The nonlinear filtering problem is a cornerstone in stochastic processes and control theory, where the objective is to estimate the conditional distribution of a signal given noisy observations. Traditional approaches, such as particle filters and sequential Monte Carlo methods, can be computationally expensive, particularly in high-dimensional settings. This project aims to develop new methods that beats the so called curse of dimensionality by leveraging neural network as function approximations to the filtering density. The research has so far consisted of applying the deep splitting method (developed for PDE) to the Bayesian filtering context. Deep splitting has been shown to solve symmetrical PDEs in up to 10000 dimensions. Utilizing cluster computing resources, such as Alvis, would enable truly scalable training of these networks, handling the extensive computational demands arising from high-dimensional state spaces and long temporal horizons. There are many ideas in the pipeline with different optimisation problems requiring advanced neural networks to solve. The main idea right now is to combine the deep Backward Stochastic Differential Equation (BSDE) with measurement updates to obtain the filtering density. More data-driven approaches that we consider are diffusion models, i.e., learning the reversed drift of an auxiliary SDE to obtain a sample of the conditional distribution. Numerical experiments validate the proposed method's efficacy, showcasing its ability to approximate filtering distributions in scenarios where traditional methods struggle due to dimensionality or computational constraints. These experiments highlight the adaptability of deep PDE methods to various nonlinear systems and noise models. A thorough error analysis has been made on the deep splitting method in this regard, showing strong convergence order. What remains is to truly scale the methods to demonstrate and explore the efficiency of the methods in a very high dimensional setting, where continuous image data would be a very interesting application.