We describe a method to extract persistent elements of a dynamic scene from an input video. We represent each scene element as a Deformable Sprite consisting of three components: 1) a 2D texture image for the entire video, 2) per-frame masks for the element, and 3) non-rigid deformations that map the texture image into each video frame. The resulting decomposition allows for applications such as consistent video editing. Deformable Sprites are a type of video auto-encoder model that is optimized on individual videos, and does not require training on a large dataset, nor does it rely on pre-trained models. Moreover, our method does not require object masks or other user input, and discovers moving objects of a wider variety than previous work. We evaluate our approach on standard video datasets and show qualitative results on a diverse array of Internet videos.