# Renormalization Group Flow Matching for Scalable Local Generative Modeling

arXiv: https://arxiv.org/abs/2608.23696 · HTML: https://mlsanity.com/paper/2608.23696/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 66 of its 127 references that are in the map.
- First posted on arXiv 24 Aug 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 30 of 66)

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- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
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- [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)
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- [Make-An-Audio: Text-To-Audio Generation with Prompt-Enhanced Diffusion Models](https://mlsanity.com/paper/2301.12661/) (2023)
- [Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equations](https://mlsanity.com/paper/2202.02514/) (2022)
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- [A Survey on Generative Diffusion Model](https://mlsanity.com/paper/2209.02646/) (2022)

## Abstract (arXiv)

Despite their remarkable success in modeling complex data, generative models face a fundamental tradeoff. Global approaches can capture full structural coherence but suffer from high computational costs, while local models are efficient but often fail to reproduce long-range correlations and global coherence. The renormalization group (RG) bridges this gap by seamlessly connecting spatial structures across different length scales, retaining quasi-local descriptions at each step while preserving long-range correlations. We introduce renormalization group flow matching (RGFM), a generative framework that systematically structures data generation across different spatial scales. By using an exact RG flow as the probability path, RGFM progressively generates data from long- to short-wavelength structures. To reconcile scalability with global structure, we exploit two key properties of the RG: quasi-locality and scale separation. We rigorously show that the RGFM probability flow can be accurately approximated by local velocity fields acting over a spatial range O(Lambda-1[ln L+ln(1/varepsilon)]) for RG wavenumber scale Lambda, linear system size L, and prescribed error tolerance varepsilon. This property enables local generative modeling with patches of size O(ln L) and a computational cost that scales nearly linearly with the system volume. We numerically demonstrate that local RGFM reproduces long-range correlations far beyond its receptive field in representative one-dimensional distributions, while conventional local flow matching exhibits substantial errors at long distances. On FFHQ images, RGFM yields far more coherent and higher-quality samples than local flow matching at 64x64 and 256x256. Our results establish RG-guided probability flows as a promising route toward scalable generative modeling that captures long-range structure using only local computation.