Stochastic interpolants unify flows and diffusions, popular generative modeling frameworks. A primary hyperparameter in these methods is the interpolation schedule that determines how to bridge a standard Gaussian base measure to an arbitrary target measure. We prove how to convert a sample path of a stochastic differential equation (SDE) with arbitrary diffusion coefficient under any schedule into the unique sample path under another arbitrary schedule and diffusion coefficient. We then extend the stochastic interpolant framework to admit a larger class of point mass schedules in which the Gaussian base measure collapses to a point mass measure. Under the assumption of Gaussian data, we identify lazy schedule families that make the drift identically zero and show that with deterministic sampling one gets a variance-preserving schedule commonly used in diffusion models, whereas with statistically optimal SDE sampling one gets our point mass schedule. Finally, to demonstrate the usefulness of our theoretical results on realistic highly non-Gaussian data, we apply our lazy schedule conversion to a state-of-the-art pretrained flow model and show that this allows for generating images in fewer steps without retraining the model.

翻译：随机插值统一了流与扩散这两种流行的生成建模框架。这些方法中的一个关键超参数是插值调度，它决定了如何将标准高斯基测度桥接到任意目标测度。我们证明了如何将具有任意扩散系数、在任意调度下的随机微分方程（SDE）样本路径，转换为在另一任意调度和扩散系数下的唯一样本路径。随后，我们将随机插值框架扩展至允许更大类别的点质量调度，其中高斯基测度坍缩为点质量测度。在高斯数据假设下，我们识别出使漂移项恒为零的惰性调度族，并证明：采用确定性采样会得到扩散模型中常用的方差保持调度，而采用统计最优的SDE采样则会得到我们的点质量调度。最后，为在现实的高度非高斯数据上展示我们理论结果的有效性，我们将惰性调度转换应用于一个最先进的预训练流模型，结果表明这能够在无需重新训练模型的情况下，以更少的步骤生成图像。