Research map / Image generation / Fast diffusion sampling
Decomposed Diffusion Sampler for Accelerating Large-Scale Inverse Problems
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 Decomposed Diffusion Sampling (DDS), which replaces manifold-constrained gradient steps with multi-step conjugate gradient updates on the tangent space of Tweedie denoised samples, enabling fast DDIM-based inverse problem solving for MRI and 3D CT.
Problem
Diffusion-based inverse problem solvers are slow and computationally expensive (MCG requires backpropagation) for large-scale medical imaging inverse problems such as multi-coil MRI and 3D CT reconstruction.
Approach
Proves that under an affine clean-manifold assumption, DPS's MCG step equals a projected gradient on the tangent space at the Tweedie denoised sample; if that tangent space is a Krylov subspace, M-step conjugate gradient initialized at the denoised sample stays in the tangent space, removing the need for MCG and enabling DDIM sampling with few NFE.
Key results
- On uniform 1D x4 MRI, DDS VP (49 NFE) reaches 35.15 dB Gaussian 1D x4 / 34.88 dB uniform 1D x4 PSNR, above DPS (1000 NFE) at 30.56 dB.
- DDS achieves 80-200x fewer NFE than prior DIS methods in multi-coil MRI, taking about 4.7 s for 49 NFE on an RTX 3090.
- On 8-view SV-CT, DDS VP (49 NFE) reaches 33.86 dB axial PSNR versus 33.49 dB for DiffusionMBIR with 4000 NFE, with sampling about 25 min vs 2 days.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| replace Score-MRI data consistency with DDS CG updates | VP DDIM sampling · Uniform 1D ×4 MRI, 49 NFE | PSNR[db]: 26.48 -> 34.61 | Helped |
| replace DDNM projection with DDS CG updates | VP DDIM sampling · Uniform 1D ×4 MRI, 49 NFE | PSNR[db]: 31.36 -> 34.61 | Helped |
| use 5 CG iterations per denoising step (ablation) | DDS · Uniform 1D ×4 MRI, 49 NFE | PSNR[db]: 31.51 -> 34.61 | Helped |
| increase CG iterations per denoising step from 5 to 10 (ablation) | DDS · Uniform 1D ×4 MRI, 49 NFE | PSNR[db]: 34.61 -> 32.48 | Hurt |
| use DDS with CG updates instead of Score-MRI sampling | VE MRI reconstruction · Uniform 1D ×4 MRI | PSNR | Helped |
| use VP rather than VE parameterization | DDS for sparse-view CT · AAPM 256×256 SV-CT | PSNR | Helped |
Surprising findings
- Using only 5 CG iterations per step adds about 0.2 s to 4.5 s sampling, so CG overhead is negligible compared with the analytic projection.
- Over-iterating CG (10 steps in the DC ablation) lowers PSNR relative to 5 steps (32.48 vs 34.61 dB).
Limitations
- The Krylov/affine-manifold assumption holds only approximately for real data; the theory relies on it.
- VE parameterization shows numerical instability at large NFE, and noisy setting requires tuned step size gamma.
Experimental setup
Datasets: fastMRI knee AAPM 256x256 CT
Benchmarks: fastMRI knee AAPM 256x256 sparse-view CT
Metrics: PSNR SSIM
Baselines: DPS Score-MRI DiffusionMBIR MCG DDNM E2E-Varnet U-Net TV Score-Med FBPConvNet ADMM-TV
Builds on: DDIM DPS DDNM Score-MRI DiffusionMBIR
Closest papers by meaning
- Improving Diffusion-based Inverse Algorithms under Few-Step Constraint via Linear Extrapolation (NeurIPS 2025 · similarity 0.88)
- DMPlug: A Plug-in Method for Solving Inverse Problems with Diffusion Models (NeurIPS 2024 · similarity 0.87)
- Fast samplers for Inverse Problems in Iterative Refinement models (NeurIPS 2024 · similarity 0.87)
- Guided Diffusion Sampling on Function Spaces with Applications to PDEs (NeurIPS 2025 · similarity 0.86)
- Diffusion State-Guided Projected Gradient for Inverse Problems (ICLR 2025 · similarity 0.86)
- SITCOM: Step-wise Triple-Consistent Diffusion Sampling For Inverse Problems (ICML 2025 · similarity 0.86)
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.