  We introduce a new generative model where samples are produced via Langevin
dynamics using gradients of the data distribution estimated with score
matching. Because gradients can be ill-defined and hard to estimate when the
data resides on low-dimensional manifolds, we perturb the data with different
levels of Gaussian noise, and jointly estimate the corresponding scores, i.e.,
the vector fields of gradients of the perturbed data distribution for all noise
levels. For sampling, we propose an annealed Langevin dynamics where we use
gradients corresponding to gradually decreasing noise levels as the sampling
process gets closer to the data manifold. Our framework allows flexible model
architectures, requires no sampling during training or the use of adversarial
methods, and provides a learning objective that can be used for principled
model comparisons. Our models produce samples comparable to GANs on MNIST,
CelebA and CIFAR-10 datasets, achieving a new state-of-the-art inception score
of 8.87 on CIFAR-10. Additionally, we demonstrate that our models learn
effective representations via image inpainting experiments.
