# On Conditional Stochastic Interpolation for Generative Nonlinear Sufficient Dimension Reduction

arXiv: https://arxiv.org/abs/2512.18971 · HTML: https://mlsanity.com/paper/2512.18971/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 68 references that are in the map.
- First posted on arXiv 22 Dec 2025.

## Builds on (most cited first, 30 of 35)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Qwen2.5-VL Technical Report](https://mlsanity.com/paper/2502.13923/) (2025)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [A Survey on Hallucination in Large Language Models: Principles, Taxonomy, Challenges, and Open Questions](https://mlsanity.com/paper/2311.05232/) (2023)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [Flow Matching on General Geometries](https://mlsanity.com/paper/2302.03660/) (2023)
- [Diffusion Models are Minimax Optimal Distribution Estimators](https://mlsanity.com/paper/2303.01861/) (2023)
- [Deep Network Approximation Characterized by Number of Neurons](https://mlsanity.com/paper/1906.05497/) (2019)
- [Riemannian Diffusion Models](https://mlsanity.com/paper/2208.07949/) (2022)
- [Generator Matching: Generative modeling with arbitrary Markov processes](https://mlsanity.com/paper/2410.20587/) (2024)
- [Optimal Flow Matching: Learning Straight Trajectories in Just One Step](https://mlsanity.com/paper/2403.13117/) (2024)
- [Fr'echet Regression for Random Objects with Euclidean Predictors](https://mlsanity.com/paper/1608.03012/) (2016)
- [Optimal Approximation Rates for Deep ReLU Neural Networks on Sobolev and Besov Spaces](https://mlsanity.com/paper/2211.14400/) (2022)
- [Llama-Embed-Nemotron-8B: A Universal Text Embedding Model for Multilingual and Cross-Lingual Tasks](https://mlsanity.com/paper/2511.07025/) (2025)
- [Understanding Scaling Laws with Statistical and Approximation Theory for Transformer Neural Networks on Intrinsically Low-dimensional Data](https://mlsanity.com/paper/2411.06646/) (2024)
- [Flow matching achieves almost minimax optimal convergence](https://mlsanity.com/paper/2405.20879/) (2024)
- [Convergence of Continuous Normalizing Flows for Learning Probability Distributions](https://mlsanity.com/paper/2404.00551/) (2024)
- [Lipschitz Singularities in Diffusion Models](https://mlsanity.com/paper/2306.11251/) (2023)
- [Conditional sampling within generative diffusion models](https://mlsanity.com/paper/2409.09650/) (2024)
- [Gaussian Interpolation Flows](https://mlsanity.com/paper/2311.11475/) (2023)
- [Convergence Analysis of Flow Matching in Latent Space with Transformers](https://mlsanity.com/paper/2404.02538/) (2024)
- [Deep Dimension Reduction for Supervised Representation Learning](https://mlsanity.com/paper/2006.05865/) (2020)
- [Tackling the Singularities at the Endpoints of Time Intervals in Diffusion Models](https://mlsanity.com/paper/2403.08381/) (2024)
- [Random Forest Weighted Local Fr'echet Regression with Random Objects](https://mlsanity.com/paper/2202.04912/) (2022)
- [Sufficient dimension reduction for classification using principal optimal transport direction](https://mlsanity.com/paper/2010.09921/) (2020)
- [Conditional Stochastic Interpolation for Generative Learning](https://mlsanity.com/paper/2312.05579/) (2023)
- [Conditional Diffusion Models Based Conditional Independence Testing](https://mlsanity.com/paper/2412.11744/) (2024)

## Built on by (most cited first, 3 of 3)

- [Belted Engression: Sufficient Dimension Reduction for Generative Distributional Regression](https://mlsanity.com/paper/2609.23789/) (2026)
- [FlowSDR: Sufficient Dimension Reduction via Conditional Normalizing Flows](https://mlsanity.com/paper/2606.01346/) (2026)
- [Sufficiently Reduced Distributional Regression](https://mlsanity.com/paper/2609.29291/) (2026)

## Abstract (arXiv)

Identifying low-dimensional sufficient structures in nonlinear sufficient dimension reduction (SDR) has long been a fundamental yet challenging problem. Most existing methods lack theoretical guarantees of exhaustiveness in identifying lower dimensional structures, either at the population level or at the sample level. We tackle this issue by proposing a new method, generative sufficient dimension reduction (GenSDR), which leverages modern generative models. We show that GenSDR is able to fully recover the information contained in the central σ-field at both the population and sample levels. In particular, at the sample level, we establish a consistency property for the GenSDR estimator from the perspective of conditional distributions, capitalizing on the distributional learning capabilities of deep generative models. Moreover, by incorporating an ensemble technique, we extend GenSDR to accommodate scenarios with non-Euclidean responses, thereby substantially broadening its applicability. Extensive numerical results demonstrate the outstanding empirical performance of GenSDR and highlight its strong potential for addressing a wide range of complex, real-world tasks.