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Score-based Diffusion Models via Stochastic Differential Equations -- a Technical Tutorial

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arxiv 2402.07487 v3 pith:REIIM6M6 submitted 2024-02-12 cs.LG math.HO

classification cs.LGmath.HO
keywords modelsdiffusionarticledifferentialequationsintroductionmatchingsampling
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This is an expository article on the score-based diffusion models, with a particular focus on the formulation via stochastic differential equations (SDE). After a gentle introduction, we discuss the two pillars in the diffusion modeling -- sampling and score matching, which encompass the SDE/ODE sampling, score matching efficiency, the consistency models, and reinforcement learning. Short proofs are given to illustrate the main idea of the stated results. The article is primarily a technical introduction to the field, and practitioners may also find some analysis useful in designing new models or algorithms.

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Cited by 4 Pith papers

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

  1. 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.

  2. 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...

  3. Dynamic data generation and dynamic portfolio selection: an application of a score-based diffusion model

    q-fin.PM 2025-07 reject novelty 6.0 of 10

    An adaptive score-based diffusion model generates sequential market scenarios with adapted-Wasserstein error bounds, and a policy-gradient agent trained on these scenarios outperforms several portfolio benchmarks.

  4. 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.

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