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Text-to-motion generation has attracted increasing attention in the research community recently, with potential applications in animation, virtual reality, robotics, and human-computer interaction. Diffusion and autoregressive models are two popular and parallel research directions for text-to-motion generation. However, diffusion models often suffer from error amplification during noise prediction, while autoregressive models exhibit mode collapse due to motion discretization. To address these limitations, we propose a flexible, high-fidelity, and semantically faithful text-to-motion framework, named Coordinate-based Dual-constrained Autoregressive Motion Generation (CDAMD). With motion coordinates as input, CDAMD follows the autoregressive paradigm and leverages diffusion-inspired multi-layer perceptrons to enhance the fidelity of predicted motions. Furthermore, a Dual-Constrained Causal Mask is introduced to guide autoregressive generation, where motion tokens act as priors and are concatenated with textual encodings. Since there is limited work on coordinate-based motion synthesis, we establish new benchmarks for both text-to-motion generation and motion editing. Experimental results demonstrate that our approach achieves state-of-the-art performance in terms of both fidelity and semantic consistency on these benchmarks.