title: Solving Inverse Problems with FLAIR
summary: 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.
paper_authors._id: 6840496b4f36daae2e47efcb
paper_authors.name: Julius Erbach
paper_authors.status: claimed_verified
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paper_authors.fullname: Julius Erbach
paper_authors.type: user
paper_authors.user: juliuse
paper_authors._id: 6840496b4f36daae2e47efcc
paper_authors.name: Dominik Narnhofer
paper_authors.status: admin_assigned
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paper_authors.avatarUrl: /avatars/41b60f776a41d85da9ea0b1ed7d7615b.svg
paper_authors.fullname: Dominik Narnhofer
paper_authors.type: user
paper_authors.user: dnarnhofer
paper_authors._id: 6840496b4f36daae2e47efcd
paper_authors.name: Andreas Dombos
paper_authors.status: admin_assigned
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paper_authors._id: 66f1afd751dca07c002dbd78
paper_authors.avatarUrl: /avatars/de1262add2c455611f361a2bc8627e18.svg
paper_authors.fullname: Andreas Dombos
paper_authors.type: user
paper_authors.user: andreeee27
paper_authors._id: 6840496b4f36daae2e47efce
paper_authors.name: Bernt Schiele
paper_authors._id: 6840496b4f36daae2e47efcf
paper_authors.name: Jan Eric Lenssen
paper_authors._id: 6840496b4f36daae2e47efd0
paper_authors.name: Konrad Schindler
paper_authors.status: admin_assigned
paper_authors.statusLastChangedAt: 2025-06-05T12:59:43.140Z
paper_authors._id: 6750649b7edd6a98a1bbcd06
paper_authors.avatarUrl: /avatars/ba27f12d0333cf2d400d4405af7efe97.svg
paper_authors.fullname: Konrad Schindler
paper_authors.type: user
paper_authors.user: konradschindler
paper_title: Solving Inverse Problems with FLAIR
paper_summary: 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.
paper_ai_summary: FLAIR, a novel training-free variational framework, leverages flow-based generative models to enhance inverse problem solutions, achieving superior reconstruction quality and sample diversity.
paper_ai_keywords: flow-based latent generative models Stable Diffusion 3 inverse imaging problems variational framework flow matching deterministic trajectory adjustments data fidelity regularization terms time-dependent calibration scheme