标题： 具有随机插值的多任务学习 显示英文标题

标题： Multitask Learning with Stochastic Interpolants

摘要： 我们提出了一种学习概率分布之间映射的框架，该框架广泛地概括了流和扩散模型的时间动态。 为了实现这一点，我们通过将标量时间变量替换为向量、矩阵或线性算子来推广随机插值，使我们能够在多个维度空间之间连接概率分布。 这种方法使得构建能够完成多种任务而无需任务特定训练的通用生成模型成为可能。 我们的基于算子的插值不仅为现有的生成模型提供了统一的理论视角，还扩展了它们的能力。 通过数值实验，我们在条件生成和修复、微调和后验采样以及多尺度建模中展示了我们方法的零样本有效性，表明其作为专用模型的通用无任务特性的潜在替代方案。 显示英文摘要

摘要： We propose a framework for learning maps between probability distributions that broadly generalizes the time dynamics of flow and diffusion models. To enable this, we generalize stochastic interpolants by replacing the scalar time variable with vectors, matrices, or linear operators, allowing us to bridge probability distributions across multiple dimensional spaces. This approach enables the construction of versatile generative models capable of fulfilling multiple tasks without task-specific training. Our operator-based interpolants not only provide a unifying theoretical perspective for existing generative models but also extend their capabilities. Through numerical experiments, we demonstrate the zero-shot efficacy of our method on conditional generation and inpainting, fine-tuning and posterior sampling, and multiscale modeling, suggesting its potential as a generic task-agnostic alternative to specialized models.