{"slug": "renormalization-group-flow-matching-for-scalable-local-generative-modeling", "title": "Renormalization Group Flow Matching for Scalable Local Generative Modeling", "summary": "Researchers introduced renormalization group flow matching (RGFM), a generative framework that structures data generation across spatial scales using an exact renormalization group flow as the probability path, enabling local computation with near-linear scaling while preserving long-range correlations. The method, demonstrated on FFHQ images at 64x64 and 256x256 resolutions, produced more coherent and higher-quality samples than conventional local flow matching, with theoretical guarantees that the probability flow can be approximated by local velocity fields over a range O(Λ⁻¹[ln L + ln(1/ε)]) for RG wavenumber scale Λ, linear system size L, and error tolerance ε.", "body_md": "arXiv:2608.23696v1 Announce Type: new\nAbstract: 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.", "url": "https://wpnews.pro/news/renormalization-group-flow-matching-for-scalable-local-generative-modeling", "canonical_source": "https://arxiv.org/abs/2608.23696", "published_at": "2026-08-26 04:00:00+00:00", "updated_at": "2026-08-26 04:12:51.396538+00:00", "lang": "en", "topics": ["machine-learning", "generative-ai"], "entities": ["arXiv", "FFHQ"], "alternates": {"html": "https://wpnews.pro/news/renormalization-group-flow-matching-for-scalable-local-generative-modeling", "markdown": "https://wpnews.pro/news/renormalization-group-flow-matching-for-scalable-local-generative-modeling.md", "text": "https://wpnews.pro/news/renormalization-group-flow-matching-for-scalable-local-generative-modeling.txt", "jsonld": "https://wpnews.pro/news/renormalization-group-flow-matching-for-scalable-local-generative-modeling.jsonld"}}