We present theoretical convergence guarantees for ODE-based generative
models, specifically flow matching. We use a pre-trained autoencoder network to
map high-dimensional original inputs to a low-dimensional latent space, where a
transformer network is trained to predict the velocity field of the
transformation from a standard normal distribution to the target latent
distribution. Our error analysis demonstrates the effectiveness of this
approach, showing that the distribution of samples generated via estimated ODE
flow converges to the target distribution in the Wasserstein-2 distance under
mild and practical assumptions. Furthermore, we show that arbitrary smooth
functions can be effectively approximated by transformer networks with
Lipschitz continuity, which may be of independent interest.

我们研究了基于 ODE 的生成模型（特别是流匹配），通过使用预训练的自编码网络将高维原始输入映射到低维潜在空间，再通过训练一个转换网络来预测从标准正态分布到目标潜在分布的变换速度场。我们的误差分析证明了这种方法的有效性，显示出通过估计 ODE 流生成的样本分布在温斯坦 - 2 距离下收敛到目标分布，在温和和实际的假设下。此外，我们还展示了具有李普希茨连续性的转换网络可以有效逼近任意平滑函数，这可能具有独立的兴趣。