研究扩散模型在噪声评分下的生成质量，证明其鲁棒性并给出最优收敛速率。
Assessing the Quality of Denoising Diffusion Models in Wasserstein Distance: Noisy Score and Optimal Bounds
- 通过有限样本分析，量化扩散模型对评分噪声的鲁棒性。
- 在Wasserstein-2距离下获得比之前更快的收敛速率。
- 结果与高斯情形最优率一致，表明理论极限已达到。
生成建模旨在从未知目标分布中生成新样本，仅依赖有限样本集合。在主流方法中，去噪扩散概率模型（DDPM）通过由估计得分函数驱动的扩散过程，将布朗运动映射为新样本。本文首先提供实证证据，表明DDPM对恒定方差的评分评估噪声具有鲁棒性。随后，我们在Wasserstein-2距离下建立了有限样本保证，具有两个关键特征：(i) 定量刻画并度量了DDPM对噪声评分估计的鲁棒性；(ii) 收敛速率优于此前已知结果。此外，我们发现所得速率与高斯情形下的已知速率一致，暗示其最优性。
原文摘要 · Abstract (English)
Generative modeling aims to produce new random examples from an unknown target distribution, given access to a finite collection of examples. Among the leading approaches, denoising diffusion probabilistic models (DDPMs) construct such examples by mapping a Brownian motion via a diffusion process driven by an estimated score function. In this work, we first provide empirical evidence that DDPMs are robust to constant-variance noise in the score evaluations. We then establish finite-sample guarantees in Wasserstein-2 distance that exhibit two key features: (i) they characterize and quantify the robustness of DDPMs to noisy score estimates, and (ii) they achieve faster convergence rates than previously known results. Furthermore, we observe that the obtained rates match those known in the Gaussian case, implying their optimality.
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