Research map / Learning theory and algorithms / Optimal transport
Energy-guided Entropic Neural Optimal Transport
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Proposes energy-guided entropic OT: reformulates the weak dual of entropic OT so a single potential network f_theta acts as an energy function for conditional plans, trained EBM-style with Langevin sampling, with generalization bounds and StyleGAN-latent unpaired I2I experiments.
Problem
Recovering entropy-regularized optimal transport (EOT) plans, especially stochastic conditional plans for unpaired data-to-data translation, in continuous high-dimensional settings where existing neural OT solvers are unstable for small epsilon or require extra models.
Approach
Using the weak dual EOT formulation, the inner optimizer over conditional distributions is a Gibbs distribution whose energy is (c(x,y)-f(y))/eps, so a single potential network f_theta trained with an EBM-style gradient (via Langevin sampling from conditionals) recovers the optimal conditional plans, with no exponentiation of dual potentials and no extra score model.
Key results
- On AFHQ 512x512 Cat->Dog the method reports FID 56.6, versus 51.04 for EGSDE and 85.9 for CycleGAN.
- On Gaussian-to-Gaussian transport at eps=0.1 and D=2, the method reaches BW2^2-UVP 0.01, the best among compared solvers in the table.
- The method trains only one MLP potential network on the StyleGAN latent space, with no encoder and no source generative model.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Energy-guided EOT instead of ILVR | StyleGAN2-ADA translation · Cat→Dog | FID: $74.37$ -> $56.6$ | Helped |
| Use Energy-guided EOT instead of SDEdit | StyleGAN2-ADA translation · Cat→Dog | FID: $74.17$ -> $56.6$ | Helped |
| Use Energy-guided EOT instead of EGSDE | StyleGAN2-ADA translation · Cat→Dog | FID: $51.04$ -> $56.6$ | Hurt |
| Use Energy-guided EOT instead of CycleGAN | StyleGAN2-ADA translation · Cat→Dog | FID: $85.9$ -> $56.6$ | Helped |
| Use Energy-guided EOT instead of MUNIT | StyleGAN2-ADA translation · Cat→Dog | FID: $104.4$ -> $56.6$ | Helped |
| Use Energy-guided EOT instead of StarGAN v2 | StyleGAN2-ADA translation · Cat→Dog | FID: $54.88$ -> $56.6$ | Hurt |
| Use Energy-guided EOT instead of ILVR | StyleGAN2-ADA translation · Wild→Dog | FID: $75.33$ -> $65.8$ | Helped |
| Use Energy-guided EOT instead of SDEdit | StyleGAN2-ADA translation · Wild→Dog | FID: $68.51$ -> $65.8$ | Helped |
| Use Energy-guided EOT instead of EGSDE | StyleGAN2-ADA translation · Wild→Dog | FID: $50.43$ -> $65.8$ | Hurt |
Limitations
- Requires MCMC (Langevin) sampling for training and inference, which may be time-consuming.
- Generalization bound is in terms of Rademacher complexity and the approximation error is not analyzed; bound is not numerically explicit.
- Uses only basic short- and long-run EBMs without persistent buffers or temperature tuning.
Experimental setup
Datasets: AFHQ Gaussian Swissroll
Benchmarks: AFHQ Cat->Dog AFHQ Wild->Dog Gaussian-to-Gaussian (D=2,16,64,128)
Metrics: FID BW2^2-UVP
Baselines: ILVR SDEdit EGSDE CycleGAN MUNIT StarGAN v2 discrete EOT solver (Sinkhorn)
Builds on: Energy-based models Sinkhorn algorithm weak optimal transport Unadjusted Langevin Algorithm StyleGAN2-ADA
Closest papers by meaning
- Progressive Entropic Optimal Transport Solvers (NeurIPS 2024 · similarity 0.90)
- Expectile Regularization for Fast and Accurate Training of Neural Optimal Transport (NeurIPS 2024 · similarity 0.89)
- Improving Neural Optimal Transport via Displacement Interpolation (ICLR 2025 · similarity 0.88)
- Energy-Guided Continuous Entropic Barycenter Estimation for General Costs (NeurIPS 2024 · similarity 0.87)
- Free energy Estimation on Any State Space (NeurIPS 2026 · similarity 0.86)
- Overcoming Spurious Solutions in Semi-Dual Neural Optimal Transport: A Smoothing Approach for Learning the Optimal Transport Plan (ICML 2025 · similarity 0.86)
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