arXiv:2606.04092cs.CVcs.LG2026-06被引 1

用低频图像做先验,让生成路径更直更快。

Optimal Transport Flow Matching by Design

  • 把先验设计成低频图像,实现最优传输的无交叉路径
  • 轨迹曲率降低2倍以上,少步生成质量显著提升
  • 兼容现有模型框架,适合快速生成场景

流匹配模型通过将简单先验分布的样本传输到复杂数据分布来学习生成。当先验与数据通过最优传输(OT)配对时,生成轨迹为直线且不交叉,可实现快速甚至单步生成。但高维空间中计算OT配对不可行,现有方法尝试求解该问题,却带来持续偏差或高昂开销。本文提出新思路:将先验视为可设计变量而非固定输入,此时先验与数据间的OT配对不再唯一。许多先验可与数据形成最优的恒等配对,我们选择其中易于采样的——自然图像的低频投影。实证表明,数据与其低频表示之间的恒等配对在实践中接近最优传输;该先验结构足够强,可用轻量模型高效采样,且剩余的流匹配任务仅需合成高频细节。进一步将先验与高斯噪声插值,可提升生成质量并保持OT配对特性。该方法无需修改流模型,天然适配隐空间模型、无分类器引导及单步生成框架。在所有基准测试中,相比现有流匹配方法,轨迹曲率减少超过2倍,少步生成质量更优。

原文摘要 · Abstract (English)

Flow matching models learn to transport samples from a simple prior distribution to a complex data distribution. When prior-data pairs are coupled via optimal transport (OT), the learned trajectories are straight and non-crossing, enabling fast, even single-step, generation. However, computing the OT coupling in high dimensions is intractable, and existing methods attempt to solve the OT problem, at the cost of persistent bias or significant overhead. Rather than solving for the OT coupling, we reformulate the problem. Once the prior is treated as a design choice rather than a fixed input, the OT coupling between prior and data is no longer unique. Many priors admit an OT-optimal identity coupling to the data, leaving us free to choose one that is also tractable to sample. We identify low-frequency projection of natural images as such a choice. The identity coupling between data and its low-frequency representation is empirically OT-optimal, the prior is structured enough to be sampled by a lightweight model at inference, and the remaining flow-matching task reduces to synthesizing high-frequency detail. Interpolating the prior with Gaussian noise further improves generation quality while preserving the OT coupling. The approach requires no modifications to the flow model itself, and integrates naturally with latent-space models, classifier-free guidance, and one-step generation frameworks. Across all benchmarks, our method reduces trajectory curvature by more than $2\times$ compared to existing flow matching methods, yielding better generation quality in the few-step regime.

流匹配最优传输快速生成低频先验

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