The gradual nature of a diffusion process that synthesizes samples in small
increments constitutes a key ingredient of Denoising Diffusion Probabilistic
Models (DDPM), which have presented unprecedented quality in image synthesis
and been recently explored in the motion domain. In this work, we propose to
adapt the gradual diffusion concept (operating along a diffusion time-axis)
into the temporal-axis of the motion sequence. Our key idea is to extend the
DDPM framework to support temporally varying denoising, thereby entangling the
two axes. Using our special formulation, we iteratively denoise a motion buffer
that contains a set of increasingly-noised poses, which auto-regressively
produces an arbitrarily long stream of frames. With a stationary diffusion
time-axis, in each diffusion step we increment only the temporal-axis of the
motion such that the framework produces a new, clean frame which is removed
from the beginning of the buffer, followed by a newly drawn noise vector that
is appended to it. This new mechanism paves the way towards a new framework for
long-term motion synthesis with applications to character animation and other
domains.

我们提出了一种将渐进扩散概念（沿着扩散时间轴操作）扩展到运动序列的方法，用于支持时变去噪，从而将两个轴相互纠缠，通过迭代去噪逐渐增加噪声位移的动作缓冲区，并产生任意长的帧流，为长期运动合成提供了新的框架。