Trans-Dimensional Generative Modeling via Jump Diffusion Models
This addresses a specific challenge in generative modeling for domains like molecular and video data where dimensionality varies, offering an incremental improvement over existing methods.
The paper tackles the problem of generative modeling for data with varying dimensionality by proposing a new class of models that jointly model state and dimension using jump diffusion processes, resulting in better performance on tasks like imputation and interpolation compared to fixed-dimensional models.
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.