  The Mean Field Variational Bayes (MFVB) method is one of the most
computationally efficient techniques for Bayesian inference. However, its use
has been restricted to models with conjugate priors or those that require
analytical calculations. This paper proposes a novel particle-based MFVB
approach that greatly expands the applicability of the MFVB method. We
establish the theoretical basis of the new method by leveraging the connection
between Wasserstein gradient flows and Langevin diffusion dynamics, and
demonstrate the effectiveness of this approach using Bayesian logistic
regression, stochastic volatility, and deep neural networks.
