Solving Inverse Problems with FLAIR
Authors: name: Julius Erbach, name: Dominik Narnhofer, name: Andreas Dombos, name: Bernt Schiele, name: Jan Eric Lenssen, name: Konrad Schindler

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 encoding into a lower-dimensional latent space makes the
underlying (forward) mapping non-linear; (ii) the data likelihood term is
usually intractable; and (iii) learned generative models struggle to recover
rare, atypical data modes during inference. We present FLAIR, a novel training
free variational framework that leverages flow-based generative models as a
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 recover atypical modes. 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.