提出一种基于对称性的单步生成模型，理论扎实且性能优异。
Midpoint Generative Models
- 利用流匹配的线性插值对称性，定义新的分布差异度量
- 在多个数据集上达到与现有方法相当的生成质量
- 适合追求理论严谨性和高效生成的科研与工程人员
我们提出中点生成模型（MGM），一种训练单步生成模型的原理性框架。该框架基于流匹配中线性插值的对称性：当两端分布相同时，对应漂移场在中点时间 $t=1/2$ 处为零。我们证明该场在中点处的范数可作为分布间的有效差异度量，称为中点散度。通过引入随机翻转插值，并将确定性线性插值替换为对称随机插值，进一步推广该散度，得到广义中点散度。最后，我们推导出该广义散度的变分形式，获得一个可训练的目标函数。所提出的MGM算法在多个基准测试中表现出与现有单步生成方法相当的性能，提供了一种高效且理论坚实的一步生成建模方案。
原文摘要 · Abstract (English)
We introduce Midpoint Generative Models (MGM), a principled framework for training one-step generative models. MGM is based on a simple symmetry of Flow Matching with linear interpolation: when the two endpoint distributions coincide, the corresponding drift field vanishes at the midpoint time, $t=1/2$. We show that the norm of this field defines a valid discrepancy between distributions, which we call the Midpoint Divergence. We extend this discrepancy beyond the midpoint by introducing randomly flipped interpolations and further generalize it by replacing deterministic linear Flow Matching interpolations with symmetric stochastic interpolants, yielding a generalized Midpoint Divergence. Finally, we derive a variational formulation of our generalized divergence, yielding a tractable objective for training a one-step generator. The resulting MGM algorithm offers an effective and theoretically grounded approach to generative modeling, achieving competitive performance against existing one-step generative modeling methods.
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