Space-Time Diffusion Bridge

In this study, we introduce a novel method for generating i.i.d. synthetic samples from high-dimensional real-valued probability distributions, defined by Ground Truth (GT) samples. Our approach integrates space-time mixing strategies across temporal and spatial dimensions. The methodology involves three interrelated stochastic processes: (a) linear processes with space-time mixing yielding Gaussian conditional densities, (b) their diffusion bridge analogs conditioned on initial and final states, and (c) nonlinear stochastic processes refined via score-matching techniques. The training regime fine-tunes both nonlinear and potentially linear models to align with GT data. We validate our space-time diffusion bridge approach through numerical experiments.