条件之困：分析与改进基于条件流生成的最优传输

摘要

小批量最优传输耦合在无条件流匹配中使路径变得平直。这导致推理计算需求降低，因为在测试时数值求解常微分方程所需的积分步骤更少，且可采用复杂度较低的数值求解器。然而，在条件设置下，小批量最优传输表现欠佳。这是因为默认的最优传输映射忽略了条件，导致训练过程中条件性偏斜的先验分布。相反，在测试时，我们无法获取偏斜的先验，而是从完整、无偏的先验分布中采样。这种训练与测试之间的差距导致了性能不佳。为弥合这一差距，我们提出了条件最优传输C^2OT，它在计算最优传输分配时，在成本矩阵中加入了条件权重项。实验表明，这一简单修正适用于8高斯到月牙、CIFAR-10、ImageNet-32x32及ImageNet-256x256中的离散与连续条件。相较于现有基线，我们的方法在不同函数评估预算下整体表现更优。代码已发布于https://hkchengrex.github.io/C2OT。

English

Minibatch optimal transport coupling straightens paths in unconditional flow matching. This leads to computationally less demanding inference as fewer integration steps and less complex numerical solvers can be employed when numerically solving an ordinary differential equation at test time. However, in the conditional setting, minibatch optimal transport falls short. This is because the default optimal transport mapping disregards conditions, resulting in a conditionally skewed prior distribution during training. In contrast, at test time, we have no access to the skewed prior, and instead sample from the full, unbiased prior distribution. This gap between training and testing leads to a subpar performance. To bridge this gap, we propose conditional optimal transport C^2OT that adds a conditional weighting term in the cost matrix when computing the optimal transport assignment. Experiments demonstrate that this simple fix works with both discrete and continuous conditions in 8gaussians-to-moons, CIFAR-10, ImageNet-32x32, and ImageNet-256x256. Our method performs better overall compared to the existing baselines across different function evaluation budgets. Code is available at https://hkchengrex.github.io/C2OT

条件之困：分析与改进基于条件流生成的最优传输

The Curse of Conditions: Analyzing and Improving Optimal Transport for Conditional Flow-Based Generation

摘要

Summary

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