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Deterministic Image-to-Image Translation via Denoising Brownian Bridge Models with Dual Approximators
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Proposes Dual-approx Bridge, a Brownian bridge model with two separately trained networks (a forward approximator for X0 and a reverse approximator for the noise) that yields near-deterministic, high-fidelity image-to-image translation with few sampling steps.
Problem
Deterministic image-to-image translation (e.g., super-resolution, label-to-photo) needs outputs that are faithful to a single ground truth and high quality, but stochastic bridge/diffusion samplers produce variable outputs and PF-ODE samplers produce blurry results.
Approach
Use a Brownian bridge SDE with a pair of dual neural approximators: a forward network predicts X0 from X_t and a separate reverse network predicts the scaled white noise, so the only sampling randomness is negligible at the start, enabling deterministic, faithful outputs at high quality.
Key results
- On Cityscapes label-to-photo with 200 steps, FID 48.70 vs 75.37 for the second-best (CycleGAN), PSNR 15.70 vs 14.61.
- With 3 sampling steps on Cityscapes, PSNR 16.99 and SSIM 57.4%, beating SDE (14.28) and PF-ODE (15.23) Brownian bridge samplers.
- On BSD100 super-resolution, LPIPS 0.1267 and PSNR 26.56, the best among compared methods; on Urban100 LPIPS 0.1207 is best but PSNR 23.23 is second to SRDiff.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use 1,000 instead of 3 sampling steps (ablation) | Dual-approx Bridge · Cityscapes | FID: 56.07 -> 42.70 | Helped |
| use 1,000 instead of 3 sampling steps (ablation) | Dual-approx Bridge · Cityscapes | PSNR: 16.99 -> 15.10 | Hurt |
| use 1,000 instead of 3 sampling steps (ablation) | Dual-approx Bridge · Cityscapes | LPIPS: 0.530 -> 0.442 | Helped |
| use 3 instead of 1,000 sampling steps (ablation) | Dual-approx Bridge · Cityscapes | SSIM: (43.2 ±0.07) % -> (57.4 ±0.00) % | Helped |
| use the dual-approximator sampler instead of the SDE-based Brownian bridge sampler | Brown Bridge Model · Cityscapes | PSNR: 14.28 ±0.21 -> 16.99 ±0.01 | Helped |
| use the dual-approximator sampler instead of the PF-ODE-based Brownian bridge sampler | Brown Bridge Model · Cityscapes | SSIM: (51.2 ±0.00) % -> (57.4 ±0.00)% | Helped |
| use Dual-approx Bridge instead of RankSRGAN | super-resolution models · BSD100 | LPIPS: 0.1714 -> 0.1267 | Helped |
| use Dual-approx Bridge instead of SRDiff | super-resolution models · Urban100 | PSNR: 23.88 -> 23.23 | Hurt |
| use Dual-approx Bridge instead of DCLGAN | Cityscapes image translation models · Cityscapes | FID: 49.4 -> 48.7 | Helped |
| use Dual-approx Bridge instead of A-Bridge | Edges2Handbags image translation models · Edges2Handbags | FID: 1.07 -> 1.36 | Hurt |
Surprising findings
- Fewer sampling steps (3) gave better faithfulness (PSNR/SSIM) than 1,000 steps, while 1,000 steps gave the best FID.
Limitations
- Only the variance-preserving SDE formulation is used.
- Image quality on Edges2Handbags is second to A-Bridge (FID 1.36 vs 1.07).
- Optimal number of sampling steps per task is not determined.
Experimental setup
Datasets: Cityscapes Edges2Handbags DF2K
Benchmarks: Cityscapes Edges2Handbags Urban100 BSD100
Metrics: FID LPIPS PSNR SSIM
Baselines: Pix2Pix CycleGAN UNIT ESRGAN RankSRGAN SRDiff A-Bridge DDBM I2SB Rectified Flow SDEdit DDIB
Builds on: Brownian bridge diffusion models DDBM score-based SDE Pix2Pix SRDiff
Closest papers by meaning
- Exploring the Design Space of Diffusion Bridge Models (NeurIPS 2025 · similarity 0.88)
- Unpaired Image-to-Image Translation via Neural Schrödinger Bridge (ICLR 2024 · similarity 0.88)
- Denoising Diffusion Bridge Models (ICLR 2024 · similarity 0.88)
- Diffusion Bridge Implicit Models (ICLR 2025 · similarity 0.88)
- FrameBridge: Improving Image-to-Video Generation with Bridge Models (ICML 2025 · similarity 0.87)
- Denoising Autoregressive Transformers for Scalable Text-to-Image Generation (ICLR 2025 · similarity 0.86)
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