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Image Restoration Through Generalized Ornstein-Uhlenbeck Bridge
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Proposes the Generalized Ornstein-Uhlenbeck Bridge (GOUB), which applies Doob's h-transform to a generalized OU process to get a point-to-point diffusion bridge from low-quality to high-quality images, plus a Mean-ODE sampler, evaluated on inpainting, deraining and 4x super-resolution.
Problem
Diffusion models for image restoration usually map noise to data or need task-specific degradation priors; existing bridge models either need costly iterative likelihood approximation or ignore the choice of diffusion process, limiting restoration quality.
Approach
Use the mean-reverting generalized OU process as the base forward SDE and apply Doob's h-transform with the terminal low-quality image as the endpoint, removing terminal variance so the diffusion is a point-to-point bridge with closed-form marginals; train by maximum likelihood (ELBO) with a noise-prediction parameterization and an L1 loss, and sample with a Mean-ODE that drops the Brownian term.
Key results
- On CelebA-HQ inpainting, Mean-ODE reaches 31.39 PSNR and 0.9392 SSIM, while GOUB reaches the best LPIPS (0.037) and FID (4.30).
- On Rain100H deraining, Mean-ODE reports 34.56 PSNR and 0.9414 SSIM, and GOUB reports 31.96 PSNR with LPIPS 0.046 and FID 18.14, beating IR-SDE on FID.
- On DIV2K 4x super-resolution, GOUB gets 26.89 PSNR and Mean-ODE 28.50 PSNR, versus 25.90 for IR-SDE; Mean-ODE beats Score-ODE by a wide margin on all three tasks.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use Mean-ODE instead of Score-ODE (ablation) | GOUB · Image inpainting | PSNR: 18.23 -> 31.39 | Helped |
| use Mean-ODE instead of Score-ODE (ablation) | GOUB · Image deraining | PSNR: 13.64 -> 34.56 | Helped |
| use Mean-ODE instead of Score-ODE (ablation) | GOUB · Image 4× super-resolution | PSNR: 28.14 -> 28.50 | Helped |
| use Mean-ODE instead of Score-ODE (ablation) | GOUB · Image inpainting | FID: 161.54 -> 12.24 | Helped |
| use Mean-ODE instead of Score-ODE (ablation) | GOUB · Image deraining | FID: 191.15 -> 32.83 | Helped |
| use Mean-ODE instead of Score-ODE (ablation) | GOUB · Image 4× super-resolution | FID: 25.51 -> 22.14 | Helped |
| use GOUB instead of VEB or VPB | image restoration bridge model · CelebA-HQ inpainting | PSNR: 27.75 -> 28.98; 27.32 -> 28.98 | Helped |
| use GOUB instead of VEB or VPB | image restoration bridge model · Rain100H deraining | PSNR: 30.39 -> 31.96; 30.89 -> 31.96 | Helped |
| use GOUB instead of VEB or VPB | image restoration bridge model · DIV2K 4× super-resolution | PSNR: 24.21 -> 26.89; 25.40 -> 26.89 | Helped |
| use Mean-ODE instead of GOUB (SDE) | GOUB · CelebA-HQ inpainting | PSNR: 28.98 -> 31.39 | Helped |
| use Mean-ODE instead of GOUB (SDE) | GOUB · Rain100H deraining | PSNR: 31.96 -> 34.56 | Helped |
| use Mean-ODE instead of GOUB (SDE) | GOUB · DIV2K 4× super-resolution | LPIPS: 0.220 -> 0.328 | Hurt |
Surprising findings
- Mean-ODE attains the highest PSNR/SSIM on inpainting and deraining but worse LPIPS and FID than GOUB or IR-SDE, indicating a pixel-fidelity versus perceptual trade-off.
Limitations
- Mean-ODE underperforms on perceptual metrics (LPIPS, FID) relative to GOUB in several tasks.
- Experiments are limited to three restoration tasks on specific datasets, with no compute or hardware details stated.
Experimental setup
Datasets: CelebA-HQ Rain100H DIV2K
Benchmarks: CelebA-HQ Rain100H DIV2K
Metrics: PSNR SSIM LPIPS FID
Baselines: PromptIR DDRM IR-SDE MPRNet M3SNet-32 MAXIM MHNet VEB VPB
Builds on: score-based SDE DDPM Doob's h-transform IR-SDE
Closest papers by meaning
- IRBridge: Solving Image Restoration Bridge with Pre-trained Generative Diffusion Models (ICML 2025 · similarity 0.90)
- UniDB: A Unified Diffusion Bridge Framework via Stochastic Optimal Control (ICML 2025 · similarity 0.89)
- Denoising Diffusion Bridge Models (ICLR 2024 · similarity 0.89)
- Diffusion Bridge Implicit Models (ICLR 2025 · similarity 0.89)
- Improving Diffusion-Based Image Restoration with Error Contraction and Error Correction (AAAI 2024 · similarity 0.88)
- Exploring the Design Space of Diffusion Bridge Models (NeurIPS 2025 · similarity 0.88)
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