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Contractive Diffusion Probabilistic Models

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arxiv 2401.13115 v3 pith:DAQSY526 submitted 2024-01-23 cs.LG

Wenpin Tang , Hanyang Zhao This is my paper
classification cs.LG
keywords dpmsdiffusionmatchingmodelsscorecdpmcdpmscontraction
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

Diffusion probabilistic models (DPMs) have emerged as a promising technique in generative modeling. The success of DPMs relies on two ingredients: time reversal of diffusion processes and score matching. In view of possibly unguaranteed score matching, we propose a new criterion -- the contraction property of backward sampling in the design of DPMs, leading to a novel class of contractive DPMs (CDPMs). Our key insight is that, the contraction property can provably narrow score matching errors and discretization errors, thus our proposed CDPMs are robust to both sources of error. For practical use, we show that CDPM can leverage weights of pretrained DPMs by a simple transformation, and does not need retraining. We corroborated our approach by experiments on synthetic 1-dim examples, Swiss Roll, MNIST, CIFAR-10 32$\times$32 and AFHQ 64$\times$64 dataset. Notably, CDPM steadily improves the performance of baseline score-based diffusion models.

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Cited by 6 Pith papers

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

  1. Score Accuracy Along the Forward Diffusion Does Not Certify Numerical Stability in Diffusion Sampling

    stat.ML 2026-07 accept novelty 7.0 of 10

    Small forward-marginal score error does not guarantee stable diffusion sampling because rare numerical trajectories can enter poorly controlled regions and trigger superlinear amplification.

  2. From Score Learning to Discretized Sampling: An End-to-End Generalization Analysis of Diffusion Models

    cs.LG 2026-07 conditional novelty 6.0 of 10

    An end-to-end TV bound for score-based diffusion models that decomposes generative error into forward truncation, reverse discretization, finite-sample generalization, and optimization gap.

  3. Tightening the Score Matching Gap for Diffusion Models

    stat.ML 2026-07 conditional novelty 6.0 of 10

    Tighter score-matching gap bounds for diffusion models via entropy flows, LSI and reflection couplings show that low-noise score accuracy dominates sample quality metrics.

  4. 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.

  5. 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.

  6. Non-asymptotic convergence bound of conditional diffusion models

    stat.ML 2025-08 conditional novelty 4.0 of 10

    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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