Simulation-free methods for training continuous-time generative models
construct probability paths that go between noise distributions and individual
data samples. Recent works, such as Flow Matching, derived paths that are
optimal for each data sample. However, these algorithms rely on independent
data and noise samples, and do not exploit underlying structure in the data
distribution for constructing probability paths. We propose Multisample Flow
Matching, a more general framework that uses non-trivial couplings between data
and noise samples while satisfying the correct marginal constraints. At very
small overhead costs, this generalization allows us to (i) reduce gradient
variance during training, (ii) obtain straighter flows for the learned vector
field, which allows us to generate high-quality samples using fewer function
evaluations, and (iii) obtain transport maps with lower cost in high
dimensions, which has applications beyond generative modeling. Importantly, we
do so in a completely simulation-free manner with a simple minimization
objective. We show that our proposed methods improve sample consistency on
downsampled ImageNet data sets, and lead to better low-cost sample generation.

通过非简单合并数据和噪声样本的 Multisample Flow Matching 算法，我们可以在完全不需要模拟的情况下，通过一个简单的最小化目标函数构造概率路径，实现连续时间生成模型训练参数、生成高质量样本和高维传输映射等目标的综合优化。