  Consistency models are a nascent family of generative models that can sample
high quality data in one step without the need for adversarial training.
Current consistency models achieve optimal sample quality by distilling from
pre-trained diffusion models and employing learned metrics such as LPIPS.
However, distillation limits the quality of consistency models to that of the
pre-trained diffusion model, and LPIPS causes undesirable bias in evaluation.
To tackle these challenges, we present improved techniques for consistency
training, where consistency models learn directly from data without
distillation. We delve into the theory behind consistency training and identify
a previously overlooked flaw, which we address by eliminating Exponential
Moving Average from the teacher consistency model. To replace learned metrics
like LPIPS, we adopt Pseudo-Huber losses from robust statistics. Additionally,
we introduce a lognormal noise schedule for the consistency training objective,
and propose to double total discretization steps every set number of training
iterations. Combined with better hyperparameter tuning, these modifications
enable consistency models to achieve FID scores of 2.51 and 3.25 on CIFAR-10
and ImageNet $64\times 64$ respectively in a single sampling step. These scores
mark a 3.5$\times$ and 4$\times$ improvement compared to prior consistency
training approaches. Through two-step sampling, we further reduce FID scores to
2.24 and 2.77 on these two datasets, surpassing those obtained via distillation
in both one-step and two-step settings, while narrowing the gap between
consistency models and other state-of-the-art generative models.
