标题： 潜在扩散模型中的最优停止 显示英文标题

标题： Optimal Stopping in Latent Diffusion Models

摘要： 我们识别并分析了潜在扩散模型（LDMs）中一个令人惊讶的现象，即扩散的最后步骤会降低样本质量。与传统观点不同，该观点认为早期停止是为了数值稳定性，但这一现象是LDMs中维度降低的固有特性。我们通过分析潜在维度和停止时间之间的相互作用，提供了一个有根据的解释。在具有线性自编码器的高斯框架下，我们描述了在什么条件下需要早期停止以最小化生成分布与目标分布之间的距离。更准确地说，我们表明低维表示受益于较早的终止，而高维潜在空间则需要较晚的停止时间。我们进一步证明，潜在维度与其他问题超参数如分数匹配参数的约束相互作用。在合成和真实数据集上的实验说明了这些特性，强调了早期停止可以提高生成质量。综上所述，我们的结果为理解潜在维度如何影响样本质量提供了理论基础，并突出了停止时间作为LDMs中的关键超参数。 显示英文摘要

摘要： 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.