通过分离匹配初末速度，提升两时点流模型的生成效果。
Distilling Two-Timed Flow Models by Separately Matching Initial and Terminal Velocities
- 分离匹配初始与终末时刻的速度，优化模型学习路径。
- 在多数据集上实现更优的少步生成性能，优于基线方法。
- 适合关注高效生成与流模型压缩的研究者使用。
流匹配模型学习一个时间依赖的向量场 $v_t(x)$，生成从已知噪声分布 $p_0$ 到数据分布 $p_1$ 的概率路径 $\\{ p_t \\_ {0 \leq t \leq 1}$。该模型可被蒸馏为两时点流模型（TTFM）$ϕ_{s,x}(t)$，在一次函数计算中将起始时间 $s$ 分布的样本变换到终止时间 $t$ 分布的样本。本文提出一种新的蒸馏损失函数——初末速度匹配（ITVM）损失，扩展了 Boffi 等人提出的拉格朗日流映射蒸馏（LFMD）损失：增加匹配初始速度的冗余项，移除终末速度项中的导数，并采用带指数移动平均（EMA）稳定的目标模型来计算终末平均速度。初步实验表明，该损失在多种数据集和模型架构上均显著提升少步生成性能。
原文摘要 · Abstract (English)
A flow matching model learns a time-dependent vector field $v_t(x)$ that generates a probability path $\{ p_t \}_{0 \leq t \leq 1}$ that interpolates between a well-known noise distribution ($p_0$) and the data distribution ($p_1$). It can be distilled into a two-timed flow model (TTFM) $ϕ_{s,x}(t)$ that can transform a sample belonging to the distribution at an initial time $s$ to another belonging to the distribution at a terminal time $t$ in one function evaluation. We present a new loss function for TTFM distillation called the \emph{initial/terminal velocity matching} (ITVM) loss that extends the Lagrangian Flow Map Distillation (LFMD) loss proposed by Boffi et al. by adding redundant terms to match the initial velocities at time $s$, removing the derivative from the terminal velocity term at time $t$, and using a version of the model under training, stabilized by exponential moving averaging (EMA), to compute the target terminal average velocity. Preliminary experiments show that our loss leads to better few-step generation performance on multiple types of datasets and model architectures over baselines.
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