Fast and Faithful: Principled Conditional Flow Matching for Inverse Problems

• URL: http://arxiv.org/abs/2609.12953v1
• Date: Fri, 11 Sep 2026 15:12:11 GMT
• Title: Fast and Faithful: Principled Conditional Flow Matching for Inverse Problems
• Abstract summary: Flow matching approaches to imaging inverse problems commonly incorporate measurements in two ways.<n>We propose a principled parametrization of the measurement-conditional velocity field to solve inverse problems.<n>Our method achieves state-of-the-art PSNR with $50times$ fewer evaluations function than the strongest flow baseline.
• Score: 8.966524060251965
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Flow matching approaches to imaging inverse problems commonly incorporate measurements in two ways. Conditioning-based approaches supply measurement-derived information as a network input, often through concatenation, while inference-guided approaches combine an unconditional velocity field with a separate data-consistency update. In these common formulations, the forward model is not explicitly enforced within the learned conditional velocity field. We propose a principled parametrization of the measurement-conditional velocity field to solve inverse problems. Under linear interpolation, we express the conditional velocity $v(x_t,t,y)$ in terms of the posterior mean $E[x_1 | x_t,y]$, and characterize that mean as the unique minimizer of a variational objective whose data-consistency term is explicit. We further prove that the velocity field defines a probability flow from the source distribution to the measurement-conditioned posterior. Splitting the variational objective yields a conditional velocity parameterization with operator-dependent data-consistency updates, which we train end-to-end under the flow-matching objective, with no additional guidance at inference. Our method achieves state-of-the-art PSNR with $50\times$ fewer function evaluations than the strongest flow baseline. Varying the sampling steps provides test-time control over the distortion-perception trade-off without retraining.

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