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

arXiv: https://arxiv.org/abs/2610.10989 · HTML: https://mlsanity.com/paper/2610.10989/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 27 references that are in the map.
- First posted on arXiv 7 Oct 2026.

## Builds on (most cited first, 16 of 16)

- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Flow Matching Guide and Code](https://mlsanity.com/paper/2412.06264/) (2024)
- [Generative Modeling via Drifting](https://mlsanity.com/paper/2602.04770/) (2026)
- [SenseFlow: Scaling Distribution Matching for Flow-based Text-to-Image Distillation](https://mlsanity.com/paper/2506.00523/) (2025)
- [Phased DMD: Few-step Distribution Matching Distillation via Score Matching within Subintervals](https://mlsanity.com/paper/2510.27684/) (2025)
- [One-Step Generative Modeling via Wasserstein Gradient Flows](https://mlsanity.com/paper/2605.11755/) (2026)
- [Diversity-Preserved Distribution Matching Distillation for Fast Visual Synthesis](https://mlsanity.com/paper/2602.03139/) (2026)
- [Generative Drifting is Secretly Score Matching: a Spectral and Variational Perspective](https://mlsanity.com/paper/2603.09936/) (2026)
- [Flash-DMD: Towards High-Fidelity Few-Step Image Generation with Efficient Distillation and Joint Reinforcement Learning](https://mlsanity.com/paper/2511.20549/) (2025)
- [A Long-Short Flow-Map Perspective for Drifting Models](https://mlsanity.com/paper/2602.20463/) (2026)
- [Reinforcing Few-step Generators via Reward-Tilted Distribution Matching](https://mlsanity.com/paper/2605.26108/) (2026)
- [1.x-Distill: Breaking the Diversity, Quality, and Efficiency Barrier in Distribution Matching Distillation](https://mlsanity.com/paper/2604.04018/) (2026)
- [Teacher-Feature Drifting: One-Step Diffusion Distillation with Pretrained Diffusion Representations](https://mlsanity.com/paper/2605.07327/) (2026)

## Abstract (arXiv)

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).