We present Articulated Motion Distillation (AMD), a framework for generating high-fidelity character animations by merging the strengths of skeleton-based animation and modern generative models. AMD uses a skeleton-based representation for rigged 3D assets, drastically reducing the Degrees of Freedom (DoFs) by focusing on joint-level control, which allows for efficient, consistent motion synthesis. Through Score Distillation Sampling (SDS) with pre-trained video diffusion models, AMD distills complex, articulated motions while maintaining structural integrity, overcoming challenges faced by 4D neural deformation fields in preserving shape consistency. This approach is naturally compatible with physics-based simulation, ensuring physically plausible interactions. Experiments show that AMD achieves superior 3D consistency and expressive motion quality compared with existing works on text-to-4D generation.