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New arXiv papers explore flow matching and optimal transport in generative models

By PulseAugur Editorial · [4 sources] ·

Two new arXiv papers delve into advanced generative modeling techniques. The first paper, "Notes on generative modeling: flow matching, diffusion, optimal transport and Schrödinger bridge" by Titouan Vayer, explores the mathematical principles connecting optimal transport with methods like Schrödinger bridge and flow matching. The second paper, "Robustness and Structure Preservation in Flow-Based Generative Models via Wasserstein Path-Space Divergences" by Ziyu Chen, introduces a novel Wasserstein path-space divergence to bound the distance between terminal distributions, offering robustness and generalization bounds for score-based generative models and flow matching. AI

IMPACT These papers advance the theoretical understanding of generative models, potentially leading to more robust and efficient AI systems.

RANK_REASON Two academic papers published on arXiv detailing advancements in generative modeling techniques.

Read on arXiv cs.AI →

AI-generated summary · Google Gemini · from 4 sources. How we write summaries →

New arXiv papers explore flow matching and optimal transport in generative models

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COVERAGE [4]

  1. arXiv cs.AI TIER_1 English(EN) · Jan Tauberschmidt, Sophie Fellenz, Sebastian J. Vollmer, Andrew B. Duncan ·

    Physics-Constrained Fine-Tuning of Flow-Matching Models for Generation and Inverse Problems

    arXiv:2508.09156v3 Announce Type: replace-cross Abstract: We present a framework for fine-tuning flow-matching generative models to enforce physical constraints and solve inverse problems in scientific systems. Starting from a model trained on low-fidelity or observational data, …

  2. arXiv stat.ML TIER_1 English(EN) · Titouan Vayer (COMPACT) ·

    Notes on generative modeling: flow matching, diffusion, optimal transport and Schr{\"o}dinger bridge

    arXiv:2606.30053v1 Announce Type: new Abstract: These notes recapitulate the high level mathematical principles behind different techniques for generative modeling. I show the connections between optimal transport and standard techniques such as Schr{\"o}dinger bridge and flow ma…

  3. arXiv stat.ML TIER_1 English(EN) · Ziyu Chen, Markos A. Katsoulakis, Benjamin J. Zhang ·

    Robustness and Structure Preservation in Flow-Based Generative Models via Wasserstein Path-Space Divergences

    arXiv:2410.01244v2 Announce Type: replace Abstract: We introduce a novel Wasserstein-1 ($W_1$) path-space divergence for stochastic and deterministic dynamics and establish a Wasserstein Uncertainty Propagation (WUP) theorem that bounds the $W_1$ distance between terminal distrib…

  4. arXiv stat.ML TIER_1 English(EN) · Titouan Vayer ·

    Notes on generative modeling: flow matching, diffusion, optimal transport and Schr{ö}dinger bridge

    These notes recapitulate the high level mathematical principles behind different techniques for generative modeling. I show the connections between optimal transport and standard techniques such as Schr{ö}dinger bridge and flow matching.

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