Improved Sample Complexity Bounds for Diffusion Model Training
This work addresses a theoretical bottleneck in diffusion model training for researchers and practitioners, providing tighter sample complexity bounds, though it is incremental as it builds on prior theoretical studies.
The paper tackles the problem of determining the sample complexity required to train an accurate diffusion model using a neural network, showing an exponential improvement in dependence on Wasserstein error and depth compared to prior bounds.
Diffusion models have become the most popular approach to deep generative modeling of images, largely due to their empirical performance and reliability. From a theoretical standpoint, a number of recent works have studied the iteration complexity of sampling, assuming access to an accurate diffusion model. In this work, we focus on understanding the sample complexity of training such a model; how many samples are needed to learn an accurate diffusion model using a sufficiently expressive neural network? Prior work showed bounds polynomial in the dimension, desired Total Variation error, and Wasserstein error. We show an exponential improvement in the dependence on Wasserstein error and depth, along with improved dependencies on other relevant parameters.