AnimatableDreamer is a framework for generating and reconstructing animatable non-rigid 3D models from single-eye videos. It is capable of creating non-rigid objects of different categories while adhering to the object movement extracted from the video. The key technology is the proposed canonical score distillation method, which simplifies the generation dimension from 4D to 3D, performs denoising across different frames in the video, and carries out the distillation process within a unique canonical space. This ensures consistent generation and realistic morphologies across different postures. With differentiable deformation, AnimatableDreamer elevates the 3D generator to 4D, providing a new perspective on the generation and reconstruction of non-rigid 3D models. Additionally, combining with the inductive knowledge of consistency diffusion models, canonical score distillation can regularize reconstruction from new perspectives, thereby enhancing the generative process in a closed loop. Extensive experiments demonstrate that this method can generate highly flexible 3D models guided by text from single-eye videos, while achieving superior reconstruction performance compared to typical non-rigid reconstruction methods.