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Light Unbalanced Optimal Transport
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Proposes U-LightOT, a lightweight non-minimax solver for continuous unbalanced entropic OT that parametrizes the plan with unnormalized Gaussian mixtures and optimizes a tractable KL-based bound on the dual.
Problem
Continuous unbalanced entropic optimal transport (UEOT) between measures known only through samples; existing solvers are heuristic, heavy, or use complex minimax GAN-style objectives.
Approach
Derive a tractable, non-minimax upper bound on KL(gamma*||gamma_theta,omega) from the dual UEOT problem, and parametrize both the marginal and the conditional potential with unnormalized Gaussian mixtures so the normalizing constant and mass have closed forms; this generalizes the balanced LightSB solver to the unbalanced case.
Key results
- On FFHQ Young->Adult translation, U-LightOT ran in 02:38 versus 03:21 (the fastest of the unbalanced baselines), 18:11 and 16:30 for the others.
- U-LightOT reports the best keep-accuracy among compared methods while keeping good target accuracy, trading off via the unbalancedness parameter tau.
- The paper proves a generalization bound with O(1/sqrt(N)) + O(1/sqrt(M)) estimation error and a universal approximation theorem for Gaussian mixture parametrization.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Increase the unbalancedness parameter τ (ablation) | U-LightOT · FFHQ image translation | accuracy (keep) | Helped |
| Increase the unbalancedness parameter τ (ablation) | U-LightOT · FFHQ image translation | accuracy (target) | Hurt |
| Increase τ from 1 (ablation) | U-LightOT · Gaussian Mixture | transport of mass to the closest target | Hurt |
| Use a large τ (ablation) | U-LightOT · FFHQ image translation | agreement with LightSB | No clear effect |
| Use U-LightOT instead of the compared unbalanced solvers | FFHQ image translation · FFHQ image translation | time (sec) | Helped |
| Use U-LightOT for unbalanced translation | FFHQ image translation · FFHQ image translation | accuracy (keep) | Helped |
Limitations
- Restricted to the Gaussian mixture parametrization of potentials.
- Generalization and approximation results rely on compact support and Lipschitz conjugate assumptions.
- Image experiments operate in a pretrained ALAE latent space rather than pixel space.
Experimental setup
Datasets: FFHQ 2D Gaussian mixtures (synthetic)
Benchmarks: FFHQ translation (keep/target accuracy) 2D Gaussian mixture toy example
Metrics: accuracy (keep) accuracy (target) wall-clock time
Baselines: LightSB OT-FM UOT-FM UOT-SD UOT-GAN
Builds on: LightSB EOT/SB benchmark Fenchel-Rockafellar duality flow matching
Closest papers by meaning
- Progressive Entropic Optimal Transport Solvers (NeurIPS 2024 · similarity 0.88)
- Decreasing Entropic Regularization Averaged Gradient for Semi-Discrete Optimal Transport (NeurIPS 2025 · similarity 0.86)
- Variational Regularized Unbalanced Optimal Transport: Single Network, Least Action (NeurIPS 2025 · similarity 0.85)
- Submodular framework for structured-sparse optimal transport (ICML 2024 · similarity 0.85)
- Universal Neural Optimal Transport (ICML 2025 · similarity 0.85)
- Energy-guided Entropic Neural Optimal Transport (ICLR 2024 · similarity 0.85)
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