提出低通流匹配，让生成模型更贴合自然数据的频谱特性。
Low-Pass Flow Matching
- 用时变频谱偏置替代白噪声，使生成路径更符合真实数据分布
- 在银河图像数据集上，采样成本大幅降低，样本质量不降反升
- 特别适合搭配自适应微分方程求解器，提升生成效率
流匹配通常依赖白噪声源，但自然数据的功率谱往往随频率衰减，两者不匹配。为此，我们提出低通流匹配，基于算子调制的插值方法，使路径在演化过程中从源谱逐渐过渡到频率衰减的偏差。我们在无条件图像生成任务中验证该方法，包括科学级银河10数据集。实验表明，该方法与自适应常微分方程求解器结合时，可显著降低采样成本，同时保持或提升样本质量，优于标准基线。
原文摘要 · Abstract (English)
Flow Matching typically relies on white noise sources, a choice often misaligned with the power spectra of natural data, which tend to decay with frequency. To address this, we introduce Low-Pass Flow Matching, a variant of Flow Matching based on an operator-modulated interpolant. This formulation induces a time-varying spectral bias that transitions from the source spectrum to a frequency-decaying bias as the path approaches the data. We validate our method on unconditional image generation tasks, including the scientific Galaxy10 dataset. Empirically, we show that our method is particularly effective when paired with adaptive ODE solvers, where it improves or preserves sample quality while substantially reducing sampling cost compared to standard baselines.
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