The Accumulation of Score Estimation Error in Diffusion Models

Diffusion models are widely used for high-quality generation, but their performance is sensitive to the accuracy of the estimated score. We first derive a stepwise Wasserstein error bound in a Gaussian-mixture setting, where the score admits a closed-form structure, and the score Hessian can be controlled explicitly, leading to sharp Wasserstein estimates. We then extend the analysis to general data distributions, which yields a more general but typically looser upper bound. This general bound can be sharpened under mild regularity: when the initial distribution has a globally Lipschitz score, the curvature contribution at small times is uniformly bounded, avoiding the worst-case blow-up. The results hold for both variance-preserving (VP) and variance-exploding (VE) diffusions, and apply to both the reverse-time SDE and the associated probability-flow ODE.

Diffusion models are widely used to generate images and videos. They work by starting from random noise and gradually turning it into realistic content. In this process, the model needs to estimate a direction for each denoising step, but these estimates are not perfect. We study how these small errors build up during generation. Our results show that errors near the final stage, when the image or video is almost formed, can be more harmful than errors made earlier. We also show that this behavior can be analyzed for several common types of diffusion models. This gives a clearer understanding of how estimation errors affect the quality of generated content.