# Generative diffusion model with inverse renormalization group flows

arXiv: https://arxiv.org/abs/2501.09064 · HTML: https://mlsanity.com/paper/2501.09064/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 17 of its 57 references that are in the map.
- First posted on arXiv 15 Jan 2025.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 17 of 17)

- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Cascaded Diffusion Models for High Fidelity Image Generation](https://mlsanity.com/paper/2106.15282/) (2021)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [Diffusion Probabilistic Models for 3D Point Cloud Generation](https://mlsanity.com/paper/2103.01458/) (2021)
- [Simple diffusion: End-to-end diffusion for high resolution images](https://mlsanity.com/paper/2301.11093/) (2023)
- [On the Importance of Noise Scheduling for Diffusion Models](https://mlsanity.com/paper/2301.10972/) (2023)
- [e3nn: Euclidean Neural Networks](https://mlsanity.com/paper/2207.09453/) (2022)
- [On Fast Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2106.00132/) (2021)
- [Generative Modelling With Inverse Heat Dissipation](https://mlsanity.com/paper/2206.13397/) (2022)
- [Blurring Diffusion Models](https://mlsanity.com/paper/2209.05557/) (2022)
- [EigenFold: Generative Protein Structure Prediction with Diffusion Models](https://mlsanity.com/paper/2304.02198/) (2023)
- [State-specific protein-ligand complex structure prediction with a multi-scale deep generative model](https://mlsanity.com/paper/2209.15171/) (2022)

## Built on by (most cited first, 10 of 10)

- [Performance of machine-learning-assisted Monte Carlo in sampling from simple statistical physics models](https://mlsanity.com/paper/2505.22598/) (2025)
- [Demonstrating Real Advantage of Machine-Learning-Enhanced Monte Carlo for Combinatorial Optimization](https://mlsanity.com/paper/2510.19544/) (2025)
- [Dreaming up scale invariance via inverse renormalization group](https://mlsanity.com/paper/2506.04016/) (2025)
- [The critical slowing down in training diffusion models](https://mlsanity.com/paper/2605.12597/) (2026)
- [Everything at Every Scale: Scale-Invariant Diffusion with Continuous Super-Resolution](https://mlsanity.com/paper/2605.26032/) (2026)
- [Interpreting the Synchronization Gap: The Hidden Mechanism Inside Diffusion Transformers](https://mlsanity.com/paper/2603.20987/) (2026)
- [Flicker-DDPM: Accelerating Denoising Diffusion via 1/f Colored Noise Injection](https://mlsanity.com/paper/2606.03393/) (2026)
- [Renormalization Group Flow Matching for Scalable Local Generative Modeling](https://mlsanity.com/paper/2608.23696/) (2026)
- [Neural Renormalization Group Flow for Percolation](https://mlsanity.com/paper/2608.26764/) (2026)
- [Generative Modeling of Stochastic Dynamics for Long-Time Evolution](https://mlsanity.com/paper/2610.00546/) (2026)

## Abstract (arXiv)

Diffusion models represent a class of generative models that produce data by denoising a sample corrupted by white noise. Despite the success of diffusion models in computer vision, audio synthesis, and point cloud generation, so far they overlook inherent multiscale structures in data and have a slow generation process due to many iteration steps. In physics, the renormalization group offers a fundamental framework for linking different scales and giving an accurate coarse-grained model. Here we introduce a renormalization group-based diffusion model that leverages multiscale nature of data distributions for realizing a high-quality data generation. In the spirit of renormalization group procedures, we define a flow equation that progressively erases data information from fine-scale details to coarse-grained structures. Through reversing the renormalization group flows, our model is able to generate high-quality samples in a coarse-to-fine manner. We validate the versatility of the model through applications to protein structure prediction and image generation. Our model consistently outperforms conventional diffusion models across standard evaluation metrics, enhancing sample quality and/or accelerating sampling speed by an order of magnitude. The proposed method alleviates the need for data-dependent tuning of hyperparameters in the generative diffusion models, showing promise for systematically increasing sample efficiency based on the concept of the renormalization group.