  We study interior $C^{1, \al}$ regularity of viscosity solutions of the
parabolic Monge-Amp\'ere equation $$u_t = b(x,t) \ddua,$$ with exponent $p >0$
and with coefficients $b$ which are bounded and measurable. We show that when
$p$ is less than the critical power $\frac{1}{n-2}$ then solutions become
instantly $C^{1, \al}$ in the interior. Also, we prove the same result for any
power $p>0$ at those points where either the solution separates from the
initial data, or where the initial data is $C^{1, \beta}$.
