Score-Based Generative Modeling through Stochastic Differential Equations
打开互动全文版（逐段中英对照 + 图/公式 + 论文问答）→从数据中创建噪声很容易，但从噪声中创建数据则是生成建模。我们提出了一种随机微分方程，通过缓慢注入噪声，将复杂的数据分布平滑地转换为已知的先验分布，并提出了相应的反向时间随机微分方程，通过缓慢去除噪声，将先验分布转换回数据分布。关键在于，反向时间随机微分方程仅依赖于扰动数据分布的时间相关梯度场（即分数）。通过利用分数生成建模的进展，我们可以用神经网络准确估计这些分数，并使用数值随机微分方程求解器生成样本。我们表明，该框架涵盖了分数生成建模和扩散概率建模中的先前方法，从而实现了新的采样程序和新的建模能力。特别是，我们引入了一个预测-校正框架来纠正离散化反向时间随机微分方程演化中的误差。我们还推导了一个等效的神经常微分方程，它从与随机微分方程相同的分布中采样，但此外还能实现精确的似然计算和更高的采样效率。此外，我们提供了一种用分数模型解决逆问题的新方法，并通过类条件生成、图像修复和着色实验进行了演示。结合多项架构改进，我们在 CIFAR-10 上实现了无条件图像生成的创纪录性能，Inception 得分为 9.89，FID 为 2.20，竞争性似然为 2.99 bits/dim，并首次从基于分数的生成模型展示了 1024×1024 图像的高保真生成。
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.