Error Propagation and Model Collapse in Diffusion Models: A Theoretical Study
This addresses a critical issue for practitioners using synthetic data in machine learning, offering theoretical insights into model collapse, though it is incremental as it builds on existing observations.
The paper tackles the problem of performance degradation in diffusion models when recursively trained on synthetic data, providing theoretical bounds on the divergence between generated and target distributions and characterizing drift regimes based on score estimation error and fresh data proportion.
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.