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First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. The paper presents new techniques, and theoretical results relating to those techniques, to optimise the Variational Gaussian lower bound to the log evidence in latent Gaussian models LGMs. The technique could be applied to a broader category of latent linear models but their presentation focuses on LGMs only. VG approximate inference is important because it has many nice properties: it is widely applicable, often quite accurate and relatively fast. This paper attempts to makes VG methods more scalable without resorting to making factorisation assumptions on the approximating Gaussian distribution. Whilst the authors show how the objective function can be `decoupled' they do not show experimentally that this leads to a clear improvement in speed or scalability over standard techniques.