title: The Curse of Conditions: Analyzing and Improving Optimal Transport for
    Conditional Flow-Based Generation
summary: 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
paper_authors._id: 67d39ae1faaad4ed2df1cc61
paper_authors.name: Ho Kei Cheng
paper_authors.status: claimed_verified
paper_authors.statusLastChangedAt: 2025-03-14T08:56:19.361Z
paper_authors._id: 63041b541dd5d3c62486c294
paper_authors.avatarUrl: /avatars/a5286d562f7b9082730f760e66c3bf29.svg
paper_authors.fullname: Ho Kei Cheng
paper_authors.type: user
paper_authors.user: hkchengrex
paper_authors._id: 67d39ae1faaad4ed2df1cc62
paper_authors.name: Alexander Schwing
paper_title: The Curse of Conditions: Analyzing and Improving Optimal Transport for
    Conditional Flow-Based Generation
paper_summary: 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
paper_ai_summary: Conditional optimal transport C^2OT improves upon minibatch optimal transport by incorporating conditional weighting, enhancing performance in both discrete and continuous settings.
paper_ai_keywords: minibatch optimal transport optimal transport coupling flow matching ordinary differential equation conditional optimal transport C^2OT prior distribution 8gaussians-to-moons CIFAR-10 ImageNet-32x32 ImageNet-256x256