# Generative models for decision-making under distributional shift

arXiv: https://arxiv.org/abs/2604.04342 · HTML: https://mlsanity.com/paper/2604.04342/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 51 of its 71 references that are in the map.
- First posted on arXiv 6 Apr 2026.

## Builds on (most cited first, 30 of 51)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [Invertible Residual Networks](https://mlsanity.com/paper/1811.00995/) (2018)
- [Certifying Some Distributional Robustness with Principled Adversarial Training](https://mlsanity.com/paper/1710.10571/) (2017)
- [Flow Matching Guide and Code](https://mlsanity.com/paper/2412.06264/) (2024)
- [Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations](https://mlsanity.com/paper/1505.05116/) (2015)
- [Rectified Flow: A Marginal Preserving Approach to Optimal Transport](https://mlsanity.com/paper/2209.14577/) (2022)
- [Joint Distribution Optimal Transportation for Domain Adaptation](https://mlsanity.com/paper/1705.08848/) (2017)
- [On Gradient Descent Ascent for Nonconvex-Concave Minimax Problems](https://mlsanity.com/paper/1906.00331/) (2019)
- [Analyzing Inverse Problems with Invertible Neural Networks](https://mlsanity.com/paper/1808.04730/) (2018)
- [Optimal transport mapping via input convex neural networks](https://mlsanity.com/paper/1908.10962/) (2019)
- [Distributionally Robust Stochastic Optimization with Wasserstein Distance](https://mlsanity.com/paper/1604.02199/) (2016)

## Built on by (most cited first, 4 of 4)

- [Decision-Focused Learning: When and Why Traditional Prediction Models Fail](https://mlsanity.com/paper/2606.21773/) (2026)
- [LLM-Powered Virtual Population for Demand Simulation and Pricing](https://mlsanity.com/paper/2606.16183/) (2026)
- [OutageDiT: A Generative Foundation Model for Power Outage Forecasting and Scenario Simulation](https://mlsanity.com/paper/2609.01896/) (2026)
- [Robustness of Diffusion Models under Distribution Shift](https://mlsanity.com/paper/2609.27546/) (2026)

## Abstract (arXiv)

Many data-driven decision problems are formulated using a nominal distribution estimated from historical data, while performance is ultimately determined by a deployment distribution that may be shifted, context-dependent, partially observed, or stress-induced. This tutorial presents modern generative models, particularly flow- and score-based methods, as mathematical tools for constructing decision-relevant distributions. From an operations research perspective, their primary value lies not in unconstrained sample synthesis but in representing and transforming distributions through transport maps, velocity fields, score fields, and guided stochastic dynamics. We present a unified framework based on pushforward maps, continuity, Fokker-Planck equations, Wasserstein geometry, and optimization in probability space. Within this framework, generative models can be used to learn nominal uncertainty, construct stressed or least-favorable distributions for robustness, and produce conditional or posterior distributions under side information and partial observation. We also highlight representative theoretical guarantees, including forward-reverse convergence for iterative flow models, first-order minimax analysis in transport-map space, and error-transfer bounds for posterior sampling with generative priors. The tutorial provides a principled introduction to using generative models for scenario generation, robust decision-making, uncertainty quantification, and related problems under distributional shift.