  In this note we prove that reconstruction from magnitudes of frame
coefficients (the so called "phase retrieval problem") can be performed using
Lipschitz continuous maps. Specifically we show that when the nonlinear
analysis map $\alpha:{\mathcal H}\rightarrow\mathbb{R}^m$ is injective, with
$(\alpha(x))_k=|<x,f_k>|^2$, where $\{f_1,\ldots,f_m\}$ is a frame for the
Hilbert space ${\mathcal H}$, then there exists a left inverse map
$\omega:\mathbb{R}^m\rightarrow {\mathcal H}$ that is Lipschitz continuous.
Additionally we obtain the Lipschitz constant of this inverse map in terms of
the lower Lipschitz constant of $\alpha$. Surprisingly the increase in
Lipschitz constant is independent of the space dimension or frame redundancy.
