Creating noise from data is easy; creating data from noise is generative modeling. We present a stochastic differential equation (SDE) that smoothly transforms a complex data distribution to a known prior distribution by slowly injecting noise, and a corresponding reverse-time SDE that transforms the prior distribution back into the data distribution by slowly removing the noise. Crucially, the reverse-time SDE depends only on the time-dependent gradient field (\aka, score) of the perturbed data distribution. By leveraging advances in score-based generative modeling, we can accurately estimate these scores with neural networks, and use numerical SDE solvers to generate samples. We show that this framework encapsulates previous approaches in score-based generative modeling and diffusion probabilistic modeling, allowing for new sampling procedures and new modeling capabilities. In particular, we introduce a predictor-corrector framework to correct errors in the evolution of the discretized reverse-time SDE. We also derive an equivalent neural ODE that samples from the same distribution as the SDE, but additionally enables exact likelihood computation, and improved sampling efficiency. In addition, we provide a new way to solve inverse problems with score-based models, as demonstrated with experiments on class-conditional generation, image inpainting, and colorization. Combined with multiple architectural improvements, we achieve record-breaking performance for unconditional image generation on CIFAR-10 with an Inception score of 9.89 and FID of 2.20, a competitive likelihood of 2.99 bits/dim, and demonstrate high fidelity generation of 1024 x 1024 images for the first time from a score-based generative model.
翻译:创建来自数据的噪音很容易; 创建来自噪音的数据很容易; 创建来自噪音的数据是基因模型。 我们展示了一种随机差异方程式(SDE),通过缓慢注入噪音,顺利地将复杂的数据分布转换成已知的先前分布,通过相应的反向时间SDE,通过缓慢去除噪音,将先前的分布转换回数据分配。 特别是, 反向时间SDE仅取决于分解反时间SDE演变中的时间依赖梯度字段(\aka,分数) 。 通过利用基于分数的基于基因模型模型的进展,我们可以通过神经网络准确估算这些分数,并利用数字SDE解析器生成样本。 我们显示,这个框架包罗了以前在基于分数的基因模型建模和传播概率模型和传播概率模型中采用的方法,允许采用新的取样程序和新的模型生成能力。 特别是,我们引入一个预测- 校正框架,以纠正离散反时间SDE的演变中错误。 我们还从基于SDE的分布中提取了对应的首次神经内值 ODE, 额外使得精确的概率计算, 并且改进了时间效率。 此外, 我们展示了以10- 度模型在10 度模型中展示了10- 度图像的升级的升级的模型,,, 在10- 的模型上展示了10-, 显示了10- 的模型的升级的升级的模型的成绩的升级的升级的升级的成绩的升级的升级的成绩的成绩的成绩的成绩的成绩, 。