Trans-Dimensional Generative Modeling via Jump Diffusion Models

TL;DR

This paper introduces a jump diffusion-based generative model capable of handling data with varying dimensions, enabling joint generation of states and dimensions, and demonstrating improved performance on molecular and video datasets.

Contribution

It presents a novel jump diffusion framework with a dimension-creating reverse process and a new training objective for variable-dimensional data generation.

Findings

Better compatibility with diffusion guidance imputation tasks

Improved interpolation over fixed-dimensional models

Effective joint generation of state and dimension data

Abstract

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.