Multi-Bandwidth Distribution Matching Distillation: On the Equivalence of Distribution Matching Distillation and Drifting Models

2026-10-07

AI Summary

This study addresses the unclear theoretical relationship between Distribution Matching Distillation (DMD) and drift models, which has hindered further optimization of one-step generative models. We provide the first rigorous proof establishing the theoretical equivalence between DMD and drift models, formulating a precise mathematical correspondence. Building upon this unified perspective and incorporating force field transformation principles, we propose a multi-bandwidth distribution matching distillation method. This work not only reveals the intrinsic connections between two mainstream generative paradigms, offering a novel theoretical foundation for understanding diffusion model distillation, but also significantly enhances model performance through the proposed approach, achieving high-quality and efficient one-step generation.

Abstract

Researchers are exploring effective one-step generative model continuously, and, Drifting Models (Deng et al., 2026), demonstrate great potential in one-step generation recently. There are works that reveal the connection between Diffusion & Flow Style Generative Models (DFSGMs) (Ho et al., 2020; Song et al., 2020a;b; Lipman et al., 2022; Liu et al., 2022) and Drifting Models (Li & Zhu, 2026; Lai et al., 2026; Turan et al., 2026). But no one has yet established a precise correspondence between the Drifting Model and the widely used distillation method- Distribution Matching Distillation (DMD/DMD2) (Yin et al., 2024b;a) to the best of our knowledge, even though their optimization objective formulas are virtually identical. In this paper, we prove that by converting the velocity-field / noise-field from the pre-trained DFSGMs into the attraction force field in Drifting Models and estimating the repulsion force field from the generative distribution, training the Drifting Model is naturally equivalent to the Distribution Matching Distillation. With this equivalent concept, we propose an improved method based on DMD from the Drifting Model's perspective- Multi-Bandwidth Distribution Matching Distillation (MBDMD).

Problem

• Distribution Matching Distillation
• Drifting Models
• one-step generation
• Diffusion & Flow Style Generative Models

Innovation

• Distribution Matching Distillation
• Drifting Models
• Multi-Bandwidth Distribution Matching Distillation
• One-step Generation
• Diffusion and Flow Style Generative Models