  We consider a discrete time random walk in a space-time i.i.d. random
environment. We use a martingale approach to show that the walk is diffusive in
almost every fixed environment. We improve on existing results by proving an
invariance principle and considering environments with an annealed $L^2$ drift.
We also state an a.s. invariance principle for random walks in general random
environments whose hypothesis requires a subdiffusive bound on the variance of
the quenched mean, under an ergodic invariant measure for the environment
chain.
