Generative models inspired by dynamical transport of measure -- such as flows and diffusions -- construct a continuous-time map between two probability densities. Conventionally, one of these is the target density, only accessible through samples, while the other is taken as a simple base density that is data-agnostic. In this work, using the framework of stochastic interpolants, we formalize how to \textit{couple} the base and the target densities. This enables us to incorporate information about class labels or continuous embeddings to construct dynamical transport maps that serve as conditional generative models. We show that these transport maps can be learned by solving a simple square loss regression problem analogous to the standard independent setting. We demonstrate the usefulness of constructing dependent couplings in practice through experiments in super-resolution and in-painting.

翻译：受测度动力输运启发的生成模型（如流模型和扩散模型）在两个概率密度之间构建连续时间映射。传统上，其中一个密度是目标密度（仅能通过样本观测），另一个则采用与数据无关的简单基密度。本研究基于随机插值器框架，形式化了基密度与目标密度的\textit{耦合}方法。该方法能够引入类别标签或连续嵌入等先验信息，构建作为条件生成模型的动力输运映射。我们证明这类输运映射可通过求解类似标准独立设定下的简单平方损失回归问题来学习。通过超分辨率重建与图像修复实验，我们验证了构建相关耦合在实际应用中的有效性。