2024/11/26 by Jerry Yao-Chieh Hu, Hu, Jerry Yao-Chieh, Weimin Wu +9 · 4 citations
Computer Science · Physics and Astronomy · #Artificial Intelligence (cs.AI) #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Neural Networks and Applications #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.2411.17522
openalex publication_date 2024/11/26 · openalex created_date 2024/12/05 · openalex updated_date 2026/07/28
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.