We show that every norm continuous one-parameter semigroup (ℐt: t ∈ ℝ+) of unital ultraweakly continuous completely positive maps on the algebra ℬ(ℋ0) of bounded operators on the separable infinite dimensional Hilbert space ℋ0 can be expressed as Open image in new window where (j t : t ∈ ℝ+) is a quantum diffusion over ℬ(ℋ0) constructed using only one dimensional quantum stochastic calculus. In general the diffusion is not inner.