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Latent Refinement via Flow Matching for Training-free Linear Inverse Problem Solving
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Proposes LFlow, a training-free latent flow-matching solver for linear inverse problems that uses a derived time-dependent posterior covariance from the optimal vector field, outperforming latent diffusion solvers on most tasks.
Problem
Flow-based inverse solvers operate in pixel space (costly, poorly scalable) and use prior-agnostic posterior covariances in guidance, weakening alignment with the generative trajectory for linear inverse problems like deblurring, super-resolution and inpainting.
Approach
Perform guidance-corrected ODE sampling in the latent space of a pretrained autoencoder with a flow prior, and derive a latent posterior covariance from the pretrained vector field (Tweedie covariance, with a Gaussian-latent optimal vector field) instead of an identity covariance.
Key results
- On FFHQ Gaussian deblurring, LFlow reports LPIPS 0.166 and SSIM 0.837, with the best LPIPS and SSIM among compared methods, while PSLD has higher PSNR (30.28 vs 29.10).
- On FFHQ box inpainting, LFlow reaches LPIPS 0.132 vs second-best PSLD 0.169.
- Runtime is about 3:30 to 10 minutes per image on a single RTX 3090, which the authors acknowledge as a limitation.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use LFlow instead of the strongest baseline | FFHQ Gaussian deblurring · FFHQ Gaussian deblurring | LPIPS: 0.182 -> 0.166 | Helped |
| Use LFlow instead of the strongest baseline | FFHQ motion deblurring · FFHQ motion deblurring | LPIPS: 0.183 -> 0.168 | Helped |
| Use LFlow instead of the strongest baseline | FFHQ ×4 super-resolution · FFHQ ×4 super-resolution | LPIPS: 0.183 -> 0.176 | Helped |
| Use LFlow instead of the strongest baseline | FFHQ box inpainting · FFHQ box inpainting | LPIPS: 0.169 -> 0.132 | Helped |
| Use LFlow instead of the strongest baseline | ImageNet Gaussian deblurring · ImageNet Gaussian deblurring | LPIPS: 0.332 -> 0.328 | Helped |
| Use LFlow instead of the strongest baseline | ImageNet motion deblurring · ImageNet motion deblurring | LPIPS: 0.347 -> 0.344 | Helped |
| Use LFlow instead of the strongest baseline | ImageNet ×4 super-resolution · ImageNet ×4 super-resolution | LPIPS: 0.356 -> 0.338 | Helped |
| Use LFlow instead of the strongest baseline | ImageNet box inpainting · ImageNet box inpainting | LPIPS: 0.274 -> 0.227 | Helped |
| Use the LFlow time-dependent posterior covariance instead of the PiGDM covariance (ablation) | LFlow · Deblurring and ×4 super-resolution on FFHQ and ImageNet | LPIPS | Helped |
| Vary the starting time t_s from the intermediate setting (ablation) | LFlow · ×4 super-resolution on FFHQ and ImageNet | LPIPS | Mixed |
Surprising findings
- LFlow achieves the best LPIPS on most tasks but not the best PSNR, and the authors attribute this to a perception-distortion trade-off.
- The latent prior does not exceed Stable Diffusion or LDM quality, which the authors attribute partly to the 32x32 latent dimension.
Limitations
- Inference runtime of several minutes per image limits time-sensitive use.
- Decoder local-isometry and Gaussian-latent assumptions are approximations.
- Latent prior quality does not exceed Stable Diffusion-based latent priors.
Experimental setup
Datasets: FFHQ ImageNet CelebA-HQ
Benchmarks: FFHQ ImageNet CelebA-HQ
Metrics: PSNR SSIM LPIPS FID
Baselines: PSLD MPGD Resample DMplug DAPS SITCOM PiGDM OT-ODE C-PiGFM
Builds on: Flow matching PiGDM OT-ODE DPS PSLD
Closest papers by meaning
- Solving Inverse Problems with FLAIR (NeurIPS 2025 · similarity 0.92)
- Flow Priors for Linear Inverse Problems via Iterative Corrupted Trajectory Matching (NeurIPS 2024 · similarity 0.91)
- Fast samplers for Inverse Problems in Iterative Refinement models (NeurIPS 2024 · similarity 0.90)
- Exact Posterior Score Estimation for Solving Linear Inverse Problems (NeurIPS 2026 · similarity 0.89)
- PnP-Flow: Plug-and-Play Image Restoration with Flow Matching (ICLR 2025 · similarity 0.88)
- Repulsive Latent Score Distillation for Solving Inverse Problems (ICLR 2025 · similarity 0.88)
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