# Multimarginal generative modeling with stochastic interpolants

arXiv: https://arxiv.org/abs/2310.03695 · HTML: https://mlsanity.com/paper/2310.03695/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 34 references that are in the map.
- First posted on arXiv 5 Oct 2023.

## Builds on (most cited first, 22 of 22)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [StarGAN v2: Diverse Image Synthesis for Multiple Domains](https://mlsanity.com/paper/1912.01865/) (2019)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [Deep Networks with Stochastic Depth](https://mlsanity.com/paper/1603.09382/) (2016)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Rectified Flow: A Marginal Preserving Approach to Optimal Transport](https://mlsanity.com/paper/2209.14577/) (2022)
- [Fast Computation of Wasserstein Barycenters](https://mlsanity.com/paper/1310.4375/) (2013)
- [On Kinetic Optimal Probability Paths for Generative Models](https://mlsanity.com/paper/2306.06626/) (2023)
- [Multi-marginal optimal transport: theory and applications](https://mlsanity.com/paper/1406.0026/) (2014)
- [Wasserstein barycenters can be computed in polynomial time in fixed dimension](https://mlsanity.com/paper/2006.08012/) (2020)
- [Tree-Based Diffusion Schr"odinger Bridge with Applications to Wasserstein Barycenters](https://mlsanity.com/paper/2305.16557/) (2023)
- [Show, Attend and Translate: Unpaired Multi-Domain Image-to-Image Translation with Visual Attention](https://mlsanity.com/paper/1811.07483/) (2018)

## Built on by (most cited first, 17 of 17)

- [SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformers](https://mlsanity.com/paper/2401.08740/) (2024)
- [Generative Flows on Discrete State-Spaces: Enabling Multimodal Flows with Applications to Protein Co-Design](https://mlsanity.com/paper/2402.04997/) (2024)
- [Any-Order Flexible Length Masked Diffusion](https://mlsanity.com/paper/2509.01025/) (2025)
- [Accelerating Diffusion Models with Parallel Sampling: Inference at Sub-Linear Time Complexity](https://mlsanity.com/paper/2405.15986/) (2024)
- [Flow matching achieves almost minimax optimal convergence](https://mlsanity.com/paper/2405.20879/) (2024)
- [Algorithms for mean-field variational inference via polyhedral optimization in the Wasserstein space](https://mlsanity.com/paper/2312.02849/) (2023)
- [Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approach](https://mlsanity.com/paper/2506.03979/) (2025)
- [Gaussian Interpolation Flows](https://mlsanity.com/paper/2311.11475/) (2023)
- [Multi-Marginal Stochastic Flow Matching for High-Dimensional Snapshot Data at Irregular Time Points](https://mlsanity.com/paper/2508.04351/) (2025)
- [B'ezierFlow: Learning B'ezier Stochastic Interpolant Schedulers for Few-Step Generation](https://mlsanity.com/paper/2512.13255/) (2025)
- [Distribution-Conditioned Transport](https://mlsanity.com/paper/2603.04736/) (2026)
- [Pairwise Optimal Transports for Training All-to-All Flow-Based Condition Transfer Model](https://mlsanity.com/paper/2504.03188/) (2025)
- [Multidimensional Adaptive Coefficient for Inference Trajectory Optimization in Flow and Diffusion](https://mlsanity.com/paper/2404.14161/) (2024)
- [Fast Sampling for Flows and Diffusions with Lazy and Point Mass Stochastic Interpolants](https://mlsanity.com/paper/2602.03789/) (2026)
- [Continuum-marginal optimal transport: a mesh-free kernel method](https://mlsanity.com/paper/2604.24226/) (2026)
- [FLUX: Geometry-Aware Longitudinal Flow Matching with Mixture of Experts](https://mlsanity.com/paper/2605.08648/) (2026)
- [Path-independent Flow Matching for Multi-parameter Generative Dynamics](https://mlsanity.com/paper/2605.13487/) (2026)

## Abstract (arXiv)

Given a set of K probability densities, we consider the multimarginal generative modeling problem of learning a joint distribution that recovers these densities as marginals. The structure of this joint distribution should identify multi-way correspondences among the prescribed marginals. We formalize an approach to this task within a generalization of the stochastic interpolant framework, leading to efficient learning algorithms built upon dynamical transport of measure. Our generative models are defined by velocity and score fields that can be characterized as the minimizers of simple quadratic objectives, and they are defined on a simplex that generalizes the time variable in the usual dynamical transport framework. The resulting transport on the simplex is influenced by all marginals, and we show that multi-way correspondences can be extracted. The identification of such correspondences has applications to style transfer, algorithmic fairness, and data decorruption. In addition, the multimarginal perspective enables an efficient algorithm for reducing the dynamical transport cost in the ordinary two-marginal setting. We demonstrate these capacities with several numerical examples.