Video sequences are frequently contaminated by noise throughout the acquisition process, resulting in considerable degradation of video display quality. In this paper, we present a novel method of video filtering. The proposed filter is developed from an optimization problem in which a Bayesian term and a noisy video sequence prior distribution are combined. The method begins by segmenting the video sequence into space-time blocks and then substituting each noisy block by a weighted average of non-local neighbor blocks. Gradient-based weights are used to dynamically adjust the edge preservation and smoothness of the reference block. The obtained formulation enables nonlinear filtering and, hence, preserving key features such as edges and corners while using the intrinsic Bayesian filtering framework. Experiments on different video sequences with varying degrees of noise show that the proposed method performs better than state-of-the-art video filtering approaches.