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Solving Diffusion ODEs with Optimal Boundary Conditions for Better Image Super-Resolution
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Proposes finding an approximately optimal initial noise (boundary condition) for diffusion ODE samplers by searching random noises on a small HR-LR reference set, yielding stable, plug-and-play improvements for diffusion-based super-resolution.
Problem
Diffusion-based image super-resolution yields unstable quality across samples because of randomness in the reverse process and in the initial noise; few-step samplers amplify this.
Approach
Treat the initial noise x_T of a diffusion ODE as a boundary condition, argue the optimal BC is approximately independent of the LR input, and pick it by Monte Carlo search over K random noises minimizing summed LPIPS on a reference set of R HR-LR pairs; the chosen BC is then reused for all test LR images.
Key results
- On bicubic SR with the same SR3 model, DDIM-50 + x_T~ reaches LPIPS 0.1053 on DIV2K-test versus 0.1075 for DDPM-1000 and 0.1257 for DDPM-100, and it is claimed to surpass DDPM-1000.
- On real-SR, DDIM-50 + x_T~ with StableSR improves DIV2K-test LPIPS from 0.3629 to 0.3169 and RealSR PSNR from 21.24 to 22.13 dB, beating the official DDPM-200 sampler (LPIPS 0.3065 on RealSR).
- Applied to DiffIR, D-4 + x_T~ achieves the best DISTS on DIV2K-test (0.1772) and LPIPS on RealSR (0.2419).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the approximately optimal boundary condition with DDIM-50 | SR3 · DIV2k-test, Urban100, and BSD100 (bicubic-SR) | LPIPS: 0.1483 -> 0.1053; 0.1333 -> 0.1164; 0.1823 -> 0.1552 | Helped |
| Use the approximately optimal boundary condition with DDIM-100 | SR3 · DIV2k-test, Urban100, and BSD100 (bicubic-SR) | LPIPS: 0.1571 -> 0.1032; 0.1335 -> 0.1136; 0.1950 -> 0.1505 | Helped |
| Use the approximately optimal boundary condition with DDIM-50 | StableSR · DIV2k-test and RealSR (real-SR) | LPIPS: 0.3629 -> 0.3169; 0.3536 -> 0.2999 | Helped |
| Use the approximately optimal boundary condition with D-4 | DiffIR · DIV2k-test and RealSR (real-SR) | DISTS: 0.1773 -> 0.1772; 0.2076 -> 0.1993 | Mixed |
| Use the approximately optimal boundary condition with D-4 | DiffIR · DIV2k-test and RealSR (real-SR) | PSNR: 22.94 -> 22.95; 25.33 -> 25.82 | Helped |
| Increase the reference-set size R (ablation) | The approximately optimal boundary-condition search with SR3 · DIV2k-test (bicubic-SR) | LPIPS | Helped |
| Increase the random-candidate-set size K (ablation) | The approximately optimal boundary-condition search with SR3 · DIV2k-test (bicubic-SR) | LPIPS | Helped |
| Use the approximately optimal boundary condition with DDIM-50 | Mid-training SR3 · DIV2k-test (bicubic-SR) | PSNR: 17.10 -> 19.15 | Helped |
Surprising findings
- A boundary condition chosen from a mid-training model (500k iterations) still improves DDIM-50 sampling, suggesting extreme-point structure matters more than a fully converged fit.
- The Monte Carlo selection gains are reported as improving sample quality beyond DDPM-1000, the commonly treated upper bound.
Limitations
- The approximately optimal BC has the same dimension as the LR input, so it cannot directly be applied to LR images of different shapes.
- The independence of the optimal BC from the LR input is an assumption supported only by a correlation experiment, not proven.
- Gains on the PSNR metric are mixed; for some settings (e.g., DPMS-20 + x_T~ and DDIM-100 + x_T~ on DIV2K) PSNR drops.
Experimental setup
Datasets: DF2K DIV2K Urban100 B100 RealSR
Benchmarks: DIV2K-test Urban100 BSD100 RealSR
Metrics: PSNR LPIPS DISTS
Baselines: DDPM-1000 DDPM-250 DDPM-100 DDIM-50 DDIM-100 DPM-Solver-20 ESRGAN RankSRGAN SRDiff StableSR DDPM-200 DiffIR Real-ESRGAN
Builds on: DDIM DPM-Solver SR3 StableSR LPIPS
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