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Diffusion State-Guided Projected Gradient for Inverse Problems
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Proposes DiffStateGrad, which projects the measurement guidance gradient onto a low-rank SVD subspace of the current diffusion state, improving robustness and worst-case performance of diffusion-based inverse solvers (PSLD, ReSample, DPS, DAPS) on linear and nonlinear image restoration.
Problem
Diffusion-based posterior sampling for inverse problems relies on approximate measurement likelihood gradients, which push the diffusion state off the data manifold, causing artifacts and sensitivity to guidance step size and measurement noise.
Approach
Project the measurement gradient onto the low-rank subspace given by the top singular vectors of the current diffusion state (adaptive rank via a variance retention threshold), so updates stay near the artifact-free prior manifold; this is a plug-in module for many diffusion inverse solvers.
Key results
- On random inpainting with a large MG step size, DiffStateGrad-PSLD improves LPIPS from 0.463 to 0.165 (PSLD in the appendix table).
- On phase retrieval, DiffStateGrad-ReSample improves PSNR from 27.61 (8.07) to 31.19 (4.33) and reduces failure rate (PSNR<20) from 26% to 4% for the DPS/DAPS setting.
- DiffStateGrad-DAPS improves SSIM on box inpainting under large measurement noise from 0.436 to 0.705.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Project the measurement gradient using the current diffusion state instead of no projection (ablation) | PSLD · FFHQ 256×256, random inpainting | PSNR: 29.05 -> 31.68 | Helped |
| Use a random matrix subspace instead of a diffusion-state subspace (ablation) | PSLD · FFHQ 256×256, random inpainting | PSNR: 27.30 -> 31.68 | Hurt |
| Project onto the measurement-gradient subspace instead of the diffusion-state subspace (ablation) | PSLD · FFHQ 256×256, random inpainting | PSNR: 29.21 -> 31.68 | Hurt |
| Apply DiffStateGrad to PSLD | PSLD · FFHQ 256×256, random inpainting | PSNR: 29.05 -> 31.68 | Helped |
| Apply DiffStateGrad to DAPS | DAPS · FFHQ 256×256, box inpainting | LPIPS: 0.136 -> 0.113 | Helped |
| Apply DiffStateGrad to DPS | DPS · FFHQ 256×256, Gaussian deblur | PSNR: 25.48 -> 26.29 | Helped |
| Apply DiffStateGrad to ReSample | ReSample · FFHQ 256×256, phase retrieval | PSNR: 27.61 (8.07) -> 31.19 (4.33) | Helped |
| Apply DiffStateGrad to PSLD at a large measurement-gradient step size | PSLD · FFHQ 256×256, random inpainting | LPIPS: 0.463 -> 0.165 | Helped |
| Apply DiffStateGrad to DAPS under large measurement noise | DAPS · FFHQ 256×256, box inpainting | SSIM: 0.436 -> 0.705 | Helped |
| Apply DiffStateGrad to the phase-retrieval solver | Phase retrieval · Phase retrieval | failure rate (PSNR <20): 26% -> 4% | Helped |
| Apply DiffStateGrad to ReSample | ReSample · FFHQ 256×256, high dynamic range | LPIPS: 0.190 (0.067) -> 0.164 (0.041) | Helped |
| Apply DiffStateGrad to PSLD at the default MG step size | PSLD · FFHQ 256×256, random inpainting | PSNR: 29.05 -> 28.14 | Hurt |
Surprising findings
- The paper reports that the choice of subspace matters more than its low-rank nature: a random-matrix projection degrades performance below no projection.
- On some tasks with default settings (e.g., PSLD on random inpainting and SR), DiffStateGrad slightly reduces performance relative to the base method.
Limitations
- Assumes the learned prior is good; may import prior biases into restoration (e.g., black hole imaging not recommended).
- Theory (proposition) relies on approximate projection and small step-size assumptions, with first-order approximations.
- Runtime efficiency is not the focus; overhead is small but not optimized.
Experimental setup
Datasets: FFHQ 256x256 validation ImageNet 256x256 validation
Benchmarks: FFHQ 256x256 ImageNet 256x256
Metrics: LPIPS PSNR SSIM NMSE failure rate
Baselines: PSLD ReSample DPS DAPS DDNM DDRM MCG MPGD-AE
Builds on: PSLD DPS DAPS ReSample MCG
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