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.

我们提出了一种新的生成模型类别，通过同时建模每个数据点的状态和维度，自然地处理各种维度的数据。该生成过程被制定为在不同维度空间之间跳跃的跳跃扩散过程。我们首先定义一个破坏维度的前向噪声过程，然后导出维度创建的时序反转生成过程，以及用于学习逼近它的新型证据下界训练目标。通过模拟我们学习到的时序反转生成过程的逼近值，联合生成状态值和维度，提供了一种有效的采样不同维度的数据的方法。我们在不同维度的分子和视频数据集上演示了我们的方法，并相对于分别生成状态值和维度的固定维度模型报告了更好的兼容性和改进的插值能力。

通过跳跃扩散模型进行跨维度生成建模