用向量/矩阵代替时间变量，实现跨维度分布的通用生成建模。
Multitask Learning with Stochastic Interpolants
- 用运算符替代标量时间，构建多维分布间的随机插值
- 零样本完成条件生成、补全、后验采样等多任务
- 适合需要灵活适配多种生成任务的场景
我们提出一种学习概率分布间映射的框架，广泛推广了流模型和扩散模型的时间动态。通过将标量时间变量替换为向量、矩阵或线性算子，实现了在多个维度空间之间连接概率分布的能力。该方法可构建无需任务特化训练的多功能生成模型。基于算子的插值不仅为现有生成模型提供统一理论视角，还拓展其能力。数值实验表明，该方法在条件生成、图像修复、微调与后验采样、多尺度建模上均表现出零样本有效性，具备作为通用无任务依赖替代方案的潜力。
原文摘要 · Abstract (English)
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.
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