It is demonstrated that quantum systems classically exhibiting strong and homogeneous chaos in a bounded region of the phase space can induce a global quantum diffusion. As an ideal model system, a small quantum chaos with finite Hilbert space dimension $N$ weakly coupled with $M$ additional degrees of freedom which is approximated by linear systems is proposed. By twinning the system the diffusion process in the additional modes can be numerically investigated without taking the unbounded diffusion space into account explicitly. Even though $N$ is not very large, diffusion occurs in the additional modes as the coupling strength increases if $M\ge 3$. If $N$ is large enough, a definite quantum transition to diffusion takes place through a critical subdiffusion characterized by an anomalous diffusion exponent.

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• Anderson localization
• Quantum chaos