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：扩散过程的渐进性质（以微小增量逐步合成样本）构成了去噪扩散概率模型（DDPM）的关键要素，该模型在图像合成领域展现出前所未有的质量，最近也被探索应用于运动领域。本文提出将渐进扩散概念（沿扩散时间轴操作）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处理，从而将两个时间轴相互纠缠。通过这一特殊公式，我们迭代去噪包含一系列噪声程度递增姿态的运动缓冲区，以自回归方式生成任意长度的连续帧序列。在固定扩散时间轴的情况下，每个扩散步骤仅沿时间轴增量处理运动序列，使框架生成一个从缓冲区前列移除的干净帧，同时将新抽取的噪声向量追加至缓冲区末尾。这种新机制为长期运动合成开辟了新路径，可应用于角色动画及其他领域。