Learning to denoise has emerged as a prominent paradigm to design state-of-the-art deep generative models for natural images. How to use it to model the distributions of both continuous real-valued data and categorical data has been well studied in recently proposed diffusion models. However, it is found in this paper to have limited ability in modeling some other types of data, such as count and non-negative continuous data, that are often highly sparse, skewed, heavy-tailed, and/or overdispersed. To this end, we propose learning to jump as a general recipe for generative modeling of various types of data. Using a forward count thinning process to construct learning objectives to train a deep neural network, it employs a reverse count thickening process to iteratively refine its generation through that network. We demonstrate when learning to jump is expected to perform comparably to learning to denoise, and when it is expected to perform better. For example, learning to jump is recommended when the training data is non-negative and exhibits strong sparsity, skewness, heavy-tailedness, and/or heterogeneity.

翻译：去噪学习已成为设计自然图像最优深度生成模型的主流范式。近年来提出的扩散模型已充分研究了如何运用该方法对连续实值数据和分类数据分布进行建模。然而，本文发现该方法在建模计数数据、非负连续数据等其他类型数据时能力有限——这类数据往往呈现高度稀疏性、偏态性、重尾性和/或过度离散性特征。为此，我们提出"学习跳跃"作为各类数据生成式建模的通用方案。该方法通过前向计数稀疏化过程构建学习目标以训练深度神经网络，并借助反向计数稠密化过程通过该网络迭代优化生成结果。我们论证了学习跳跃何时能与去噪学习表现相当，以及何时能预期获得更优性能。例如，当训练数据为非负且呈现显著稀疏性、偏态性、重尾性和/或异质性时，推荐采用学习跳跃方法。