  Score-based diffusion models synthesize samples by reversing a stochastic
process that diffuses data to noise, and are trained by minimizing a weighted
combination of score matching losses. The log-likelihood of score-based
diffusion models can be tractably computed through a connection to continuous
normalizing flows, but log-likelihood is not directly optimized by the weighted
combination of score matching losses. We show that for a specific weighting
scheme, the objective upper bounds the negative log-likelihood, thus enabling
approximate maximum likelihood training of score-based diffusion models. We
empirically observe that maximum likelihood training consistently improves the
likelihood of score-based diffusion models across multiple datasets, stochastic
processes, and model architectures. Our best models achieve negative
log-likelihoods of 2.83 and 3.76 bits/dim on CIFAR-10 and ImageNet 32x32
without any data augmentation, on a par with state-of-the-art autoregressive
models on these tasks.
