A Flexible Diffusion Model
This work addresses a theoretical gap in diffusion models for researchers, but it is incremental as it builds on existing SDE variants.
The authors tackled the limitation of hand-crafted forward SDEs in diffusion models by proposing a general framework for parameterizing the spatial part of the forward SDE, with theoretical guarantees and validation on synthetic datasets, MNIST, and CIFAR10.
Diffusion (score-based) generative models have been widely used for modeling various types of complex data, including images, audios, and point clouds. Recently, the deep connection between forward-backward stochastic differential equations (SDEs) and diffusion-based models has been revealed, and several new variants of SDEs are proposed (e.g., sub-VP, critically-damped Langevin) along this line. Despite the empirical success of the hand-crafted fixed forward SDEs, a great quantity of proper forward SDEs remain unexplored. In this work, we propose a general framework for parameterizing the diffusion model, especially the spatial part of the forward SDE. An abstract formalism is introduced with theoretical guarantees, and its connection with previous diffusion models is leveraged. We demonstrate the theoretical advantage of our method from an optimization perspective. Numerical experiments on synthetic datasets, MINIST and CIFAR10 are also presented to validate the effectiveness of our framework.