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

Keywords: Conditional Diffusion Transformer, Statistical Rates, Approximation, Estimation

TL;DR: We investigate the approximation and (minimax optimal) estimation rates of Conditional Diffusion Transformers (DiTs) with classifier-free guidance.

Abstract: 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.

Primary Area: generative models

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Submission Number: 5826