The Ito equation is shown to be a geodesic flow of $L^2$ metric on the semidirect product space $\widehat{{\mathrm{𝐷𝑖𝑓𝑓}}^s\left(S^1\right)⨀C^{\infty }\left(S^1\right)}$, where ${\mathrm{𝐷𝑖𝑓𝑓}}^s\left(S^1\right)$ is the group of orientation preserving Sobolev $H^s$ diffeomorphisms of the circle. We also study a geodesic flow of a $H^1$ metric.