In this paper, we present a novel method for generating i.i.d. samples from complex, high-dimensional real-valued probability distributions. These target distributions are implicitly defined by a set of Ground Truth (GT) samples. Our approach hinges on the design of a continuous and finite-time stochastic diffusion process, as well as its reverse counterpart. These processes are engineered to facilitate  optimal transport from a tractable initial probability distribution to the target distribution represented by the GT samples. A key feature of our method is the integration of space-time mixing strategies -- across both temporal and spatial dimensions. This integration exploits the inherent linearity of the spatio-temporal aspects of the stochastic process, along with the Gaussian nature of the conditional probability densities involved.