Space-Time Diffusion Bridge
Hamidreza Behjoo, Michael Chertkov

TL;DR
This paper introduces a space-time diffusion bridge method for generating high-dimensional synthetic data samples that are independent and identically distributed, leveraging stochastic processes and optimal transport techniques.
Contribution
It presents a novel space-time diffusion approach combining linear, diffusion bridge, and nonlinear processes for efficient high-dimensional data synthesis.
Findings
Validated through numerical experiments
Potential for simulation-free inference
Lays groundwork for future theoretical development
Abstract
In this study, we introduce a novel method for generating new synthetic samples that are independent and identically distributed (i.i.d.) from high-dimensional real-valued probability distributions, as defined implicitly by a set of Ground Truth (GT) samples. Central to our method is the integration of space-time mixing strategies that extend across temporal and spatial dimensions. Our methodology is underpinned by three interrelated stochastic processes designed to enable optimal transport from an easily tractable initial probability distribution to the target distribution represented by the GT samples: (a) linear processes incorporating space-time mixing that yield Gaussian conditional probability densities, (b) their diffusion bridge analogs that are conditioned to the initial and final state vectors, and (c) nonlinear stochastic processes refined through score-matching techniques.…
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Taxonomy
TopicsGeophysics and Sensor Technology · Transportation Safety and Impact Analysis · Structural Response to Dynamic Loads
MethodsSparse Evolutionary Training · Diffusion · ALIGN
