In this work, we investigate the problem of estimating time-varying noise distribution parameter on a factor graph. A new message passing scheme is proposed by incorporating the variational Bayes (VB) into the belief propagation algorithm for estimating of time-varying noise distribution parameter in a low-density parity-check decoder. The scheme can also be used for the estimation of the correlation noise model parameter in distributed video coding. A Bayesian estimator is used to estimate this parameter by obtaining its posterior distribution given the channel output. The VB algorithm is employed to approximate the complex form of the posterior distribution with a simple distribution. Finally, this distribution is used to derive a closed-form expression for the messages on the augmented factor graph for online parameter estimation and decoding process at the same time.