We propose a new class of generative models that naturally handle data of varying dimensionality by jointly modeling the state and dimension of each datapoint. The generative process is formulated as a jump diffusion process that makes jumps between different dimensional spaces. We first define a dimension destroying forward noising process, before deriving the dimension creating time-reversed generative process along with a novel evidence lower bound training objective for learning to approximate it. Simulating our learned approximation to the time-reversed generative process then provides an effective way of sampling data of varying dimensionality by jointly generating state values and dimensions. We demonstrate our approach on molecular and video datasets of varying dimensionality, reporting better compatibility with test-time diffusion guidance imputation tasks and improved interpolation capabilities versus fixed dimensional models that generate state values and dimensions separately.

翻译：我们提出了一类新型生成模型，通过联合建模每个数据点的状态与维度，自然处理变维数据。生成过程被形式化为一种跳跃扩散过程，该过程在不同维度空间之间进行跳跃。我们首先定义了一个破坏维度的正向加噪过程，进而推导出创建维度的反向时间生成过程，并提出了基于证据下界的新型训练目标来学习该过程的近似。通过模拟学习得到的反向时间生成过程的近似，我们能够通过联合生成状态值与维度，有效采样变维数据。我们在分子与视频数据集上验证了该方法，结果显示：与分别生成状态值和维度的固定维度模型相比，本方法在测试时扩散引导插补任务中表现出更好的兼容性，并拥有更优的插值能力。