Transport for Conditional Sampling: Foundations and Applications
Abstract
Conditional sampling is central to Bayesian inference, generative modeling, and causal inference: given a joint law for random variables X and Y and an observation Y=y, one seeks to sample from the conditional law of X| Y=y. Even when the joint distribution is accurately represented, this task can be computationally difficult as it may require evaluating intractable normalizing constants or solving a new inference problem for each observation. Measure transport provides an approach to this problem by identifying a map with triangular structure that directly pushes forward a reference to the conditional of a joint distribution for any observation. This article reviews the theoretical, methodological, and algorithmic foundations of triangular transports, with the Knothe-Rosenblatt rearrangement as a canonical construction. We discuss methods for estimating triangular maps from finite samples, as well as their use in simulation-based inference and causal inference. While our primary aim is to review existing formulations, we also present new ideas and open questions for conditional sampling using transport.
Related
- The Normalized Maximum Likelihood for Regular Non-Smooth Models: Measure-Theoretic Foundations and Geometric Sampling
- Integral Dependence over One-Sided Ideals, Part I: Foundations and Classical Applications
- From foundations to applications: reverse mathematics and philosophy
- Conditional Decomposition Discrepancy: Separating Conditional Bias from Sampling Bias in Small-Sample Cross-Domain Cost Forecasting
- Direct Conditional Transition Sampling for Diffusion Inverse Problems
BibTeX
@misc{baptista2026transport,
title = {{Transport for Conditional Sampling: Foundations and Applications}},
author = {Ricardo Baptista and Benjamin Bloem-Reddy and Bamdad Hosseini},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01436},
eprint = {2611.01436},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01436},
}
RIS
TY - UNPB
TI - Transport for Conditional Sampling: Foundations and Applications
AU - Ricardo Baptista
AU - Benjamin Bloem-Reddy
AU - Bamdad Hosseini
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01436
UR - https://arxiv.org/abs/2611.01436
AB - Conditional sampling is central to Bayesian inference, generative modeling, and causal inference: given a joint law for random variables X and Y and an observation Y=y, one seeks to sample from the conditional law of X| Y=y. Even when the joint distribution is accurately represented, this task can be computationally difficult as it may require evaluating intractable normalizing constants or solving a new inference problem for each observation. Measure transport provides an approach to this problem by identifying a map with triangular structure that directly pushes forward a reference to the conditional of a joint distribution for any observation. This article reviews the theoretical, methodological, and algorithmic foundations of triangular transports, with the Knothe-Rosenblatt rearrangement as a canonical construction. We discuss methods for estimating triangular maps from finite samples, as well as their use in simulation-based inference and causal inference. While our primary aim is to review existing formulations, we also present new ideas and open questions for conditional sampling using transport.
ER -