We introduce a general framework for constructing generative models using one-dimensional noising processes. Beyond diffusion processes, we outline examples that demonstrate the flexibility of our approach. Motivated by this, we propose a novel framework in which the 1D processes themselves are learnable, achieved by parameterizing the noise distribution through quantile functions that adapt to the data. Our construction integrates seamlessly with standard objectives, including Flow Matching and consistency models. Learning quantile-based noise naturally captures heavy tails and compact supports when present. Numerical experiments highlight both the flexibility and the effectiveness of our method.

翻译：我们提出了一个利用一维加噪过程构建生成模型的通用框架。除了扩散过程，我们还概述了展示该方法灵活性的示例。受此启发，我们提出了一种新颖的框架，其中一维过程本身是可学习的，这是通过使用适应数据的分位数函数对噪声分布进行参数化来实现的。我们的构建与包括流匹配和一致性模型在内的标准目标函数无缝集成。基于分位数的噪声学习能够自然地捕获数据中可能存在的重尾分布和紧支撑特性。数值实验突显了我们方法的灵活性和有效性。