Solving Inverse Problems with FLAIR

TL;DR

FLAIR tackles inverse imaging with a training-free variational framework that leverages flow-based latent priors to approximate the posterior $p(x|y)$. It decouples data fidelity from prior regularization, introducing a degradation-agnostic flow-matching objective and a deterministic trajectory adjustment that guides samples to posterior-consistent regions while preserving data-consistency via hard constraints. Empirically, it achieves state-of-the-art perceptual quality and fidelity across high-resolution tasks (super-resolution, motion deblurring, inpainting) on FFHQ and DIV2K, with evidence of robust sample diversity. The approach inherits the limitations of the underlying generative model, including potential biases and resolution constraints, and requires careful hyperparameter tuning for trajectory adjustments.

Abstract

Flow-based latent generative models such as Stable Diffusion 3 are able to generate images with remarkable quality, even enabling photorealistic text-to-image generation. Their impressive performance suggests that these models should also constitute powerful priors for inverse imaging problems, but that approach has not yet led to comparable fidelity. There are several key obstacles: (i) the data likelihood term is usually intractable; (ii) learned generative models cannot be directly conditioned on the distorted observations, leading to conflicting objectives between data likelihood and prior; and (iii) the reconstructions can deviate from the observed data. We present FLAIR, a novel, training-free variational framework that leverages flow-based generative models as prior for inverse problems. To that end, we introduce a variational objective for flow matching that is agnostic to the type of degradation, and combine it with deterministic trajectory adjustments to guide the prior towards regions which are more likely under the posterior. To enforce exact consistency with the observed data, we decouple the optimization of the data fidelity and regularization terms. Moreover, we introduce a time-dependent calibration scheme in which the strength of the regularization is modulated according to off-line accuracy estimates. Results on standard imaging benchmarks demonstrate that FLAIR consistently outperforms existing diffusion- and flow-based methods in terms of reconstruction quality and sample diversity. Our code is available at https://inverseflair.github.io/.

Figures (16)

• Figure 1: Starting from the adjoint based initialization, we alternate between (i) regularizer updates via a flow-matching loss that aligns the velocity $u_t$ of the variational distribution with the learned velocity field $v_\theta$, and (ii) hard data consistency steps that project the current estimate onto the measurement manifold.
• Figure 1: The Flow-Matching loss over time $t$.
• Figure 2: Qualitative comparison. FLAIR produces posterior samples of high perceptual quality while maintaining high data likelihood. Best viewed zoomed in.
• Figure 2: Qualitative comparison. FLAIR in pixel space produces posterior samples of high perceptual quality while maintaining high data likelihood as well. Best viewed zoomed in.
• Figure 3: Zoomed-in reconstructions for x12 Super Resolution. We show posterior samples (col. 1–4) of FLAIR, FlowDPS, and RSD, posterior mean and standard deviation (over 32 samples, col. 5,6). $0$$0.16$

Theorems & Definitions (2)

• Proposition 1
• Proposition 2