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Solving Inverse Problems with FLAIR
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FLAIR is a training-free variational framework that uses Stable Diffusion 3.5-Medium's flow-matching velocity field as a prior for latent inverse problems, with deterministic trajectory adjustment, decoupled hard data consistency, and calibrated time-dependent regularizer weights.
Problem
Using large latent flow-based generative models as priors for inverse imaging problems (super-resolution, motion deblurring, inpainting) is hard because the likelihood is intractable, the prior conflicts with the observation, and reconstructions deviate from the data, leading to blur and mode collap
Approach
Replace the score-based regularizer of variational posterior sampling with a flow-matching velocity loss, anchor the noisy trajectory to a model-predicted endpoint (deterministic trajectory adjustment) instead of pure noise, decouple hard data-consistency steps from regularization, and weight the regularizer by the inverse of offline-calibrated flow-matching error.
Key results
- On FFHQ 768x768 SR x8, FLAIR reaches LPIPS 0.213 and FID 13.3 versus 0.341 and 30.5 for the best baseline (FlowChef).
- On FFHQ inpainting, FLAIR achieves LPIPS 0.184 and FID 8.7, versus 0.344 and 42.5 for FlowDPS.
- In pixel space on CelebA-HQ 256, FLAIR achieves inpainting LPIPS 0.097 and FID 14.2, outperforming DDNM (0.158, 26.9).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add hard data consistency (ablation) | FLAIR · ×12 super-resolution on FFHQ and DIV2K | LPIPS: 0.297 -> 0.259 (FFHQ); 0.467 -> 0.427 (DIV2K) | Helped |
| add deterministic trajectory adjustment (ablation) | FLAIR · ×12 super-resolution on FFHQ and DIV2K | LPIPS: 0.432 -> 0.259 (FFHQ); 0.622 -> 0.427 (DIV2K) | Helped |
| use calibrated regularizer weight instead of λR(t)=t (ablation) | FLAIR · ×12 super-resolution on FFHQ and DIV2K | LPIPS: 0.363 -> 0.259 (FFHQ); 0.583 -> 0.427 (DIV2K) | Helped |
| use data-specific captions rather than a generic prompt | FLAIR · FFHQ and DIV2K | LPIPS: 0.278 -> 0.271 (FFHQ); 0.488 -> 0.421 (DIV2K) | Mixed |
| use data-specific captions rather than a generic prompt | FLAIR · DIV2K | SSIM: 0.546 -> 0.525 | Hurt |
Surprising findings
- PSNR favors over-smoothed posterior-mean-like outputs, so the authors argue PSNR is ill-suited; ensembling 8 samples improves PSNR while LPIPS also drops.
- The authors report that PSLD adaptation did not yield meaningful results.
Limitations
- Inherits biases and resolution limits of the underlying generative model and struggles with out-of-distribution modes.
- Introduces additional hyperparameters for the deterministic trajectory adjustment.
- Hard data consistency makes runtime substantially higher than baselines.
Experimental setup
Datasets: FFHQ DIV2K CelebA-HQ
Benchmarks: FFHQ 768x768 DIV2K 768x768 CelebA-HQ 256x256 (pixel space)
Metrics: LPIPS FID patchwise FID SSIM PSNR
Baselines: ReSample FlowDPS FlowChef RSD DDNM DPS Moment Matching ΠGDM
Builds on: Stable Diffusion 3 variational diffusion posterior sampling Repulsive Score Distillation ReSample FlowDPS
Closest papers by meaning
- Latent Refinement via Flow Matching for Training-free Linear Inverse Problem Solving (NeurIPS 2025 · similarity 0.92)
- Text-to-Image Rectified Flow as Plug-and-Play Priors (ICLR 2025 · similarity 0.91)
- Flow Priors for Linear Inverse Problems via Iterative Corrupted Trajectory Matching (NeurIPS 2024 · similarity 0.91)
- Prompt-tuning Latent Diffusion Models for Inverse Problems (ICML 2024 · similarity 0.90)
- A Variational Perspective on Solving Inverse Problems with Diffusion Models (ICLR 2024 · similarity 0.89)
- Semantic Image Inversion and Editing using Rectified Stochastic Differential Equations (ICLR 2025 · similarity 0.89)
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