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

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$^2$OT) 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-32$\times$32, and ImageNet-256$\times$256.Our method performs better overall compared to the existing baselines across different function evaluation budgets.Code will be made available.