  As synthetic data becomes higher quality and proliferates on the internet,
machine learning models are increasingly trained on a mix of human- and
machine-generated data. Despite the successful stories of using synthetic data
for representation learning, using synthetic data for generative model training
creates "self-consuming loops" which may lead to training instability or even
collapse, unless certain conditions are met. Our paper aims to stabilize
self-consuming generative model training. Our theoretical results demonstrate
that by introducing an idealized correction function, which maps a data point
to be more likely under the true data distribution, self-consuming loops can be
made exponentially more stable. We then propose self-correction functions,
which rely on expert knowledge (e.g. the laws of physics programmed in a
simulator), and aim to approximate the idealized corrector automatically and at
scale. We empirically validate the effectiveness of self-correcting
self-consuming loops on the challenging human motion synthesis task, and
observe that it successfully avoids model collapse, even when the ratio of
synthetic data to real data is as high as 100%.
