  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.
