Multi-Scale Generative Modeling with Heat Dissipation Flow Matching

2026-05-19

AI Summary

This work addresses key limitations of existing fuzzy-based generative models, which are largely confined to stochastic differential equation (SDE) frameworks and struggle to integrate ordinary differential equation (ODE)-based approaches such as flow matching. These models also face ill-posed inverse thermal diffusion processes and high-dimensional regression challenges. To overcome these issues, the paper introduces Heat Diffusion Flow Matching (HDFM), the first method to incorporate continuous thermal diffusion into the flow matching framework. HDFM mitigates ill-posedness by interpolating thermal diffusion trajectories and reduces regression complexity through an x-prediction strategy, effectively injecting multi-scale priors. Experiments demonstrate that HDFM outperforms state-of-the-art baselines across multiple datasets, and ablation studies confirm the efficacy of the proposed fuzzy modeling and x-prediction mechanism.

Abstract

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.

Problem

• blur-based generative modeling
• ill-posed inverse heat-dissipation
• high-dimensional regression
• flow matching
• multi-scale priors

Innovation

• Heat Dissipation Flow Matching
• blur-based generative modeling
• multi-scale priors
• x-prediction
• Flow Matching