arXiv:2510.08409stat.MLcs.LG2025-10被引 1

发现扩散模型最后几步会降低生成质量,提出按隐空间维度调整停止时机。

Optimal Stopping in Latent Diffusion Models

  • 基于高斯线性自编码框架,分析隐空间维度与停止时间的相互作用。
  • 低维隐空间需提前停止,高维则需延后,以最小化生成分布差距。
  • 实验验证早停可提升真实数据集上的生成质量,适合优化扩散模型训练。

我们发现并分析了潜空间扩散模型(LDMs)中一个意外现象:扩散过程的最后几步会降低样本质量。与传统认为早停仅出于数值稳定性不同,该现象源于LDM中的降维机制。通过在高斯框架下使用线性自编码器分析潜空间维度与停止时间的交互,我们揭示了最小化生成分布与目标分布距离所需的早停条件。具体而言,低维表示需更早终止,而高维潜空间则需更晚停止。此外,潜空间维度还与得分匹配的参数约束等超参数相互影响。在合成和真实数据集上的实验验证了这些特性,表明早停能有效提升生成质量。研究为理解潜空间维度如何影响生成效果提供了理论基础,并强调停止时间是LDM中的关键超参数。

原文摘要 · Abstract (English)

We identify and analyze a surprising phenomenon of Latent Diffusion Models (LDMs) where the final steps of the diffusion can degrade sample quality. In contrast to conventional arguments that justify early stopping for numerical stability, this phenomenon is intrinsic to the dimensionality reduction in LDMs. We provide a principled explanation by analyzing the interaction between latent dimension and stopping time. Under a Gaussian framework with linear autoencoders, we characterize the conditions under which early stopping is needed to minimize the distance between generated and target distributions. More precisely, we show that lower-dimensional representations benefit from earlier termination, whereas higher-dimensional latent spaces require later stopping time. We further establish that the latent dimension interplays with other hyperparameters of the problem such as constraints in the parameters of score matching. Experiments on synthetic and real datasets illustrate these properties, underlining that early stopping can improve generative quality. Together, our results offer a theoretical foundation for understanding how the latent dimension influences the sample quality, and highlight stopping time as a key hyperparameter in LDMs.

扩散模型隐空间早停生成质量

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