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Let $\{u(t,x)\}_{t>0,x\in{{\mathbb R}^{d}}}$ be the solution to a$d$-dimensional parabolic Anderson model with initial condition ${\delta}_{0}$and driven by a Gaussian noise that is white in time and has a spatiallyhomogeneous covariance given by a nonnegative-definite measure $f$ whichsatisfies Dalang's condition. Let$S_{N,t}:=N^{-d}\int_{{[0,N]}^d}{[U(t,x)-1]}~{\rm d}x$ denote the spatialaverage on ${{\mathbb R}^{d}}$.  We obtain various functional central limit theorems (CLTs) for spatialaverages based on the quantitative analysis of $f$ and spatial dimension $d$.In particular, when $f$ is given by Riesz kernel, i.e., $f({\rm x})={\Vert x\Vert}^{-\beta}{\rm d}x$, $\beta\in(0,2\wedge d)$, the functional CLT is alsobased on the index $\beta$.

Functional central limit theorems for spatial averages of the parabolic Anderson model with delta initial condition in dimension $d\geq 1$