  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.
