What Do Flow-Based Inverse Solvers Approximate? A Posterior-Transport View
A growing family of training-free solvers -- FlowDPS, FLOWER, PnP-Flow and their diffusion ancestors (DPS, DAPS) -- repurpose a pretrained flow-matching prior to solve imaging inverse problems by adding a measurement-guidance term to the deterministic probability-flow ODE. Despite strong empirical results, what these per-step corrections actually approximate -- and how far the resulting samples are from the true posterior $p(x\mid y)$ -- has not been characterized. We give a posterior-transport account of flow-based inverse problem solving. Our starting point is a simple but consequential fact: for a \emph{deterministic} flow prior, Bayesian conditioning is realized entirely by a \emph{re...
| Authors | Jian Xu, Delu Zeng, John Paisley et al. |
|---|---|
| Primary category | cs.CV |
| Published | 23 June 2026 |
| Last updated at source | 27 June 2026 |
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