Conditional flow matching improves image recovery from noisy measurements
Fast and Faithful: Principled Conditional Flow Matching for Inverse Problems
Computer Vision and Pattern Recognition
Summary
Imaging inverse problems involve figuring out the original image from partial or noisy measurements. The authors propose a new approach that uses a mathematical idea called conditional flow matching to better reconstruct images by integrating measurement information directly into the recovery process. Their method is faster and produces higher-quality images than previous flow-based techniques. It also lets users balance the trade-off between image sharpness and distortion at test time without retraining the model.
What this means in practice
- •For medical imaging teams: Recover higher quality images from partial or noisy medical scans faster without extra inference steps.
- •For remote sensing analysts: Improve reconstruction of satellite or aerial images from limited measurement data with controllable quality trade-offs.
Authors
Shirin Shoushtari, Edward P. Chandler, Xiao Shi, Ulugbek S. Kamilov
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.