We extend a recent diffusion model, in which the continuous time dynamics of the K-scattering process have been proposed, to include the effect of the presence of a coherent offset in the scattering amplitude. The weak scattering amplitudes are characterized in terms of continuous time biased random walk models, and the corresponding stochastic dynamics derived. The stochastic differential geometry of the resultant amplitude fluctuations is derived in relation to that of pure K-scattering. Asymptotic distributions of amplitude, intensity, and phase are provided, and the condition for detailed balance shown to hold.