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Approximating Measures on Function Spaces: Transport and Truncation

arXiv · AI, language, vision and robotics · article · Sep 15, 2026 · UTC

Measures on function spaces arise throughout Bayesian inverse problems and generative modeling, often with low-dimensional structure relative to a tractable reference measure. We introduce the class $\mathcal{P}_ψ(μ)$ of measures that differ from a reference measure $μ$ only through a finite-dimensional map $ψ$ while preserving the reference conditionals on its fibers. Class members are determined by their $d$-dimensional pushforwards under $ψ$ and admit convenient block-triangular transport map representations. Draws are taken from this $d$-dimensional distribution and then completed to funct

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