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Fast samplers for Inverse Problems in Iterative Refinement models
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Proposes Conditional Conjugate Integrators (C-ΠGDM/C-ΠGFM), a training-free sampler that projects the conditional diffusion/flow dynamics for linear inverse problems into a better-conditioned space, reaching good quality in as few as 5 steps.
Problem
Existing posterior-sampling methods for linear inverse problems (super-resolution, inpainting, deblurring) with pretrained diffusion/flow models need hundreds to thousands of steps for high-quality results.
Approach
Extends conjugate integrators to conditional guided dynamics: an invertible time-dependent affine transform A_t, built from the degradation operator's projector P and the guidance weight, separates linear and nonlinear terms so the projected ODE is solved with Euler in few steps, recovering high-frequency details early.
Key results
- On ImageNet 4x super-resolution, C-ΠGDM reaches FID 37.31 at 5 NFE versus 38.18 for DPS (1000 NFE) and 49.06 for ΠGDM at 5 NFE.
- On CelebA-HQ flow super-resolution at 5 NFE, C-ΠGFM achieves FID 13.08 vs 21.84 for ΠGFM.
- C-ΠGFM improves inpainting FID at 5 NFE to 26.95 vs 161.49 for ΠGFM on CelebA-HQ.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use C-ΠGFM instead of ΠGFM | CelebA-HQ flow inpainting · Inpainting (NFE=5) | FID: 161.49 -> 26.95 | Helped |
| Use C-ΠGFM instead of ΠGFM | CelebA-HQ flow super-resolution · Super-Resolution (NFE=5) | FID: 21.84 -> 13.08 | Helped |
| Use C-ΠGFM instead of ΠGFM | CelebA-HQ flow deblurring · Deblurring (NFE=5) | FID: 18.97 -> 12.86 | Helped |
| Use C-ΠGDM instead of ΠGDM | ImageNet diffusion super-resolution · Super-Resolution (NFE=5) | FID: 49.06 -> 37.31 | Helped |
| Use C-ΠGDM instead of ΠGDM | ImageNet diffusion deblurring · Deblurring (NFE=5) | FID: 63.94 -> 44.42 | Helped |
| Tune λ away from its optimal value (ablation) | C-ΠGDM/C-ΠGFM · Super-Resolution on CelebA-HQ and ImageNet | sample quality | Hurt |
| Use a very large or very small guidance weight w rather than a suitable tuned value (ablation) | C-ΠGDM/C-ΠGFM · Super-Resolution on CelebA-HQ and ImageNet | sample quality | Hurt |
| Use a larger τ for super-resolution or deblurring rather than the smaller τ suited to inpainting (ablation) | C-ΠGDM/C-ΠGFM · Super-resolution and deblurring; inpainting | sample quality | Mixed |
Surprising findings
- Optimal lambda for the conjugate transform differs from zero, and ΠGDM/ΠGFM (lambda=0) cannot exploit this flexibility.
- Performance plateaus at NFE=20 for super-resolution and deblurring with the Euler solver, suggesting stochastic samplers or better solvers are needed for further gains.
Limitations
- Restricted to linear inverse problems with known degradation operator and Euler solver.
- Performance plateaus at higher NFE, and hyperparameters (w, lambda, tau) are tuned per task.
- Noisy and nonlinear extensions are only qualitatively demonstrated.
Experimental setup
Datasets: ImageNet FFHQ AFHQ-Cat LSUN-Bedroom CelebA-HQ
Benchmarks: ImageNet 4x super-resolution CelebA-HQ super-resolution/inpainting/deblurring FFHQ AFHQ-Cat LSUN-Bedroom
Metrics: FID KID LPIPS
Baselines: ΠGDM ΠGFM DPS DDRM
Builds on: Conjugate Integrators ΠGDM DDIM one-sided stochastic interpolants
Closest papers by meaning
- A Variational Perspective on Solving Inverse Problems with Diffusion Models (ICLR 2024 · similarity 0.91)
- Solving Video Inverse Problems Using Image Diffusion Models (ICLR 2025 · similarity 0.91)
- Adapt and Diffuse: Sample-adaptive Reconstruction via Latent Diffusion Models (ICML 2024 · similarity 0.90)
- InvFusion: Bridging Supervised and Zero-shot Diffusion for Inverse Problems (NeurIPS 2025 · similarity 0.90)
- SITCOM: Step-wise Triple-Consistent Diffusion Sampling For Inverse Problems (ICML 2025 · similarity 0.90)
- Latent Refinement via Flow Matching for Training-free Linear Inverse Problem Solving (NeurIPS 2025 · similarity 0.90)
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