Autoregressive Generative Modeling with Noise Conditional Maximum Likelihood Estimation

We introduce a simple modification to the standard maximum likelihood estimation (MLE) framework. Rather than maximizing a single unconditional likelihood of the data under the model, we maximize a family of noise conditional likelihoods consisting of the data perturbed by a continuum of noise levels. We find that models trained this way are more robust to noise, obtain higher test likelihoods, and generate higher quality images. They can also be sampled from via a novel score-based sampling scheme which combats the classical covariate shift problem that occurs during sample generation in autoregressive models. Applying this augmentation to autoregressive image models, we obtain 3.32 bits per dimension on the ImageNet 64x64 dataset, and substantially improve the quality of generated samples in terms of the Frechet Inception distance (FID) -- from 37.50 to 12.09 on the CIFAR-10 dataset. Likelihood maximization models, i.e., models trained by maximizing log-likelihood, are a leading class of modern generative models. Of these, autoregressive models boast state-of-the-art performance in many domains, including images Child et al. (2019), text Vaswani et al. (2017), and audio Oord et al. (2016). However, while log-likelihood is broadly agreed upon as one of the most rigorous metrics for goodness-of-fit in statistical and generative modeling, models with high likelihoods do not necessarily produce samples of high visual quality.