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We consider reaction-diffusion equations of KPP type in one spatialdimension, perturbed by a Fisher-Wright white noise, under the assumption ofuniqueness in distribution. Examples include the randomly perturbed Fisher-KPPequations $ \partial_t u = \partial_x^2 u + u(1-u) + \epsilon \sqrt{u(1-u)}\dotW, $ and $ \partial_t u = \partial_x^2 u + u(1-u) + \epsilon \sqrt{u}\dot W, $where $\dot W= \dot W(t,x)$ is a space-time white noise.  We prove the Brunet-Derrida conjecture that the speed of traveling fronts isasymptotically $ 2-\pi^2 |\log \epsilon^2|^{-2} $ up to a factor of order $(\log|\log\epsilon|)|\log\epsilon|^{-3}$.

Effect of Noise on Front Propagation in Reaction-Diffusion equations of KPP type