Fast and Faithful: Principled Conditional Flow Matching for Inverse Problems

2026-09-11

AI Summary

本文提出一种基于变分目标的测量条件速度场参数化方法，用于解决成像逆问题，通过端到端训练实现高效且准确的求解。

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.

Problem

• inverse problems
• flow matching
• conditional velocity field
• data-consistency
• variational objective

Innovation

• measurement-conditional velocity field
• variational objective
• data-consistency updates
• end-to-end training
• flow-matching