Unbalanced W-Flow: Unbalanced Wasserstein Drifting under Finite-Batch Marginal Fluctuations

Key points

• Teacher-free one-step generative models such as W-Flow learn directly from distributional objectives, with the Sinkhorn divergence providing the strongest empirical performance among the energies studied in W-Flow.1
• However, Sinkhorn divergence is based on balanced optimal transport, whose exact marginal constraints can induce undesirable transport under finite minibatch fluctuations.1
• We further characterize the finite-batch velocity error of balanced and unbalanced transport by comparing each minibatch field with its population counterpart.1
• Our analysis identifies conditions under which marginal relaxation yields smaller minibatch-to-population velocity error, and shows that for separated matched modes, balanced sensitivity grows with inter-mode separation while the corresponding Unbalanced Optimal Transport (UOT) sensitivity remains controlled by local transport geometry.1

Sources (1)

• [1]Unbalanced W-Flow: Unbalanced Wasserstein Drifting under Finite-Batch Marginal Fluctuations
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 13, 03:28 PM

  We introduce UW-Flow, which replaces the balanced Sinkhorn energy with a debiased unbalanced Sinkhorn divergence and derives the corresponding Wasserstein velocity.

  Teacher-free one-step generative models such as W-Flow learn directly from distributional objectives, with the Sinkhorn divergence providing the strongest empirical performance among the energies studied in W-Flow.

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