Given the video of a still background occluded by a fluid dynamic texture (FDT), this paper addresses the problem of separating the video sequence into its two constituent layers. One layer corresponds to the video of the unoccluded background, and the other to that of the dynamic texture, as it would appear if viewed against a black background. The model of the dynamic texture is unknown except that it represents fluid flow. We present an approach that uses the image motion information to simultaneously obtain a model of the dynamic texture and separate it from the background which is required to be still. Previous methods have considered occluding layers whose dynamics follows simple motion models (e.g. periodic or 2D parametric motion). FDTs considered in this paper exhibit complex stochastic motion. We consider videos showing an FDT layer (e.g. pummeling smoke or heavy rain) in front of a static background layer (e.g. brick building). We propose a novel method for simultaneously separating these two layers and learning a model for the FDT. Due to the fluid nature of the DT, we are required to learn a model for both the spatial appearance and the temporal variations (due to changes in density) of the FDT, along with a valid estimate of the background. We model the frames of a sequence as being produced by a continuous HMM, characterized by transition probabilities based on the Navier-Stokes equations for fluid dynamics, and by generation probabilities based on the convex matting of the FDT with the background. We learn the FDT appearance, the FDT temporal variations, and the background by maximizing their joint probability using Interactive Conditional Modes (ICM). Since the learned model is generative, it can be used to synthesize new videos with different backgrounds and density variations. Experiments on videos that we compiled demonstrate the performance of our method.