  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.
