论文标题
灵活的扩散模型
A Flexible Diffusion Model
论文作者
论文摘要
扩散（基于得分）生成模型已被广泛用于建模各种类型的复杂数据，包括图像，音频和点云。最近，已经揭示了前向后的随机微分方程（SDE）与基于扩散的模型之间的深厚连接，并提出了几种新的SDE变体（例如，Sub-VP，批评抑制的Langevin）。尽管手工制作的固定前进SDE取得了经验成功，但仍未探索大量适当的正向SDE。在这项工作中，我们提出了一个通用框架，用于参数化扩散模型，尤其是向前SDE的空间部分。引入了一种抽象的形式主义，并具有理论上的保证，并且它与以前的扩散模型的联系得到了利用。我们从优化的角度展示了我们方法的理论优势。还提出了关于合成数据集，矿工和CIFAR10的数值实验，以验证我们框架的有效性。
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.
