Score-based diffusion models generate samples from an unknown target distribution using a time-reversed diffusion process. While such models represent state-of-the-art approaches in industrial applications such as artificial image generation, it has recently been noted that their performance can be further improved by considering injection noise with heavy tailed characteristics. Here, I present a generalization of generative diffusion processes to a wide class of non-Gaussian noise processes. I consider forward processes driven by standard Gaussian noise with super-imposed Poisson jumps representing a finite activity Levy process. The generative process is shown to be governed by a generalized score function that depends on the jump amplitude distribution. Both probability flow ODE and SDE formulations are derived using basic technical effort, and are implemented for jump amplitudes drawn from a multivariate Laplace distribution. Remarkably, for the problem of capturing a heavy-tailed target distribution, the jump-diffusion Laplace model outperforms models driven by alpha-stable noise despite not containing any heavy-tailed characteristics. The framework can be readily applied to other jump statistics that could further improve on the performance of standard diffusion models.

翻译：基于分数的扩散模型利用时间反转的扩散过程从未知目标分布中生成样本。尽管此类模型在人工图像生成等工业应用中代表了最先进的方法，但最近有研究指出，通过考虑具有重尾特性的注入噪声，其性能可得到进一步提升。本文提出了一种将生成扩散过程推广至广泛非高斯噪声过程的通用框架。所考虑的前向过程由标准高斯噪声驱动，并叠加表示有限活动 Lévy 过程的泊松跳跃。研究表明，生成过程受依赖于跳跃幅度分布的广义分数函数控制。通过基础技术推导，我们建立了概率流常微分方程和随机微分方程两种表述形式，并针对从多元拉普拉斯分布中抽取跳跃幅度的情形进行了实现。值得注意的是，在捕获重尾目标分布的问题上，跳跃扩散拉普拉斯模型的表现优于由 α 稳定噪声驱动的模型，尽管其本身并不包含任何重尾特性。该框架可轻松应用于其他跳跃统计特性，有望进一步提升标准扩散模型的性能。