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Unpaired Image-to-Image Translation via Neural Schrödinger Bridge
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Proposes UNSB, which solves the Schrödinger Bridge problem as a sequence of adversarial learning steps (with a Markovian discriminator and CUT-style regularization) to enable scalable unpaired high-resolution image-to-image translation.
Problem
Schrödinger Bridge methods fail on unpaired image-to-image translation at high resolution because of the curse of dimensionality, which makes empirical optimal transport couplings inaccurate; diffusion models also assume Gaussian priors that limit unpaired translation.
Approach
Reformulate the SB problem as a Lagrangian with a KL constraint on the target marginal, so each time step becomes an adversarial learning problem; use a time-conditional generator that predicts the target image from the current state, an advanced Markovian discriminator, and a patch-wise contrastive regularizer, and iteratively refine the prediction over NFE steps.
Key results
- On Horse2Zebra, UNSB with NFE=5 reaches FID 35.7 and KID 0.587, versus 45.5 for CUT (one-step GAN) and 97.3 for SDEdit.
- On Summer2Winter, UNSB achieves FID 73.9 and KID 0.421 at 0.045 s per image, outperforming CUT (84.3 FID).
- Ablation on Horse2Zebra shows that adding the Markovian discriminator, regularization, and multi-step sampling each improves FID, from 230 (no components) to 35.7 (full UNSB).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use UNSB instead of CUT | Unpaired image translation · Horse2Zebra | FID: 45.5 -> 35.7 | Helped |
| use UNSB instead of CUT | Unpaired image translation · Summer2Winter | FID: 84.3 -> 73.9 | Helped |
| use UNSB instead of CUT | Unpaired image translation · Label2Cityscape | FID: 56.4 -> 53.2 | Helped |
| use UNSB instead of CycleGAN | Unpaired image translation · Map2Satellite | FID: 54.6 -> 47.6 | Helped |
| use UNSB instead of StarGAN v2 | Male2Female translation · CelebA-HQ-256 | FID: 48.55 -> 37.87 | Helped |
| add a patch discriminator instead of an instance discriminator (ablation) | UNSB · Horse2Zebra | FID: 104 -> 66.3 | Helped |
| add regularization (ablation) | UNSB with patch discriminator, NFE 5 · Horse2Zebra | FID: 58.9 -> 35.7 | Helped |
| increase NFE from 1 to 5 (ablation) | UNSB with patch discriminator and no regularization · Horse2Zebra | FID: 66.3 -> 58.9 | Helped |
| add regularization (ablation) | UNSB with patch discriminator, NFE 1 · Summer2Winter | FID: 155.5 -> 75.6 | Helped |
| increase NFE from 1 to 5 (ablation) | UNSB with patch discriminator and regularization · Summer2Winter | FID: 75.6 -> 73.9 | Helped |
| use an instance discriminator rather than no discriminator (ablation) | UNSB without regularization, NFE 5 · Horse2Zebra | FID: 230 -> 104 | Helped |
| replace instance discriminator with patch discriminator (ablation) | UNSB without regularization, NFE 1 · Summer2Winter | FID: 185.5 -> 155.5 | Helped |
Surprising findings
- Sinkhorn-Knopp-based SB and the SB-based SBCFM baseline produce outputs unrelated to the input at 256x256 resolution, with FID around 229.5 on Horse2Zebra.
- NFE=1 UNSB often performs worse than one-step GAN methods, and FID increases at large NFE on Map2Satellite due to artifacts.
Limitations
- NFE=1 performance is weaker than some one-step GAN baselines; artifacts appear at large NFE on some datasets.
- On the entropic OT benchmark, UNSB (cFID 63.0) underperforms ENOT (cFID 40.5), with preliminary ad-hoc hyperparameters.
- Results on 512x512 are only preliminary at training epoch 100.
Experimental setup
Datasets: Horse2Zebra Summer2Winter Label2Cityscape Map2Satellite CelebA-HQ AFHQ
Benchmarks: Horse2Zebra Summer2Winter Label2Cityscape Map2Satellite CelebA-HQ Male2Female Zebra2Horse entropic OT benchmark (CelebA 64x64)
Metrics: FID KID cFID NFE generation time
Baselines: NOT CycleGAN MUNIT DistanceGAN GcGAN CUT SDEdit P2P SBCFM DSB SB-FBSDE EGSDE
Builds on: Schrödinger Bridge Denoising Diffusion GAN CUT Neural Optimal Transport Sinkhorn-Knopp
Closest papers by meaning
- Adversarial Schrödinger Bridge Matching (NeurIPS 2024 · similarity 0.90)
- Schrodinger Bridge Flow for Unpaired Data Translation (NeurIPS 2024 · similarity 0.90)
- Finding Local Diffusion Schrodinger Bridge using Kolmogorov-Arnold Network (CVPR 2025 · similarity 0.88)
- Deterministic Image-to-Image Translation via Denoising Brownian Bridge Models with Dual Approximators (CVPR 2025 · similarity 0.88)
- BridgeTwist: Twisting Schrödinger Bridges for Training-Free Conditional Sampling (NeurIPS 2026 · similarity 0.86)
- Exploring the Design Space of Diffusion Bridge Models (NeurIPS 2025 · similarity 0.86)
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