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Survey details geometry and stochastic analysis of flow and diffusion models

By PulseAugur Editorial · [1 sources] ·

A new survey paper explores the mathematical underpinnings of flow and diffusion models, which are crucial for learning and sampling high-dimensional probability distributions across various domains like images, proteins, and language. The paper details how these models utilize three distinct geometries: the data's state space, the space of probability measures, and the space of paths generated by the process. It highlights the central role of integration by parts and Malliavin calculus in training these models, extending the analysis to normalizing flows, flow matching, diffusion models, Schrödinger bridges, and stochastic control. AI

IMPACT Provides a foundational mathematical understanding for advanced generative modeling techniques.

RANK_REASON The item is a survey paper detailing mathematical concepts and methods related to generative models. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv stat.ML →

AI-generated summary · Google Gemini · from 1 sources. How we write summaries →

Survey details geometry and stochastic analysis of flow and diffusion models

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The item is a survey paper detailing mathematical concepts and methods related to generative models. [lever_c_demoted from research: ic=1 ai=1.0]
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COVERAGE [1]

  1. arXiv stat.ML TIER_1 English(EN) · Ehsan Mirafzali, Razvan Marinescu ·

    Geometry and Stochastic Analysis of Flow and Diffusion Models: A Survey

    arXiv:2611.12107v1 Announce Type: cross Abstract: Flow-based and diffusion-based models have become the principal means of learning and sampling high-dimensional probability distributions, from images and video to proteins, molecules and physical fields, and increasingly language…

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