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Starting from a sequence of independent Wright-Fisher diffusion processes on$[0,1]$, we construct a class of reversible infinite dimensional diffusionprocesses on $\DD_\infty:= \{{\bf x}\in  Let $M$ be a complete Riemnnian manifold and $\mu$ the distribution of thediffusion process generated by $\ff 1 2\DD+Z$ where $Z$ is a $C^1$-vectorfield. When $\Ric-\nn Z$ is bounded below and $Z$ has, for instance, lineargrowth, the transportation-cost inequality with respect to the uniform distanceis established for $\mu$ on the path space over $M$. A simple example is givento show the optimality of the condition.

Transportation Cost Inequality on Path Spaces with Uniform Distance