Pith. sign in

REVIEW 6 cited by

Linear Convergence of Diffusion Models Under the Manifold Hypothesis

Not yet reviewed by Pith; the record is open.

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

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2410.09046 v2 pith:KS2PA7X7 submitted 2024-10-11 stat.ML cs.LGmath.STstat.TH

Peter Potaptchik , Iskander Azangulov , George Deligiannidis This is my paper
classification stat.MLcs.LGmath.STstat.TH
keywords linearmanifoldmodelsconvergencediffusiondimensionalhypothesisapplications
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

Score-matching generative models have proven successful at sampling from complex high-dimensional data distributions. In many applications, this distribution is believed to concentrate on a much lower $d$-dimensional manifold embedded into $D$-dimensional space; this is known as the manifold hypothesis. The current best-known convergence guarantees are either linear in $D$ or polynomial (superlinear) in $d$. The latter exploits a novel integration scheme for the backward SDE. We take the best of both worlds and show that the number of steps diffusion models require in order to converge in Kullback-Leibler~(KL) divergence is linear (up to logarithmic terms) in the intrinsic dimension $d$. Moreover, we show that this linear dependency is sharp.

Discussion (0). Sign in to comment.

Forward citations

Cited by 6 Pith papers

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

  1. Fast Score-Based Sampling via Log-Concave Reductions

    math.ST 2025-12 conditional novelty 7.0 of 10

    Score-based sampling reduces to a short sequence of strongly log-concave sampling problems, giving √d polylog(1/ε) complexity bounds and logarithmic dependence on the condition number for log-concave targets.

  2. MAD: Manifold Attracted Diffusion

    stat.ML 2025-09 conditional novelty 7.0 of 10

    Score-based diffusion can be modified at inference time so that samples from noisy training data are pulled toward the clean data manifold.

  3. Faster Diffusion Models via Higher-Order Approximation

    cs.LG 2025-06 conditional novelty 7.0 of 10

    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...

  5. Implicit Regularisation in Diffusion Models: An Algorithm-Dependent Generalisation Analysis

    stat.ML 2025-07 conditional novelty 6.0 of 10

    Score stability bounds the generalization gap of diffusion models, identifying early stopping, coarse discretization, and SGD noise as sources of implicit regularization.

  6. Fast Convergence for High-Order ODE Solvers in Diffusion Probabilistic Models

    cs.LG 2025-06 conditional novelty 6.0 of 10

    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.

Pith tools