arXiv:2507.22270cs.LG2025-07被引 2

通过加权机制让生成路径更直更快,同时保持高效计算。

Weighted Conditional Flow Matching

  • 用吉布斯核加权训练样本,引导生成路径更接近直线。
  • 在真实与合成数据上,生成质量、保真度和多样性均优于或持平基线。
  • 无需昂贵的批量最优传输,适合大规模高效生成任务。

条件流匹配(CFM)因其计算高效和有效性,已成为训练连续归一化流的强大框架。然而,标准CFM常产生偏离先验与目标分布间直线插值的路径,导致推理时需细粒度离散化,影响生成速度与精度。近期方法通过诱导更短更直的轨迹提升性能,但通常依赖计算成本高的小批量最优传输(OT)。受熵正则最优传输(EOT)启发,我们提出加权条件流匹配(W-CFM),通过吉布斯核对每对训练样本 $(x, y)$ 加权,修改经典CFM损失。我们证明该加权可恢复熵正则OT耦合,仅在边缘分布上引入可控偏差,并给出边缘几乎不变的条件。此外,我们在大批次极限下建立了W-CFM与小批量OT方法的等价性,说明其克服了批大小带来的计算与性能瓶颈。实验表明,W-CFM在多种合成与真实数据集上进行无条件生成时,生成样本质量、保真度和多样性均达到或超过其他基线,同时保持原始CFM的计算效率。

原文摘要 · Abstract (English)

Conditional flow matching (CFM) has emerged as a powerful framework for training continuous normalizing flows due to its computational efficiency and effectiveness. However, standard CFM often produces paths that deviate significantly from straight-line interpolations between prior and target distributions, making generation slower and less accurate due to the need for fine discretization at inference. Recent methods enhance CFM performance by inducing shorter and straighter trajectories but typically rely on computationally expensive mini-batch optimal transport (OT). Drawing insights from entropic optimal transport (EOT), we propose Weighted Conditional Flow Matching (W-CFM), a novel approach that modifies the classical CFM loss by weighting each training pair $(x, y)$ with a Gibbs kernel. We show that this weighting recovers the entropic OT coupling up to some bias in the marginals, and we provide the conditions under which the marginals remain nearly unchanged. Moreover, we establish an equivalence between W-CFM and the minibatch OT method in the large-batch limit, showing how our method overcomes computational and performance bottlenecks linked to batch size. Empirically, we test our method on unconditional generation on various synthetic and real datasets, confirming that W-CFM achieves comparable or superior sample quality, fidelity, and diversity to other alternative baselines while maintaining the computational efficiency of vanilla CFM.

流模型生成模型最优传输高效生成

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