Error Propagation and Model Collapse in Diffusion Models: A Theoretical Study

TL;DR

This paper provides a theoretical analysis of error propagation and model collapse in score-based diffusion models, revealing how synthetic data training causes distribution drift and performance degradation.

Contribution

It introduces bounds on distribution divergence during recursive training, characterizing drift regimes based on score error and data mix, supported by empirical validation.

Findings

Bounds on divergence growth during training

Identification of drift regimes based on score error

Empirical validation on synthetic and image data

Abstract

Machine learning models are increasingly trained or fine-tuned on synthetic data. Recursively training on such data has been observed to significantly degrade performance in a wide range of tasks, often characterized by a progressive drift away from the target distribution. In this work, we theoretically analyze this phenomenon in the setting of score-based diffusion models. For a realistic pipeline where each training round uses a combination of synthetic data and fresh samples from the target distribution, we obtain upper and lower bounds on the accumulated divergence between the generated and target distributions. This allows us to characterize different regimes of drift, depending on the score estimation error and the proportion of fresh data used in each generation. We also provide empirical results on synthetic data and images to illustrate the theory.