Flow matching models have shown great potential in image generation tasks among probabilistic generative models. Building upon the ideas of continuous normalizing flows, flow matching models generalize the transport path of the diffusion models from a simple prior distribution to the data. Most flow matching models in the literature do not explicitly model the underlying structure/manifold in the target data when learning the flow from a simple source distribution like the standard Gaussian. This leads to inefficient learning, especially for many high-dimensional real-world datasets, which often reside in a low-dimensional manifold. Existing strategies of incorporating manifolds, including data with underlying multi-modal distribution, often require expensive training and hence frequently lead to suboptimal performance. To this end, we present \texttt{Latent-CFM}, which provides simplified training/inference strategies to incorporate multi-modal data structures using pretrained deep latent variable models. Through experiments on multi-modal synthetic data and widely used image benchmark datasets, we show that \texttt{Latent-CFM} exhibits improved generation quality with significantly less training ($\sim 50\%$ less in some cases) and computation than state-of-the-art flow matching models. Using a 2d Darcy flow dataset, we demonstrate that our approach generates more physically accurate samples than competitive approaches. In addition, through latent space analysis, we demonstrate that our approach can be used for conditional image generation conditioned on latent features.

本研究解决了流匹配模型在高维实际数据集中的低效学习问题，尤其是在数据潜在结构和流动路径建模方面的不足。提出的\texttt{Latent-CFM}方法通过利用预训练的深度潜变量模型，有效地整合了多模态数据结构，实现了更简化的训练和推理策略，并在生成质量上显著提升，训练时间减少约50%。

利用潜变量的高效流匹配