  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.
