) sampling error are stated as general consequences of the OCP solution, yet the derivation of the Fisher-information ODE and the proof that the objective upper-bounds KL error are not shown to be independent of the parametric assumption on the data distribution that appears only later for closed-form schedules. If those steps rely on properties that hold solely inside the parametric family, the claimed generality and the assertion that the conditions cover practical schedules do not follow.

    Authors: We thank the referee for identifying this point of potential confusion. The Fisher-information ODE follows directly from the Fokker-Planck equation of the diffusion process and the definition of Fisher information; these steps use only the general form of the forward process and do not invoke the parametric density assumption. Likewise, the upper bound on KL sampling error is obtained via a general integral inequality relating Fisher information to KL divergence that holds for arbitrary smooth densities. The parametric assumption is introduced strictly later, solely to obtain closed-form solutions. To eliminate any ambiguity we will revise §1 and the abstract to explicitly separate the general results from the parametric case and will add a short appendix containing the full derivations. revision: yes

  2. Referee: [§3] §3 (OCP formulation) and the paragraph following Eq. (X): the objective functional is asserted to be an upper bound on KL sampling error, but the manuscript supplies neither the explicit steps relating the integrated Fisher information to the KL divergence nor a verification that the bound remains valid without the parametric density assumption. This step is load-bearing for the central rate claim.

    Authors: We agree that the manuscript would benefit from an explicit derivation of the bound. The connection proceeds by applying the chain rule to the time-dependent Fisher information along the diffusion trajectory and then invoking the standard integral representation of KL divergence in terms of Fisher information; both steps are valid for general data distributions. We will insert the complete proof immediately after the statement of the objective functional in the revised §3 and will add a remark confirming that the parametric family is not required for this inequality. revision: yes

Circularity Check

0 steps flagged

No circularity: OCP solution for sufficient conditions on noise schedules is independent of parametric fits

full rationale

The paper's central derivation recasts schedule design as an optimal control problem with Fisher information evolving by ODE as state and schedule as control; the objective functional is shown to upper-bound KL error, and solving the OCP yields sufficient conditions for tilde O(d/n) error. This chain is presented as holding generally. The parametric assumption on the data distribution is introduced separately and only to derive closed-form schedule expressions that generalize empirical ones (with tunable parameters). No equation or step reduces the claimed sufficient conditions or error bound to a fitted quantity by construction, nor does any load-bearing premise rely on a self-citation chain or imported uniqueness result. Empirical tuning of the closed-form parameters to achieve better FID scores is downstream validation rather than part of the theoretical derivation. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The framework assumes the diffusion process admits an ODE description of Fisher information evolution and that the KL sampling error is bounded by a functional of that Fisher information. The closed-form schedules rest on an additional parametric assumption about the data distribution whose form is not stated in the abstract.

free parameters (1)
  • additional tunable parameters in generalized exponential/sigmoid schedules
    These parameters are introduced to generalize standard schedules and are tuned on image benchmarks to achieve superior FID.
axioms (2)
  • domain assumption The diffusion process state (Fisher information) evolves according to an ODE whose control input is the noise schedule.
    Invoked when recasting the design problem as optimal control.
  • domain assumption The objective functional of the optimal control problem is an upper bound on the Kullback-Leibler sampling error.
    Central to claiming that the solved schedules achieve low sampling error.

pith-pipeline@v0.9.0 · 5755 in / 1600 out tokens · 31982 ms · 2026-05-22T07:52:21.754679+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel echoes
    ?
    echoes

    ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

    By solving this optimal control problem, we obtain sufficient conditions on noise schedules under which state-of-the-art O(d/n) sampling error is achievable... Under a further parametric assumption... closed-form expressions for the noise schedules... generalize standard empirical schedules such as exponential and sigmoid schedules

  • IndisputableMonolith/Foundation/BranchSelection.lean branch_selection echoes
    ?
    echoes

    ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

    the objective of the optimal control problem is a functional involving the Fisher information, which is shown to be an upper bound on the Kullback-Leibler sampling error

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

48 extracted references · 48 canonical work pages · 1 internal anchor

  1. [1]

    Akiba, S

    T. Akiba, S. Sano, T. Yanase, T. Ohta, and M. Koyama. Optuna: A next-generation hyper- parameter optimization framework. InThe 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, pages 2623–2631, 2019

    work page 2019

  2. [2]

    B. D. Anderson. Reverse-time diffusion equation models.Stochastic Processes and their Applications, 12(3), 1982

    work page 1982

  3. [3]

    Bakry, I

    D. Bakry, I. Gentil, and M. Ledoux.Analysis and Geometry of Markov Diffusion Operators, volume 348. Springer Science & Business Media, 2013

    work page 2013

  4. [4]

    Benton, V

    J. Benton, V . D. Bortoli, A. Doucet, and G. Deligiannidis. Nearlyd-linear convergence bounds for diffusion models via stochastic localization. InInternational Conference on Learning Rep- resentations, 2024

    work page 2024

  5. [5]

    Blachman

    N. Blachman. The convolution inequality for entropy powers.IEEE Transactions on Informa- tion Theory, 11(2):267–271, Apr. 1965

    work page 1965

  6. [6]

    Block, Y

    A. Block, Y . Mroueh, and A. Rakhlin. Generative Modeling with Denoising Auto-Encoders and Langevin Sampling. Oct. 2022

    work page 2022

  7. [7]

    V . D. Bortoli. Convergence of denoising diffusion models under the manifold hypothesis. Transactions on Machine Learning Research, (arXiv:2208.05314), May 2023

    work page arXiv 2023

  8. [8]

    Boucheron, G

    S. Boucheron, G. Lugosi, and P. Massart.Concentration Inequalities: A Nonasymptotic Theory of Independence. Oxford University Press, Feb. 2013

    work page 2013

  9. [9]

    H. Chen, H. Lee, and J. Lu. Improved analysis of score-based generative modeling: User- friendly bounds under minimal smoothness assumptions. InInternational Conference on Ma- chine Learning, pages 4735–4763. PMLR, 2023

    work page 2023

  10. [10]

    M. Chen, K. Huang, T. Zhao, and M. Wang. Score approximation, estimation and distribu- tion recovery of diffusion models on low-dimensional data. InInternational Conference on Machine Learning, pages 4672–4712. PMLR, 2023

    work page 2023

  11. [11]

    S. Chen, S. Chewi, J. Li, Y . Li, A. Salim, and A. Zhang. Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions. InThe Eleventh Interna- tional Conference on Learning Representations, 2023

    work page 2023

  12. [12]

    S. Chen, V . Kontonis, and K. Shah. Learning general gaussian mixtures with efficient score matching.arXiv preprint arXiv:2404.18893, 2024

    work page arXiv 2024

  13. [13]

    T. Chen. On the importance of noise scheduling for diffusion models, 2023

    work page 2023

  14. [14]

    Y . Chen, E. Vanden-Eijnden, and J. Xu. Lipschitz-guided design of interpolation schedules in generative models.arXiv preprint arXiv:2509.01629, 2025. 10

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  15. [15]

    Conforti, A

    G. Conforti, A. Durmus, and M. G. Silveri. Kl convergence guarantees for score diffusion models under minimal data assumptions.SIAM Journal on Mathematics of Data Science, 7 (1):86–109, 2025

    work page 2025

  16. [16]

    A. Dembo. Simple proof of the concavity of the entropy power with respect to added Gaussian noise.IEEE Transactions on Information Theory, 35(4):887–888, July 1989. ISSN 1557-9654

    work page 1989

  17. [17]

    Esposito

    R. Esposito. On a relation between detection and estimation in decision theory.Inf. Control, 12(2):116–120, Feb. 1968

    work page 1968

  18. [18]

    Gao and L

    X. Gao and L. Zhu. Convergence analysis for general probability flow odes of diffusion models in wasserstein distances.arXiv preprint arXiv:2401.17958, 2024

    work page arXiv 2024

  19. [19]

    Gatmiry, J

    K. Gatmiry, J. Kelner, and H. Lee. Learning mixtures of gaussians using diffusion models. arXiv preprint arXiv:2404.18869, 2024

    work page arXiv 2024

  20. [20]

    L. Gross. Logarithmic Sobolev Inequalities.American Journal of Mathematics, 97(4):1061– 1083, 1975. ISSN 0002-9327. doi: 10.2307/2373688

    work page doi:10.2307/2373688 1975

  21. [21]

    U. G. Haussmann and E. Pardoux. Time reversal of diffusions.The Annals of Probability, pages 1188–1205, 1986

    work page 1986

  22. [22]

    Hinze, R

    M. Hinze, R. Pinnau, M. Ulbrich, and S. Ulbrich.Optimization with PDE constraints. Springer Science & Business Media, 2008

    work page 2008

  23. [23]

    J. Ho, A. Jain, and P. Abbeel. Denoising diffusion probabilistic models.Advances in neural information processing systems, 33:6840–6851, 2020

    work page 2020

  24. [24]

    K. Hornik. Approximation capabilities of multilayer feedforward networks.Neural networks, 4(2):251–257, 1991

    work page 1991

  25. [25]

    Jabri, D

    A. Jabri, D. Fleet, and T. Chen. Scalable adaptive computation for iterative generation, 2023

    work page 2023

  26. [26]

    Karras, M

    T. Karras, M. Aittala, T. Aila, and S. Laine. Elucidating the design space of diffusion-based generative models.Advances in neural information processing systems, 35:26565–26577, 2022

    work page 2022

  27. [27]

    H. Lee, J. Lu, and Y . Tan. Convergence of score-based generative modeling for general data distributions. InInternational Conference on Algorithmic Learning Theory, pages 946–985. PMLR, 2023

    work page 2023

  28. [28]

    X. Liu, L. Wu, M. Ye, and Q. Liu. Let us build bridges: Understanding and extending diffusion generative models.arXiv preprint arXiv:2208.14699, 2022

    work page arXiv 2022

  29. [29]

    X. Liu, C. Gong, and Q. Liu. Flow straight and fast: Learning to generate and transfer data with rectified flow. InThe Eleventh International Conference on Learning Representations, 2023

    work page 2023

  30. [30]

    A. Q. Nichol and P. Dhariwal. Improved denoising diffusion probabilistic models. InInterna- tional conference on machine learning. PMLR, 2021

    work page 2021

  31. [31]

    H. Risken. Fokker-planck equation. InThe Fokker-Planck equation: methods of solution and applications. Springer, 1989

    work page 1989

  32. [32]

    H. Robbins. An empirical Bayes approach to statistics. InThird Berkeley Symp. Math Statist. Probab, 1956

    work page 1956

  33. [33]

    J. Song, C. Meng, and S. Ermon. Denoising diffusion implicit models. InInternational Con- ference on Learning Representations, 2021

    work page 2021

  34. [34]

    Song and S

    Y . Song and S. Ermon. Generative modeling by estimating gradients of the data distribution. Advances in neural information processing systems, 32, 2019

    work page 2019

  35. [35]

    Y . Song, C. Durkan, I. Murray, and S. Ermon. Maximum likelihood training of score-based diffusion models.Advances in neural information processing systems, 34, 2021. 11

    work page 2021

  36. [36]

    Y . Song, J. Sohl-Dickstein, D. P. Kingma, A. Kumar, S. Ermon, and B. Poole. Score-based generative modeling through stochastic differential equations. InInternational Conference on Learning Representations, 2021

    work page 2021

  37. [37]

    A. Stam. Some inequalities satisfied by the quantities of information of Fisher and Shannon. Information and Control, 2(2), June 1959

    work page 1959

  38. [38]

    concavity of entropy power

    C. Villani. A short proof of the “concavity of entropy power”.IEEE Transactions on Informa- tion Theory, 46(4), July 2000

    work page 2000

  39. [39]

    von Platen, S

    P. von Platen, S. Patil, A. Lozhkov, P. Cuenca, N. Lambert, K. Rasul, M. Davaadorj, D. Nair, S. Paul, W. Berman, Y . Xu, S. Liu, and T. Wolf. Diffusers: State-of-the-art diffusion models. https://github.com/huggingface/diffusers, 2022

    work page 2022

  40. [40]

    M. Xu, L. Yu, Y . Song, C. Shi, S. Ermon, and J. Tang. Geodiff: A geometric diffusion model for molecular conformation generation. InInternational Conference on Learning Representations, 2022

    work page 2022

  41. [41]

    variance preserving

    Y . Zhang, W. Xu, M. Zhou, M. Fazel, and S. S. Du. Convergence dynamics of over- parameterized score matching for a single gaussian.arXiv preprint arXiv:2511.22069, 2025. 12 A Additional Related Works Early theoretical analyses of diffusion models [6, 7, 11] focused predominantly on SDE samplers utilizing first-order discretization schemes under constant ...

    work page arXiv 2025

  42. [42]

    concavity of entropy power

    is given by dXt = p g(t)dBt, whereg(t)is chosen to grow exponentially witht. Sigmoid:The sigmoid schedule [13] corresponds to the forward process (43) with ¯αt = σ(h(1))−σ(h(t)) σ(h(1))−σ(h(0)) , h(t) = t(θmax −θ min) +θ min τsig , whereσis the sigmoid function. The mapt7→h(t)is interpreted as the corresponding timescale. Using the relationf(t) =−(2¯α t)−...

    work page

  43. [43]

    The VP-linear schedule(f lin, glin)described byf lin(t) =g lin(t)/2andg lin(t) =g min + (gmax −g min)t/Tachieves the error bound KL(p⋆∥ˆp⋆)≲ α2 T 2σ2 T ∥X⋆∥2 L2 +hdκ 4gmax [T gmax + 1] max 1, J⋆ d .(95)

    work page

  44. [44]

    learnable

    The VP-constant schedule(f const, gconst)withf const =g const/2achieves the error bound KL(p⋆∥ˆp⋆)≲ α2 T 2σ2 T ∥X⋆∥2 L2 +hdκ 4gconst J⋆ d + log 1 + J⋆ d egconstT −1 (96) Proof.See Section F.1. As discussed earlier, the best bounds [11, 15] available for VP-constant schedules grow linearly with J⋆/d. Proposition 4 shows an explicit dependence on the parame...

    work page

  45. [45]

    The ani- mals (birds, frogs, reptiles) consistently feature anatomically correct proportions, sharp textures (feathers, scales), and realistic lighting

    Best: Image 4 (ACS) This model demonstrates the highest level of structural integrity and photorealism. The ani- mals (birds, frogs, reptiles) consistently feature anatomically correct proportions, sharp textures (feathers, scales), and realistic lighting. While minor artifacts exist in highly complex scenes (like human hands), it has the fewest severe ha...

    work page

  46. [46]

    Second Best: Image 1 (Linear) This model produces generally passable results but struggles significantly more with coherence than Image 4. Artifacts are noticeable upon closer inspection; for example, snakes appear as disjointed floating segments, and human hands/faces interacting with animals are heavily distorted or melted. It achieves decent textures b...

    work page

  47. [47]

    When generating limbs, hands, or complex shapes (such as the person in the top right or the creatures in row 5), the geome- try collapses into unnatural, fleshy blobs

    Third Place: Image 3 (Sigmoid) This model suffers from severe ”melting” and blending artifacts. When generating limbs, hands, or complex shapes (such as the person in the top right or the creatures in row 5), the geome- try collapses into unnatural, fleshy blobs. While the color palettes and lighting are somewhat realistic, the structural failure of the s...

    work page

  48. [48]

    flamingo

    Worst: Image 2 (Cosine) This model exhibits the most severe failures in both photorealism and coherence. Many panels do not resemble identifiable subjects, resulting in abstract, morphed, or heavily glitched outputs (e.g., the white mass in row 2, the blue blob in row 4, or the severely mangled human figures). The generation frequently breaks down into un...

    work page