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Amortized Optimal Transport from Sliced Potentials

NeurIPS 2026 · Learning theory and algorithms › Optimal transport · approach: Sinkhorn and entropic OT algorithms · 0 citations (OpenAlex)

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Proposes RA-OT and OA-OT, two amortized OT methods that predict entropic Kantorovich potentials as linear combinations of sliced-OT potentials, recovering plans for repeated OT problems with a parameter count independent of atom number.

Problem

Computing entropic optimal transport plans repeatedly across many measure pairs is expensive; existing amortized approach Meta-OT needs many parameters and fixed atom counts.

Approach

Use Kantorovich potentials from sliced OT (closed-form 1D solutions over L projections) as features, and map them linearly (L coefficients) to the original OT potential, fitted either by least squares on exact potentials (RA-OT) or by optimizing the Kantorovich dual (OA-OT).

Key results

• On MNIST with M=10, OA-OT reaches plan RMSE 6.16e-6 versus 16.16e-6 for Meta-OT and 93.51e-6 for Min-STP.
• On spherical transport with M=200, Meta-OT achieves the lowest RMSE (3.62e-7) while OA-OT reaches 3.66e-7 and RA-OT 7.55e-7, with OA-OT and RA-OT far below Min-STP's 115e-7.
• In 2D CFM, RA-OT and OA-OT give 2.5x-4.5x training speedup over OT-CFM, but Sinkhorn W2^2 is worse than OT-CFM (e.g., 0.5072 vs 0.1956 on 8gaussians).

Surprising findings

• On the spherical transport task, Meta-OT achieves lower RMSE than the proposed methods at larger M (e.g., M=200), contrary to the paper's general claims.
• In 2D flow matching, the amortized methods have substantially higher W2^2 than OT-CFM on 8gaussians and moons despite comparable straightness.

Limitations

• Restricted to discrete setting and entropic OT; continuous case is defined but not experimented.
• Linear amortized model with only L coefficients may limit expressivity; only one shift test (rotation) examined.
• Experiments use small pools of 1,000 measure pairs and modest hardware.

Experimental setup

Datasets: MNIST WikiArt images (about 200, for color transfer) Earth landmass and population density data (CC-licensed dataset) CIFAR-10 2D toy datasets (8gaussians, moons, scurve)

Benchmarks: MNIST grayscale transport spherical supply-demand transport color transfer 2D conditional flow matching CIFAR-10 flow matching fine-tuning

Metrics: RMSE of plan training time inference time Sinkhorn W2^2 NPE FID NFE

Baselines: Meta-OT Min-STP min-SWGG I-CFM OT-CFM

Builds on: Meta-OT sliced optimal transport Sinkhorn algorithm OT-CFM

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