  We present the Groupwise Diffusion Model (GDM), which divides data into
multiple groups and diffuses one group at one time interval in the forward
diffusion process. GDM generates data sequentially from one group at one time
interval, leading to several interesting properties. First, as an extension of
diffusion models, GDM generalizes certain forms of autoregressive models and
cascaded diffusion models. As a unified framework, GDM allows us to investigate
design choices that have been overlooked in previous works, such as
data-grouping strategy and order of generation. Furthermore, since one group of
the initial noise affects only a certain group of the generated data, latent
space now possesses group-wise interpretable meaning. We can further extend GDM
to the frequency domain where the forward process sequentially diffuses each
group of frequency components. Dividing the frequency bands of the data as
groups allows the latent variables to become a hierarchical representation
where individual groups encode data at different levels of abstraction. We
demonstrate several applications of such representation including
disentanglement of semantic attributes, image editing, and generating
variations.
