发现流匹配的闭式解能更好生成样本，与噪声无关
On the Closed-Form of Flow Matching: Generalization Does Not Arise from Target Stochasticity
- 用闭式公式替代随机损失，简化训练过程
- 在图像数据集上，闭式解性能不降反升
- 适合关注生成模型优化与理论解释的研究者
现代深度生成模型可生成几乎无法与真实数据区分的高质量合成样本。大量研究试图解释为何扩散模型和流匹配等方法泛化能力极强。现有解释包括深度网络的归纳偏置以及条件流匹配损失的随机性。本文表明，损失的随机性并非推动流匹配泛化的核心因素。首先，我们在高维设置下实证发现，随机与闭式流匹配损失的数值几乎相同；其次，在标准图像数据集上使用最先进的流匹配模型，两种变体表现相当，且闭式解甚至带来性能提升。
原文摘要 · Abstract (English)
Modern deep generative models can now produce high-quality synthetic samples that are often indistinguishable from real training data. A growing body of research aims to understand why recent methods, such as diffusion and flow matching techniques, generalize so effectively. Among the proposed explanations are the inductive biases of deep learning architectures and the stochastic nature of the conditional flow matching loss. In this work, we rule out the noisy nature of the loss as a key factor driving generalization in flow matching. First, we empirically show that in high-dimensional settings, the stochastic and closed-form versions of the flow matching loss yield nearly equivalent losses. Then, using state-of-the-art flow matching models on standard image datasets, we demonstrate that both variants achieve comparable statistical performance, with the surprising observation that using the closed-form can even improve performance.
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