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

Jialin Zhu; Xing Liu; Feixiang He; He Wang

cs.LGOct 7, 2026

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

Authors: Jialin Zhu, Xing Liu, Feixiang He, He Wang

Organizations: Baidu Inc., China · Central South University, China · AI Centre, University College London, UK

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).

Figures & tables

Method	Signal Scale ( $\alpha_{t}$ )	Noise Scale ( $\sigma_{t}$ )
Flow Matching	$t$	$1-t$
VP Diffusion	$\alpha_{t}\in[0,1]$	$\sqrt{1-\alpha_{t}^{2}}$
VE Diffusion	$1$	$\sigma_{t}\in[0,\sigma_{\max}]$

Table 1: Comparison of noise perturbation schedules across different generative frameworks.

Method	steps	FID ( $\downarrow$ )
DMD	328k	2.7238
DMD	410k	2.6432
MBDMD	328k	2.5728
MBDMD	410k	2.4697

Table 2 : Comparison of FID of MBDMD and vanilla DMD.

Method	$K$	Sampling	Best FID ( $\downarrow$ )	Iso-FLOP best FID ( $\downarrow$ )
DMD	1	N/A	2.6432	2.6432
DMD	3	i.i.d	2.5274	2.5702
MBDMD	3	strat	2.4697	2.5680
MBDMD	5	strat	2.4819	2.5109

Table 3 : Comparison of FIDs with different

K

and sampling method of MBDMD and vanilla DMD.

Method	Seg 1 avg. FID ( $\downarrow$ )	Seg 2 avg. FID ( $\downarrow$ )	Seg 3 avg. FID ( $\downarrow$ )	Seg 4 avg. FID ( $\downarrow$ )	Seg 5 avg. FID ( $\downarrow$ )	Seg 6 avg. FID ( $\downarrow$ )	Seg 7 avg. FID ( $\downarrow$ )	Seg 8 avg. FID ( $\downarrow$ )
MBDMD $K=3$	25.531	4.285	3.644	3.378	3.244	3.110	3.124	3.036
MBDMD $K=5$	27.350	4.405	3.652	3.421	3.215	3.141	3.114	3.055
MBDMD $K=7$	29.064	4.517	3.744	3.433	3.225	3.200	3.096	3.063

Table 4 : Comparison of mean FIDs in every sub-interval of MBDMD with different

K

Method	steps	FID ( $\downarrow$ )
DMD	157k	1.5643
DMD	200k	1.5518
MBDMD	157k	1.5304
MBDMD	200k	1.5304

Table 5 : Comparison of FID of MBDMD and vanilla DMD with GAN loss.

Method	Fwd Pass ( $\downarrow$ )	FID ( $\downarrow$ )	Patch FID ( $\downarrow$ )	Clip ( $\uparrow$ )
DMD2	1	19.01	26.98	0.336
MBDMD	1	18.81	26.86	0.335

Table 6 : Comparison of FID of MBDMD and vanilla DMD.

Appendix figures & tables1 asset

Supplementary material from the paper’s appendix.

Appendix

Figure 1 : A 2D toy experiments to show that Fake Score Model can be replaced by the repulsion kernel function calculation. In this figure, (a) is the ground-truth; (b) is the results generated by pure kernel calculation for both attraction and repulsion; (c) shows the result by transferring velocity from pretrained Flow Matching Model to calculate attraction force and use kernel calculation for repulsion; (d) is the result from DMD which using velocity from pretrained Flow Matching Model to calculate attraction force and using a online updating Fake Score Model to calculate repulsion force.

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Iterative generative models such as Flow Matching and Diffusion models have demonstrated strong test-time scaling behavior, where additional inference computation can improve generation quality. In contrast, Drift Models offer efficient one-step generation, but their direct generation paradigm limits such flexibility. In this work, we propose Drift Flow Matching (DFM), a framework that connects drifting generative modeling with flow-based iterative generation. DFM preserves the efficiency of direct transport maps while enabling generation to be refined through multiple inference steps when desired. This bridges the gap between one-step Drift Models and multi-step Flow Matching methods, and provides a novel generative paradigm that can adapt sampling computation to different quality--efficiency requirements. Extensive experiments across different tasks and datasets demonstrate the effectiveness and generality of the proposed framework.

Abstract

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