Research map / Image generation / Fast diffusion sampling
Learning Single Index Models with Diffusion Priors
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 SIM-DMIS, a training-free method that recovers signals from unknown, possibly discontinuous single index model measurements by partially inverting and resampling a pretrained unconditional diffusion model, using ~150 NFEs.
Problem
Signal recovery from nonlinear single index model measurements with unknown or discontinuous link functions (e.g., 1-bit, cubic) using diffusion model priors, which prior diffusion methods handle only with known differentiable links and at high NFE cost.
Approach
Estimate the signal direction from A^T y/m, rescale and place it at an intermediate noise level t* chosen via a tuning constant, then partially invert the DDIM/DM2M trajectory to T and resample to epsilon, so the link function is never needed.
Key results
- On FFHQ 1-bit (m=n/8), SIM-DMIS reaches 19.87 PSNR / 0.60 SSIM with 150 NFEs, versus QCS-SGM at 12.91 PSNR with 11,555 NFEs and DAPS-N at 16.59 PSNR with 1,000 NFEs.
- On ImageNet cubic measurements (m=n/16), SIM-DMIS achieves 16.28 PSNR versus 11.47 for DPS-N (1,000 NFEs).
- On CIFAR-10 1-bit with m=1000, SIM-DMIS achieves 18.61 PSNR versus 12.24 for DPS-L.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use partial inversion from an intermediate time before sampling (SIM-DMIS instead of SIM-DMFIS full inversion) (ablation) | SIM-DMIS · FFHQ 256×256, 1-bit (m=24576) | PSNR: 8.48$\pm$0.13 -> 19.87$\pm$2.77 | Helped |
| Use partial inversion from an intermediate time before sampling (SIM-DMIS instead of SIM-DMS sampling only) (ablation) | SIM-DMIS · FFHQ 256×256, cubic (m=24576) | PSNR: 14.44$\pm$2.13 -> 17.56$\pm$2.56 | Helped |
| Use partial inversion from an intermediate time before sampling (SIM-DMIS instead of SIM-DMFIS full inversion) (ablation) | SIM-DMIS · ImageNet 256×256, 1-bit (m=12288) | PSNR: 11.89$\pm$2.24 -> 18.06$\pm$3.16 | Helped |
| Increase C_s from 50 to 60 (ablation) | SIM-DMS · CIFAR-10, 1-bit (m=500), C_s'=55 | PSNR: 14.441 -> 14.971 | Helped |
| Increase C_s from 50 to 60 (ablation) | SIM-DMS · CIFAR-10, 1-bit (m=500), C_s'=55 | LPIPS: 0.444 -> 0.447 | Hurt |
| Lower C_s' from 60 to 50 (ablation) | SIM-DMS · CIFAR-10, 1-bit (m=500), C_s=55 | PSNR: 14.205 -> 15.337 | Helped |
| Lower C_s' from 60 to 50 (ablation) | SIM-DMS · CIFAR-10, 1-bit (m=500), C_s=55 | LPIPS: 0.447 -> 0.440 | No clear effect |
| Increase NFE from 20 to 100 (ablation) | SIM-DMS · CIFAR-10, 1-bit (m=500), C_s=55, C_s'=55 | PSNR: 14.860 -> 14.860 | No clear effect |
Surprising findings
- Full inversion followed by sampling (SIM-DMFIS) performs much worse than partial inversion, e.g. 8.48 PSNR vs 19.87 on FFHQ 1-bit.
- DPS-N and DAPS-N, which use the known link function, are outperformed by the link-agnostic SIM-DMIS on 1-bit measurements.
Limitations
- Relies on tuning constants C_s and C_s' that depend on unknown link function constants.
- Theoretical guarantee is for a Lipschitz generator and regularity conditions; the error bound is asymptotic in step size.
- Recovers only the direction of the signal due to the scale ambiguity of SIMs.
Experimental setup
Datasets: FFHQ 256x256 ImageNet 256x256 CIFAR-10
Benchmarks: FFHQ 256x256 (1-bit, cubic) ImageNet 256x256 (1-bit, cubic) CIFAR-10 32x32 (1-bit, cubic)
Metrics: PSNR SSIM LPIPS NFE
Baselines: QCS-SGM DPS-N DPS-L DAPS-N DAPS-L OneShot SIM-DMS SIM-DMFIS
Builds on: DDIM DM2M DPS DAPS QCS-SGM
Closest papers by meaning
- A Variational Perspective on Solving Inverse Problems with Diffusion Models (ICLR 2024 · similarity 0.90)
- Analyzing and Guiding Zero-Shot Posterior Sampling in Diffusion Models (NeurIPS 2026 · similarity 0.89)
- Coupled Data and Measurement Space Dynamics for Enhanced Diffusion Posterior Sampling (NeurIPS 2025 · similarity 0.89)
- SITCOM: Step-wise Triple-Consistent Diffusion Sampling For Inverse Problems (ICML 2025 · similarity 0.89)
- Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstruction (NeurIPS 2024 · similarity 0.89)
- Adapt and Diffuse: Sample-adaptive Reconstruction via Latent Diffusion Models (ICML 2024 · similarity 0.89)
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.