Generative models based on dynamical transport of measure, such as diffusion models, flow matching models, and stochastic interpolants, learn an ordinary or stochastic differential equation whose trajectories push initial conditions from a known base distribution onto the target. While training is cheap, samples are generated via simulation, which is more expensive than one-step models like GANs. To close this gap, we introduce flow map matching -- an algorithm that learns the two-time flow map of an underlying ordinary differential equation. The approach leads to an efficient few-step generative model whose step count can be chosen a-posteriori to smoothly trade off accuracy for computational expense. Leveraging the stochastic interpolant framework, we introduce losses for both direct training of flow maps and distillation from pre-trained (or otherwise known) velocity fields. Theoretically, we show that our approach unifies many existing few-step generative models, including consistency models, consistency trajectory models, progressive distillation, and neural operator approaches, which can be obtained as particular cases of our formalism. With experiments on CIFAR-10 and ImageNet 32x32, we show that flow map matching leads to high-quality samples with significantly reduced sampling cost compared to diffusion or stochastic interpolant methods.

翻译：基于测度动态输运的生成模型，如扩散模型、流匹配模型和随机插值模型，通过学习一个常微分方程或随机微分方程，其轨迹将初始条件从已知的基分布推送到目标分布。虽然训练成本低廉，但样本生成需要通过模拟进行，这比GAN等一步生成模型更为昂贵。为弥补这一差距，我们提出了流图匹配——一种学习底层常微分方程双时间流图的算法。该方法导出了一个高效的多步生成模型，其步数可在后验中选择，以平滑地权衡精度与计算开销。利用随机插值框架，我们引入了用于直接训练流图以及从预训练（或其他已知）速度场进行蒸馏的损失函数。理论上，我们证明了该方法统一了许多现有的多步生成模型，包括一致性模型、一致性轨迹模型、渐进蒸馏和神经算子方法，这些均可作为我们形式化框架的特例而得到。通过在CIFAR-10和ImageNet 32x32上的实验，我们表明流图匹配能够以显著低于扩散或随机插值方法的采样成本生成高质量样本。