  This article starts over the backwards diffusion problem by replacing the
\emph{noncausal} diffusion equation, the direct problem, by the \emph{causal}
diffusion model developed in \cite{Kow11} for the case of constant diffusion
speed. For this purpose we derive an analytic representation of the Green
function of causal diffusion in the wave vector-time space for arbitrary (wave
vector) dimension $N$. We prove that the respective backwards diffusion problem
is ill-posed, but not exponentially ill-posed, if the data acquisition time is
larger than a characteristic time period $\tau$ ($2\,\tau$) for space dimension
$N\geq 3$ (N=2). In contrast to the noncausal case, the inverse problem is
well-posed for N=1. Moreover, we perform a theoretical and numerical comparison
between causal and noncausal diffusion in the \emph{space-time domain} and the
\emph{wave vector-time domain}. The paper is concluded with numerical
simulations of the backwards diffusion problem via the Landweber method.
