Denoising Diffusion (score-based) generative models have been widely used for modeling various types of complex data, including images, audio, point clouds, and biomolecules. 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 several hand-crafted forward SDEs, a great quantity of potentially promising forward SDEs remains unexplored. In this work, we propose a general framework for parameterizing the diffusion models, especially the spatial part of the forward SDEs. A systematic formalism is introduced with theoretical guarantees, and its connection with previous diffusion models is leveraged. Finally, we demonstrate the theoretical advantage of our method from the variational optimization perspective. Numerical experiments on synthetic datasets, MNIST and CIFAR10 are presented to validate the effectiveness of our framework.