# Multi-Scale Generative Modeling with Heat Dissipation Flow Matching

arXiv: https://arxiv.org/abs/2605.19371 · HTML: https://mlsanity.com/paper/2605.19371/

## 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 24 of its 32 references that are in the map.
- First posted on arXiv 19 May 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, 24 of 24)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [GR00T N1: An Open Foundation Model for Generalist Humanoid Robots](https://mlsanity.com/paper/2503.14734/) (2025)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks](https://mlsanity.com/paper/1901.06523/) (2019)
- [Cold Diffusion: Inverting Arbitrary Image Transforms Without Noise](https://mlsanity.com/paper/2208.09392/) (2022)
- [Generative Modelling With Inverse Heat Dissipation](https://mlsanity.com/paper/2206.13397/) (2022)
- [Blurring Diffusion Models](https://mlsanity.com/paper/2209.05557/) (2022)
- [Deconstructing Denoising Diffusion Models for Self-Supervised Learning](https://mlsanity.com/paper/2401.14404/) (2024)
- [Simpler Diffusion (SiD2): 1.5 FID on ImageNet512 with pixel-space diffusion](https://mlsanity.com/paper/2410.19324/) (2024)
- [Diffusion Models in Low-Level Vision: A Survey](https://mlsanity.com/paper/2406.11138/) (2024)
- [Deep Generative Models through the Lens of the Manifold Hypothesis: A Survey and New Connections](https://mlsanity.com/paper/2404.02954/) (2024)
- [f-DM: A Multi-stage Diffusion Model via Progressive Signal Transformation](https://mlsanity.com/paper/2210.04955/) (2022)
- [LayerSync: Self-aligning Intermediate Layers](https://mlsanity.com/paper/2510.12581/) (2025)
- [Beyond Blur: A Fluid Perspective on Generative Diffusion Models](https://mlsanity.com/paper/2506.16827/) (2025)

## Abstract (arXiv)

Diffusion models are widely used in image generation, with most relying on noise-based corruption and denoising. A distinct branch instead uses blur as the main corruption, preserving better color budgets and multi-scale detail by providing multi-scale priors. However, blur-based models remain in SDE-based frameworks and are not integrated into ODE-based frameworks, such as Flow Matching (FM). Meanwhile, in the blur-based formulation, the classical inverse heat-dissipation (IHD) process faces an ill-posed challenge. Moreover, under the data-manifold assumption, regressing blurred images from high-dimensional noise (or velocity) space is also difficult. We propose Heat Dissipation Flow Matching (HDFM), which introduces a continuous blurred (heat-dissipation) process into FM to inject multi-scale priors. HDFM aligns an interpolated heat-dissipation path to address ill-posedness and adopts x-prediction to mitigate high-dimensional regression difficulty. Toy experiments and ablation studies show that HDFM consistently benefits from both blur and x-prediction. The performance of HDFM outperforms most baseline methods on all datasets.