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Convergence Analysis for General Probability Flow ODEs of Diffusion Models in Wasserstein Distances

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arxiv 2401.17958 v2 pith:JT53BLV6 submitted 2024-01-31 stat.ML cs.LGmath.PR

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keywords flowprobabilityanalysisconvergencesamplersgeneralode-basedodes
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Score-based generative modeling with probability flow ordinary differential equations (ODEs) has achieved remarkable success in a variety of applications. While various fast ODE-based samplers have been proposed in the literature and employed in practice, the theoretical understandings about convergence properties of the probability flow ODE are still quite limited. In this paper, we provide the first non-asymptotic convergence analysis for a general class of probability flow ODE samplers in 2-Wasserstein distance, assuming accurate score estimates and smooth log-concave data distributions. We then consider various examples and establish results on the iteration complexity of the corresponding ODE-based samplers. Our proof technique relies on spelling out explicitly the contraction rate for the continuous-time ODE and analyzing the discretization and score-matching errors using synchronous coupling; the challenge in our analysis mainly arises from the inherent non-autonomy of the probability flow ODE and the specific exponential integrator that we study.

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Cited by 9 Pith papers

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

  1. Diffusion Bootstrap for High-Dimensional Linear Models

    stat.ME 2026-07 conditional novelty 7.0 of 10

    A diffusion pairs bootstrap recovers correct OLS variance in proportional high-dimensional linear models under score approximation, while terminal Wasserstein consistency alone does not.

  2. A Sharp KL-Convergence Analysis for Diffusion Models under Minimal Assumptions

    stat.ML 2025-08 conditional novelty 7.0 of 10

    A new analysis shows O~(d/epsilon) steps suffice for KL-close diffusion sampling under only L2 score error and finite second moment assumptions, improving the known O~(d/epsilon^2).

  3. Faster Diffusion Models via Higher-Order Approximation

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    A new higher-order ODE sampler for diffusion models is proven to reach ε total-variation accuracy with eO(d^{1+2/K}/ε^{1/K}) iterations under mild assumptions.

  4. Assessing the Quality of Denoising Diffusion Models in Wasserstein Distance: Noisy Score and Optimal Bounds

    stat.ML 2025-06 conditional novelty 7.0 of 10

    Denoising diffusion models achieve Wasserstein-2 sampling error of order √D/K up to logarithmic factors for a broad class of distributions, matching the Gaussian lower bound, and score-evaluation noise vanishes as the...

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    Proposes GOU process with anisotropic drift to embed data geometry in diffusion models, claiming better mode separation, correlation preservation, and convergence than isotropic baselines.

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    A TV convergence bound O(d^{7/4} ε^{1/2} + d(dH)^p) is proved for p-th order (exponential) Runge-Kutta samplers of probability-flow ODEs under C² smoothness of the learned score.

  7. A Unified Kullback--Leibler Divergence Analysis of Generative Diffusion Models via Entropy Production Rate

    math.NA 2026-08 conditional novelty 5.0 of 10

    Diffusion model generation error is decomposed through an entropy-production-rate identity that claims O(h²) Euler–Maruyama KL bounds and unifies score SDE, PF-ODE, flow matching, and stochastic interpolant analyses.

  8. Diffusion enabled Optimal Transport distances for graph matching

    cs.LG 2026-07 conditional novelty 5.0 of 10

    Diffusing node features before semi-relaxed fused Gromov–Wasserstein matching improves synthetic graph alignment accuracy and ARI over plain srFGW, most under medium noise.

  9. Non-asymptotic convergence bound of conditional diffusion models

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    CARD's generated conditional distribution is shown to converge in Wasserstein distance to the true conditional distribution, with a separate score-estimation error bound controlled by network resolution and distributi...

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