We present an elementary and self-contained account of the analogies existing between classical diffusion and the imaginary-time evolution of quantum systems. These analogies are used to develop a new quantum simulation method which allows the calculation of the groundstate expectation values of local observables without any mixed estimates nor population-control bias, as well as static and dynamic (in imaginary time) response functions. This method, which we name Reptation Quantum Monte Carlo, is demonstrated with a few case applications to He-4, including the calculation of total and potential energies, static and imaginary-time dependent density response functions, and low-lying excitation energies. Finally we discuss the relationship of our technique to other simulation schemes.
