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.

翻译：扩散过程通过小增量逐步合成样本的渐进特性，构成了去噪扩散概率模型(DDPM)的关键要素。该模型已在图像合成中展现出前所未有的质量，并近期被探索应用于运动领域。本研究提出将渐进扩散概念（沿扩散时间轴运作）适配至运动序列的时间轴。核心思路是扩展DDPM框架以支持时变去噪，从而实现两轴的纠缠。基于这一特殊公式，我们通过迭代去噪包含一系列逐步添加噪声姿态的运动缓冲区，自回归地生成任意长度的帧序列。在固定扩散时间轴的情况下，每个扩散步骤仅沿运动时间轴递增，使框架生成一个从缓冲区起始端移除的新干净帧，随后在其末端附加一个新采样的噪声向量。这一新机制为长时运动合成开辟了新路径，可应用于角色动画及其他领域。