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DiffFPR: Diffusion Prior for Oversampled Fourier Phase Retrieval
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Combines a pretrained DDIM diffusion prior with the RAAR iterative phase-retrieval engine, using damped measurement-guided updates on the Tweedie estimate, to solve oversampled multi-channel Fourier phase retrieval.
Problem
Oversampled Fourier phase retrieval for color images, where trivial/equivalent solutions (channel orientation misalignment, 180° rotation, sign ambiguity) make iterative methods like RAAR recover channels with mismatched orientations.
Approach
Insert RAAR iterations on the Tweedie estimate x̂0(xt) inside each DDIM sampling step, with a damped update weighted by sqrt(alpha_t), so the diffusion prior pulls the iterate onto the clean image manifold and corrects channel orientation, instead of DPS-style gradient guidance.
Key results
- On FFHQ noiseless 4x oversampling, DiffFPR reaches 37.24 dB PSNR / 0.902 SSIM versus 22.50 dB / 0.601 for RAAR and 24.85 dB for DPS*.
- DiffFPR achieved a 100% success rate (PSNR > 20 dB) on 1K FFHQ and ImageNet images, versus 52.4% and 48.2% for RAAR.
- On FFHQ at 128x128 resized, DiffFPR obtains 37.59 PSNR vs 32.71 for HIO and 13.11 for CDM.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add the diffusion prior and measurement-guided RAAR to RAAR | RAAR · FFHQ, σy=0.00 | PSNR: 22.50 -> 37.24 | Helped |
| add the diffusion prior and measurement-guided RAAR to RAAR | RAAR · ImageNet, σy=0.00 | PSNR: 21.80 -> 31.76 | Helped |
| add the diffusion prior and measurement-guided RAAR to RAAR | RAAR · FFHQ, σy=0.01 | PSNR: 12.74 -> 29.17 | Helped |
| add the diffusion prior and measurement-guided RAAR to RAAR | RAAR · ImageNet, σy=0.01 | PSNR: 12.80 -> 25.94 | Helped |
| add the diffusion prior and measurement-guided RAAR to RAAR | RAAR · FFHQ, σy=0.05 | PSNR: 12.51 -> 22.15 | Helped |
| add the diffusion prior and measurement-guided RAAR to RAAR | RAAR · ImageNet, σy=0.05 | PSNR: 12.66 -> 19.81 | Helped |
| replace the inner RAAR engine with HIO (ablation) | DiffFPR · FFHQ, σy=0.00 | PSNR: 37.24 -> 36.28 | Hurt |
| replace the inner RAAR engine with HIO (ablation) | DiffFPR · FFHQ, σy=0.01 | PSNR: 29.17 -> 23.01 | Hurt |
| replace the inner RAAR engine with HIO (ablation) | DiffFPR · FFHQ, σy=0.05 | PSNR: 22.15 -> 14.08 | Hurt |
| use post-projection instead of measurement guidance before sampling (ablation) | DiffFPR · FFHQ, σy=0.00 | PSNR: degraded by 15.46dB | Hurt |
| increase inner RAAR iterations from 1 to 2 (ablation) | DiffFPR with 500 diffusion steps · FFHQ, σy=0.00 | PSNR: 32.29 -> 44.44 | Helped |
| increase inner RAAR iterations from 2 to 4 (ablation) | DiffFPR with 500 diffusion steps · FFHQ, σy=0.00 | PSNR: 44.44 -> 49.98 | Helped |
Surprising findings
- DPS, the standard diffusion posterior sampling baseline, frequently fails on Fourier phase retrieval, succeeding (PSNR > 20 dB) on only 14.5% of FFHQ and 4.0% of ImageNet images.
- Applying the measurement projection after the unconditional sampling step (post-projection) degrades PSNR by 15.46 dB relative to the pre-projection order used by the method.
Limitations
- Less effective under noise: accumulated traditional-engine errors introduce noise artifacts in noisy measurements (PSNR 29.17 at sigma 0.01, 22.15 at sigma 0.05 on FFHQ).
- Evaluated only on synthetic data; real-world phase retrieval not tested.
- Requires running each method three times and selecting the best result, and computation is higher than RAAR.
Experimental setup
Datasets: FFHQ 256x256 ImageNet 256x256
Benchmarks: FFHQ ImageNet
Metrics: PSNR SSIM LPIPS
Baselines: RAAR DPS HIO DIP SIREN E2E CDM
Builds on: RAAR DDIM Diffusion Posterior Sampling (DPS) Douglas-Rachford splitting
Closest papers by meaning
- DiffSCI: Zero-Shot Snapshot Compressive Imaging via Iterative Spectral Diffusion Model (CVPR 2024 · similarity 0.86)
- DiffFNO: Diffusion Fourier Neural Operator (CVPR 2025 · similarity 0.85)
- Diffusion State-Guided Projected Gradient for Inverse Problems (ICLR 2025 · similarity 0.85)
- Rethinking Diffusion Model for Multi-Contrast MRI Super-Resolution (CVPR 2024 · similarity 0.85)
- FaithDiff: Unleashing Diffusion Priors for Faithful Image Super-resolution (CVPR 2025 · similarity 0.85)
- FAM Diffusion: Frequency and Attention Modulation for High-Resolution Image Generation with Stable Diffusion (CVPR 2025 · similarity 0.84)
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