发表机构
Hanyang University（汉阳大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究针对带随机特征的条件扩散模型，在高维比例极限下推导损失渐近表达式，发现过参数化时存在“恶性泛化”现象，且信息更丰富的条件会使模型在更小宽度时记忆训练样本，相关结论经 U-Net 实验验证。
AI 中文摘要
条件扩散模型可在指定条件下生成多样、新颖且高质量的样本，但目前对其记忆与泛化的理论理解仍有限，现有研究主要在无条件场景下刻画这些行为。本研究在高维比例极限下分析随机特征条件得分模型，推导训练损失与测试损失的渐近表达式；通过分解测试损失，发现在过参数化 regime 中，增加模型宽度可提升对依赖条件的均值的预测，同时降低条件内预测方差，该现象被称为“恶性泛化”。此外，对训练损失的分析表明，信息更丰富的条件会使模型在更小宽度时就对训练样本产生记忆。这些理论发现得到了在真实数据上使用 U-Net 架构开展的实验的支持。
英文摘要
Conditional diffusion models generate diverse, novel, and high-quality samples under prescribed conditions. However, theoretical understanding of their memorization and generalization remains limited, while recent works have characterized these behaviors primarily in unconditional settings. In this work, we analyze a random-feature conditional score model in the high-dimensional proportional limit, deriving asymptotic expressions for training and test losses. By decomposing the test loss, we show that in the overparameterized regime, increasing model width improves prediction of the condition-dependent mean while reducing within-condition prediction variance, a phenomenon we term "malign generalization." Furthermore, analyzing the training loss reveals that more informative conditions lead to memorization of training samples at smaller widths. These theoretical findings are supported by experiments with U-Net architectures on realistic data.
