This paper presents a learning-based method for low-level vision problems, using a Markov network of image and scene patches. The method allows learning parameters from synthetic examples and efficient propagation of image information. It is applied to super-resolution and motion estimation problems, showing good results. The approach uses a factorization approximation to simplify learning and inference, and Monte Carlo simulations justify this approximation. The method combines scene estimation with statistical learning, using a Markov network to model dependencies between image and scene patches. The network is used to estimate the underlying scene from image data, with the Markov assumption and factorization approximation allowing efficient computation. The method is tested on three examples: joint Gaussian processes, missing image details, and motion estimation. The results show that the method works well for loopy networks and provides accurate scene estimates. The paper also discusses the use of sampled inference for probabilistic reasoning, which allows fast message propagation and accurate posterior probability estimation. The method is applied to super-resolution and motion estimation, showing good results and resolving the aperture problem. The technique may apply to other vision problems, such as line drawing interpretation and distinguishing shading from reflectance. The paper concludes that the method provides a general approach for learning-based low-level vision problems, with applications in various domains.This paper presents a learning-based method for low-level vision problems, using a Markov network of image and scene patches. The method allows learning parameters from synthetic examples and efficient propagation of image information. It is applied to super-resolution and motion estimation problems, showing good results. The approach uses a factorization approximation to simplify learning and inference, and Monte Carlo simulations justify this approximation. The method combines scene estimation with statistical learning, using a Markov network to model dependencies between image and scene patches. The network is used to estimate the underlying scene from image data, with the Markov assumption and factorization approximation allowing efficient computation. The method is tested on three examples: joint Gaussian processes, missing image details, and motion estimation. The results show that the method works well for loopy networks and provides accurate scene estimates. The paper also discusses the use of sampled inference for probabilistic reasoning, which allows fast message propagation and accurate posterior probability estimation. The method is applied to super-resolution and motion estimation, showing good results and resolving the aperture problem. The technique may apply to other vision problems, such as line drawing interpretation and distinguishing shading from reflectance. The paper concludes that the method provides a general approach for learning-based low-level vision problems, with applications in various domains.