This paper proposes a new inference for the correlated topic model (CTM) [3]. CTM is an extension of LDA [4] for modeling correlations among latent topics. The proposed inference is an instance of the stochastic gradient variational Bayes (SGVB) [7,8]. By constructing the inference network with the diagonal logistic normal distribution, we achieve a simple inference. Especially, there is no need to invert the covariance matrix explicitly. We performed a comparison with LDA in terms of predictive perplexity. The two inferences for LDA are considered: the collapsed Gibbs sampling (CGS) [5] and the collapsed variational Bayes with a zero-order Taylor expansion approximation (CVB0) [1]. While CVB0 for LDA gave the best result, the proposed inference achieved the perplexities comparable with those of CGS for LDA.