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.

翻译：摘要：训练连续时间生成模型的免模拟方法构建了在噪声分布与单个数据样本之间传播的概率路径。近期研究（如流匹配）推导出对每个数据样本最优的路径。然而，这些算法依赖于独立的数据与噪声样本，未利用数据分布中的底层结构来构建概率路径。我们提出多样本流匹配——一种更通用的框架，在满足正确边际约束的同时，能够利用数据与噪声样本之间的非平凡耦合。在极低的开销成本下，这一泛化使我们能够：(i) 减少训练中的梯度方差；(ii) 为学习到的向量场获得更线性的流，从而通过更少的函数评估生成高质量样本；(iii) 获得高维空间中成本更低的传输映射，其应用范围超越生成式建模。重要的是，我们以完全免模拟的方式实现这一目标，且仅需简单的极小化目标函数。我们证明，所提方法在降采样后的ImageNet数据集上提升了样本一致性，并实现了更优的低成本样本生成。