揭示扩散模型组合的理论机制，解释为何某些组合能泛化到新长度。
Mechanisms of Projective Composition of Diffusion Models
- 提出投影式组合的数学定义，明确组合成功的标准
- 证明线性得分组合在特定条件下可实现投影组合
- 给出判断新组合成败的简单启发式方法
我们研究扩散模型中组合的理论基础，重点关注分布外外推和长度泛化。已有工作表明，通过线性得分组合可实现良好效果，包括某些情况下的长度泛化（Du et al., 2023; Liu et al., 2022）。然而，对这种组合为何以及如何起效的理论理解仍不完整，甚至对“组合成功”的定义也尚不清晰。本文开始填补这些基本空白：首先明确定义一种期望的组合结果，称为投影式组合；然后研究三个核心问题：(1) 线性得分组合在何种条件下可严格实现投影式组合；(2) 反向扩散采样能否生成期望的组合分布；(3) 组合失败的条件是什么。我们将理论分析与先前经验观察联系起来，解释了过去难以理解的成功或失败原因。最后，我们提出一个简单的启发式方法，帮助预测新组合的成功可能性。
原文摘要 · Abstract (English)
We study the theoretical foundations of composition in diffusion models, with a particular focus on out-of-distribution extrapolation and length-generalization. Prior work has shown that composing distributions via linear score combination can achieve promising results, including length-generalization in some cases (Du et al., 2023; Liu et al., 2022). However, our theoretical understanding of how and why such compositions work remains incomplete. In fact, it is not even entirely clear what it means for composition to "work". This paper starts to address these fundamental gaps. We begin by precisely defining one possible desired result of composition, which we call projective composition. Then, we investigate: (1) when linear score combinations provably achieve projective composition, (2) whether reverse-diffusion sampling can generate the desired composition, and (3) the conditions under which composition fails. We connect our theoretical analysis to prior empirical observations where composition has either worked or failed, for reasons that were unclear at the time. Finally, we propose a simple heuristic to help predict the success or failure of new compositions.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。