We propose a novel Auto-Regressive (AR) image generation approach that models images as hierarchical compositions of interpretable visual layers. While AR models have achieved transformative success in language modeling, replicating this success in vision tasks remains challenging due to inherent spatial dependencies in images. Addressing the unique challenges of vision tasks, our method (CART) adds image details iteratively via semantically meaningful decompositions. We demonstrate the flexibility and generality of CART by applying it across three distinct decomposition strategies: (i) Base-Detail Decomposition (Mumford-Shah smoothness), (ii) Intrinsic Decomposition (albedo/shading), and (iii) Specularity Decomposition (diffuse/specular). This next-detail strategy outperforms traditional next-token and next-scale approaches, improving controllability, semantic interpretability, and resolution scalability. Experiments show CART generates visually compelling results while enabling structured image manipulation, opening new directions for controllable generative modeling via physically or perceptually motivated image factorization.