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Deep generative models have made tremendous progress in modeling complexdata, often exhibiting generation quality that surpasses a typical human'sability to discern the authenticity of samples. Undeniably, a key driver ofthis success is enabled by the massive amounts of web-scale data consumed bythese models. Due to these models' striking performance and ease ofavailability, the web will inevitably be increasingly populated with syntheticcontent. Such a fact directly implies that future iterations of generativemodels must contend with the reality that their training is curated from bothclean data and artificially generated data from past models. In this paper, wedevelop a framework to rigorously study the impact of training generativemodels on mixed datasets (of real and synthetic data) on their stability. Wefirst prove the stability of iterative training under the condition that theinitial generative models approximate the data distribution well enough and theproportion of clean training data (w.r.t. synthetic data) is large enough. Weempirically validate our theory on both synthetic and natural images byiteratively training normalizing flows and state-of-the-art diffusion models onCIFAR10 and FFHQ.

On the Stability of Iterative Retraining of Generative Models on their own Data