Embedding textured images in manifolds reveals latent information regarding texture structure and allows useful analysis of these high dimensional images in a low dimensional space. We present a framework for analysis and synthesis of natural stochastic textures (NST) which constitute an important subset of textures that are modelled as realizations of random processes. The randomness of NST differentiates them from other types of images and requires a dedicated method for analysis and synthesis. We demonstrate several applications of this framework. The first is synthesis of new types of NST. The second is NST analysis, reaffirming our previous findings regarding the fundamental properties of NST, and showing that they emerge naturally in the latent parameter space. Finally, we show the advantage of producing a manifold representation with intrinsic geometry.