  Denoising Score Matching with Annealed Langevin Sampling (DSM-ALS) has
recently found success in generative modeling. The approach works by first
training a neural network to estimate the score of a distribution, and then
using Langevin dynamics to sample from the data distribution assumed by the
score network. Despite the convincing visual quality of samples, this method
appears to perform worse than Generative Adversarial Networks (GANs) under the
Fr\'echet Inception Distance, a standard metric for generative models.
  We show that this apparent gap vanishes when denoising the final Langevin
samples using the score network. In addition, we propose two improvements to
DSM-ALS: 1) Consistent Annealed Sampling as a more stable alternative to
Annealed Langevin Sampling, and 2) a hybrid training formulation, composed of
both Denoising Score Matching and adversarial objectives. By combining these
two techniques and exploring different network architectures, we elevate score
matching methods and obtain results competitive with state-of-the-art image
generation on CIFAR-10.
