FIRM: Flow-based Imaging via Regularized Minimization
Flow matching methods for imaging inverse problems typically incorporate measurements through network conditioning or guidance during sampling. Neither approach explicitly applies the forward operator within the learned conditional velocity field. We develop a principled measurement-conditional velocity parameterization that does. For a linear interpolation path, we express the optimal velocity through the posterior mean $E[x_1|x_t, y]$ and show that this mean is the unique minimizer of a variational objective with an explicit data-consistency term. The velocity defined by this minimizer provably transports the source distribution to the measurement-conditioned posterior. This result lead...
| Authors | Shirin Shoushtari, Edward P. Chandler, Xiao Shi et al. |
|---|---|
| Primary category | cs.CV |
| Published | 11 September 2026 |
| Last updated at source | 27 September 2026 |
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