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Articulated object pose estimation is a core task in embodied AI. Existing methods typically regress poses in a continuous space, but often struggle with 1) navigating a large, complex search space and 2) failing to incorporate intrinsic kinematic constraints. In this work, we introduce DICArt (DIsCrete Diffusion for Articulation Pose Estimation), a novel framework that formulates pose estimation as a conditional discrete diffusion process. Instead of operating in a continuous domain, DICArt progressively denoises a noisy pose representation through a learned reverse diffusion procedure to recover the GT pose. To improve modeling fidelity, we propose a flexible flow decider that dynamically determines whether each token should be denoised or reset, effectively balancing the real and noise distributions during diffusion. Additionally, we incorporate a hierarchical kinematic coupling strategy, estimating the pose of each rigid part hierarchically to respect the object's kinematic structure. We validate DICArt on both synthetic and real-world datasets. Experimental results demonstrate its superior performance and robustness. By integrating discrete generative modeling with structural priors, DICArt offers a new paradigm for reliable category-level 6D pose estimation in complex environments.