Research map / Image generation / Fast diffusion sampling
Deep Equilibrium Diffusion Restoration with Parallel Sampling
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Proposes DeqIR, a training-free zero-shot diffusion image restoration method that reformulates the whole DDIM sampling chain as a deep equilibrium fixed-point system solved in parallel with Anderson acceleration, and optimizes the initial noise via DEQ inversion.
Problem
Diffusion-based image restoration relies on long serial sampling chains, which are slow, costly, and make gradients with respect to inputs hard to compute.
Approach
Model the entire sampling chain of a pre-trained diffusion IR model as a joint multivariate fixed-point system (DEQ), enabling parallel sampling with few timesteps, and compute gradients via implicit differentiation (DEQ inversion) to optimize the initial noise for better quality and controllability.
Key results
- On ImageNet 4x SR, DeqIR reaches PSNR 27.44 with 15 iterations vs DDNM's 100 steps; for 2x SR it gets 32.35 PSNR / 0.082 LPIPS vs DDNM's 31.81 / 0.097.
- On anisotropic deblurring (ImageNet), DeqIR with 15 iterations reaches 39.47 PSNR, above DDNM's 38.40 with 100 steps.
- Ours-10 (10 steps) runs in 12.11 s vs DDNM's 12.67 s on anisotropic deblurring, with the authors reporting comparable running time.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Increase timesteps from 2 to 35 (ablation) | DeqIR · ImageNet anisotropic deblurring | LPIPS | Helped |
| Increase Anderson acceleration iterations (ablation) | DeqIR · ImageNet anisotropic deblurring | LPIPS | Helped |
| Vary the analytic-formulation hyperparameter η (ablation) | DeqIR · ImageNet anisotropic deblurring | LPIPS | Mixed |
| Use DeqIR instead of DDNM | ImageNet 4×SR · ImageNet 4×SR | PSNR: 26.49 -> 27.47 | Helped |
| Use DeqIR instead of DDNM | ImageNet Gaussian deblurring · ImageNet Gaussian deblurring | PSNR: 43.83 -> 43.42 | Hurt |
| Use DeqIR instead of DDNM | ImageNet anisotropic deblurring · ImageNet anisotropic deblurring | PSNR: 38.40 -> 39.47 | Helped |
| Use DeqIR instead of DDNM | CelebA-HQ colorization · CelebA-HQ colorization | LPIPS: 0.139 -> 0.092 | Helped |
| Use DeqIR instead of DDNM | CelebA text-mask inpainting · CelebA text-mask inpainting | PSNR: 39.45 -> 39.72 | Helped |
| Use DeqIR instead of DDNM | CelebA stripe-mask inpainting · CelebA stripe-mask inpainting | PSNR: 36.75 -> 36.99 | Helped |
Surprising findings
- Parallel fixed-point sampling needs only about 15 iterations, far fewer than the 100 serial DDNM steps, while matching or exceeding quality.
Limitations
- Supervised extension via DEQ inversion is left to future work.
- Worse than supervised DiffIR on 4x SR and inferior to some metrics on inpainting stripe mask SSIM/LPIPS.
- Hyper-parameters such as eta and timesteps are tuned per task.
Experimental setup
Datasets: ImageNet CelebA-HQ
Benchmarks: ImageNet CelebA-HQ
Metrics: PSNR SSIM LPIPS FID Consistency running time
Baselines: DPS DDRM DDNM DiffPIR DGP ILVR Palette RePaint SRGAN BSRGAN LDM DiffIR
Builds on: DEQ DEQ-DDIM DDNM DDIM Anderson acceleration
Closest papers by meaning
- Improving Diffusion-Based Image Restoration with Error Contraction and Error Correction (AAAI 2024 · similarity 0.90)
- A Variational Perspective on Solving Inverse Problems with Diffusion Models (ICLR 2024 · similarity 0.89)
- i-DEQ: A stable inertial Deep Equilibrium model for image restoration (NeurIPS 2026 · similarity 0.89)
- Fast samplers for Inverse Problems in Iterative Refinement models (NeurIPS 2024 · similarity 0.89)
- Blind Image Restoration via Fast Diffusion Inversion (NeurIPS 2024 · similarity 0.88)
- DGSolver: Diffusion Generalist Solver with Universal Posterior Sampling for Image Restoration (NeurIPS 2025 · similarity 0.88)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.