On Statistical Rates of Conditional Diffusion Transformers: Approximation, Estimation and Minimax Optimality
This work provides foundational statistical limits for diffusion transformers, offering practical guidance for developing more efficient and accurate models in machine learning.
The paper tackles the problem of analyzing the approximation and estimation rates of conditional diffusion transformers (DiTs) with classifier-free guidance, showing that both conditional and latent variants achieve minimax optimality under specific data assumptions, with latent DiTs achieving lower bounds than conditional DiTs.
We investigate the approximation and estimation rates of conditional diffusion transformers (DiTs) with classifier-free guidance. We present a comprehensive analysis for ``in-context'' conditional DiTs under four common data assumptions. We show that both conditional DiTs and their latent variants lead to the minimax optimality of unconditional DiTs under identified settings. Specifically, we discretize the input domains into infinitesimal grids and then perform a term-by-term Taylor expansion on the conditional diffusion score function under Hölder smooth data assumption. This enables fine-grained use of transformers' universal approximation through a more detailed piecewise constant approximation and hence obtains tighter bounds. Additionally, we extend our analysis to the latent setting under the linear latent subspace assumption. We not only show that latent conditional DiTs achieve lower bounds than conditional DiTs both in approximation and estimation, but also show the minimax optimality of latent unconditional DiTs. Our findings establish statistical limits for conditional and unconditional DiTs, and offer practical guidance toward developing more efficient and accurate DiT models.