  The present paper is concerned with properties of multiple Schramm--Loewner
evolutions (SLEs) labelled by a parameter $\kappa\in (0,8]$. Specifically, we
consider the solution of the multiple Loewner equation driven by a time change
of Dyson's Brownian motions in the non-colliding regime. Although it is often
considered that several properties of the solution can be studied by means of
commutation relations of SLEs and the absolute continuity, this method is
available only in the case that the curves generated by commuting SLEs are
separated. Beyond this restriction, it is not even obvious that the solution of
the multiple Loewner equation generates multiple curves. To overcome this
difficulty, we employ the coupling of Gaussian free fields and multiple SLEs.
Consequently, we prove the longstanding conjecture that the solution indeed
generates multiple continuous curves. Furthermore, these multiple curves are
(i) simple disjoint curves when $\kappa\in (0,4]$, (ii) intersecting curves
when $\kappa\in (4,8)$, and (iii) space-filling curves when $\kappa=8$.
