On Statistical Rates of Conditional Diffusion Transformers: Approximation,  Estimation and Minimax Optimality
Jerry Yao-Chieh Hu Weimin Wu Yi-Chen Lee Yu-Chao Huang Minshuo Chen Han Liu
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 various common assumptions: generic and strong Hölder, linear latent (subspace), and Lipschitz score function assumptions. Importantly, we establish minimax optimality of DiTs by leveraging score function regularity. Specifically, we discretize the input domains into infinitesimal grids and then perform term-by-term Taylor expansions on the conditional diffusion score function under the 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 latent settings. Our findings establish statistical limits for DiTs and offer practical guidance toward more efficient and accurate designs.
Conditional Diffusion Transformer, Statistical Rates, Approximation, Estimation
We investigate the approximation and (minimax optimal) estimation rates of Conditional Diffusion Transformers (DiTs) with classifier-free guidance.