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, whereby samples from the base are computed conditionally given samples from the target in a way that is different from (but does preclude) incorporating information about class labels or continuous embeddings. This enables us 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：受测度动力学传输启发的生成模型（如流模型和扩散模型）在两种概率密度之间构建连续时间映射。传统上，其中一个是仅通过样本可访问的目标密度，另一个是作为与数据无关的简单基础密度。本文利用随机插值器框架，形式化地建立了基础密度与目标密度之间的\textit{耦合}机制，其中基础密度的样本根据目标密度样本条件性地计算，这种计算方式不同于（但不排除）融入类别标签或连续嵌入信息。由此我们构建了可充当条件生成模型的动力学传输映射。研究证明，此类传输映射可通过求解与标准独立设定等效的简单平方损失回归问题来学习。通过超分辨率重建和图像修复实验，我们展示了构建依赖耦合在实际应用中的有效性。