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Improving Diffusion-based Inverse Algorithms under Few-Step Constraint via Linear Extrapolation
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Proposes Learnable Linear Extrapolation (LLE), a lightweight method that learns linear combination coefficients over previous estimates to boost few-step diffusion-based inverse algorithms, unified under a Sampler-Corrector-Noiser canonical form.
Problem
Diffusion-based inverse algorithms need many denoising steps; existing fast ODE solvers transfer poorly to inverse problems because algorithms are heterogeneous and rely on approximations/heuristics that create large errors for analytical high-order solvers.
Approach
A canonical Sampler-Corrector-Noiser decomposition unifies diffusion inverse algorithms; LLE then learns per-timestep linear combination coefficients mixing the current corrected estimate with all previous estimates (decoupled into range and null space for linear problems), trained on ~50 generated samples with ground-truth supervision.
Key results
- On CelebA-HQ noisy linear tasks with 3 steps, LLE raises ΠGDM deblurring PSNR from 20.39 to 21.73 and DPS inpainting PSNR from 23.57 to 27.51.
- With 5 steps on CelebA-HQ, LLE improves ΠGDM deblurring PSNR from 22.46 to 25.95.
- On nonlinear deblurring at 3 steps, LLE improves DPS on FFHQ noiseless from 15.75 to 16.94 PSNR.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add LLE to DDNM | DDNM · CelebA-HQ noisy linear tasks, 3 steps | PSNR: 27.80 -> 28.08 (deblur); 16.64 -> 24.38 (inpainting); 27.09 -> 27.84 (4× SR); 16.55 -> 17.29 (CS 50%) | Helped |
| Add LLE to DPS | DPS · Nonlinear deblurring, 3 steps, FFHQ and CelebA-HQ | PSNR: 15.75 -> 16.94; 15.75 -> 16.93; 16.09 -> 19.06; 16.09 -> 19.06 | Helped |
| Use decoupled range-space and null-space coefficients (ablation) | LLE for linear inverse problems · CelebA-HQ linear tasks, 3 steps | PSNR: 32.81 -> 33.05; 20.74 -> 22.56; 25.64 -> 25.90; 18.39 -> 18.47 | Helped |
Surprising findings
- LLE gains are largest when the base algorithm performs poorly, while it roughly matches or slightly improves already strong algorithms.
Limitations
- Search space is restricted to the linear span of previous estimates; nonlinear extensions are left for future work.
- Evaluated datasets (CelebA-HQ, FFHQ) have demographic imbalances, limiting generalization to underrepresented groups.
Experimental setup
Datasets: CelebA-HQ FFHQ ImageNet
Benchmarks: CelebA-HQ FFHQ ImageNet
Metrics: PSNR SSIM LPIPS FID
Baselines: DDRM DDNM ΠGDM DMPS DPS DiffPIR ReSample RED-diff DAPS
Builds on: optimal linear subspace search DDIM high-order diffusion ODE solvers DPS DDNM
Closest papers by meaning
- Self-diffusion for Solving Inverse Problems (NeurIPS 2025 · similarity 0.90)
- Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealing (CVPR 2025 · similarity 0.90)
- Unleashing the Denoising Capability of Diffusion Prior for Solving Inverse Problems (NeurIPS 2024 · similarity 0.90)
- A Variational Perspective on Solving Inverse Problems with Diffusion Models (ICLR 2024 · similarity 0.90)
- Integrating Intermediate Layer Optimization and Projected Gradient Descent for Solving Inverse Problems with Diffusion Models (ICML 2025 · similarity 0.90)
- Linearly Constrained Diffusion Implicit Models (NeurIPS 2025 · similarity 0.90)
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