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 $O(Λ^{-1}[\ln L+\ln(1/\varepsilon)])$ for RG wavenumber scale $Λ$, 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.