Learning Domain Trajectories with Flow Matching for Gradual Domain Adaptation

Yubo Huang; Yushe Cao; Zixi Wang; Jingzehua Xu; Xin Lai; Xiongyu Hu; Shuai Zhang

cs.LGOct 22, 2026

Learning Domain Trajectories with Flow Matching for Gradual Domain Adaptation

Authors: Yubo Huang, Yushe Cao, Zixi Wang, Jingzehua Xu, Xin Lai, Xiongyu Hu, Shuai Zhang

Organizations: Key Laboratory of Transportation Tunnel Engineering, Ministry of Education, Southwest Jiaotong University, Chengdu, China · Tsinghua University, Beijing, China · School of Information and Software Engineering, University of Electronic Science and Technology of China, Chengdu, China · Department of Mechanical Engineering, The University of Hong Kong, Hong Kong, China ·

Abstract

Large distribution shifts remain a primary obstacle for domain generalization and unsupervised adaptation. Although gradual domain adaptation alleviates this difficulty by introducing ordered intermediate domains, most existing approaches still operate in a discrete, step-wise manner, which can accumulate errors and often relies on unstable Min--Max optimization. We propose FlowGDA, a flow-matching framework that models gradual adaptation as continuous transport on a statistical manifold in a representation space. FlowGDA learns time-dependent velocity fields that induce smooth domain trajectories, using a simulation-free regression objective rather than adversarial training. To prevent semantic drift, we couple left-to-right transport between consecutive domains with a source-anchored transport and a semantic consistency loss, and we further stabilize learning via a two-stage sequential optimization scheme. Extensive experiments demonstrate that our method outperforms state-of-the-art techniques, validating flow matching as an effective alternative for domain adaptation.

Figures & tables

Figure 1: Motivation of gradual domain adaptation under large distribution shifts. Gradual domain adaptation introduces intermediate domains to form a smooth transition path, reducing the discrepancy between consecutive domains and facilitating stable knowledge transfer.

Figure 2: Domain evolution on a statistical manifold. Discrete steps can accumulate errors, while the continuous flow $u_{\theta}(z,t)$ transports $\mathcal{D}_{s}$ toward $\mathcal{D}_{t}$ .

Figure 3: Overview of FlowGDA. FlowGDA models gradual domain transport with source-to-left and left-to-right velocity fields, enforces semantic consistency using a fixed source classifier, and trains sequentially over domain pairs with curriculum-based two-stage optimization.

Category	Method	Rotated MNIST	Color-Shift MNIST	Portraits	Cover Type
UDA	DANN [ 10 ]	44.2	56.5	73.8	N/A
	DeepCORAL [ 30 ]	49.6	63.5	71.9	N/A
	DeepJDOT [ 20 ]	51.6	65.8	72.5	N/A
Gradual	GST [ 16 ]	83.8	74.0	82.6	73.5
	GOAT [ 14 ]	86.4	91.8	83.6	69.9
	AST [ 29 ]	90.6	N/A	84.8	N/A

Table 1: Target-domain accuracy (%) on four GDA benchmarks; ”N/A” means not reported.

Panel of Figure 4 — Figure 4: Rotated MNIST sensitivity to intermediate-domain choice. (a) Accuracy vs. intermediate rotation (mean $\pm$ std over five runs). (b) Removing the intermediate domain causes the largest degradation.

Variant	Rotated MNIST	Color-Shift MNIST	Portraits	Cover Type	Avg. $\Delta$ (pp)
FlowGDA (full)	97.0	99.2	87.6	76.1	–
Single flow	95.5 ( $-1.5$ )	98.0 ( $-1.2$ )	85.6 ( $-2.0$ )	73.6 ( $-2.5$ )	$-1.8$
w/o semantic loss $\mathcal{L}_{cls}$	95.0 ( $-2.0$ )	97.6 ( $-1.6$ )	84.8 ( $-2.8$ )	73.3 ( $-2.8$ )	$-2.3$
Time-only velocity	95.8 ( $-1.2$ )	98.2 ( $-1.0$ )	85.7 ( $-1.9$ )	74.2 ( $-1.9$ )	$-1.5$
Joint optimization	96.3 ( $-0.7$ )	98.6 ( $-0.6$ )	86.5 ( $-1.1$ )	74.9 ( $-1.2$ )	$-0.9$

Table 2: Dataset-wise ablation study: target accuracy (%) with drops from full FlowGDA in parentheses.

Appendix figures & tables5 assets

Supplementary material from the paper’s appendix.

Appendix

Panel of Figure 5 — Figure 5: Effect of intermediate-domain quality on Rotated MNIST. Accuracy is reported as mean $\pm$ std over five runs.

Dataset	0 domains	1 domain	2 domains	4 domains	6 domains
Rotated MNIST	92.6	95.1	96.5	96.8	97.0
Color-Shift MNIST	94.7	97.9	99.1	99.2	99.2
Portraits	80.9	83.2	85.1	86.4	87.6
Cover Type	71.6	69.2	74.7	75.5	76.1

Appendix

Table 3: Effect of the number of intermediate domains. Values denote target-domain accuracy (%).

Ordering	Rotated MNIST	Color-Shift MNIST	Portraits	Cover Type
Ordered trajectory	97.0	99.2	87.6	76.1
Local shuffle	95.6	98.0	85.4	74.0
Random permutation	92.8	94.7	81.7	70.5
Reversed order	90.7	92.6	79.8	69.2

Appendix

Table 4: Robustness to domain ordering. Values denote target-domain accuracy (%).

Schedule	Early pairs	Middle pairs	Late pairs	Portraits	Cover Type
Full FlowGDA	Train	Train	Train	87.6	76.1
Skip early pairs	Skip	Train	Train	83.1	71.8
Skip middle pairs	Train	Skip	Train	85.2	73.6
Skip late pairs	Train	Train	Skip	86.1	74.9
Only early pairs	Train	Skip	Skip	84.7	72.6
Only late pairs	Skip	Skip	Train	81.4	70.7

Appendix

Table 5: Impact of early, middle, and late transport steps. “Train” means velocity fields are optimized for the corresponding block, while “Skip” means identity transport is used. Values denote target-domain accuracy (%).

Factor	Setting	Accuracy
$\lambda_{cls}$	0	84.8
	$10^{-2}$	86.3
	0.05	87.2
	0.1	87.6
	0.2	87.1
	0.5	86.0

Appendix

Table 6: Hyperparameter sensitivity on Portraits. Values denote target-domain accuracy (%).

Domain Adaptation

Domain adaptation transfers machine-learning models across changing data distributions, often using unlabeled or limited target-domain examples.

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Open paper AskPDF arXiv

Training fast generators on new domains with limited data remains challenging for two reasons. First, adapting a pretrained diffusion or flow model to a new domain leaves its costly multi-step sampling unaddressed, and existing acceleration methods are tied to the source parameterization--

ε

x

v

, or

u

--leaving heterogeneous pretrained models with no common acceleration target. Second, while adversarial refinement is proven effective for few-step quality, it is formulated only for instantaneous-velocity flows, not for the finite-interval average velocities that MeanFlow (MF) models predict. We address both problems. We propose MeanFlow-Transfer, which maps heterogeneous source outputs into a shared velocity representation, uses it to initialize an MF generator from the source weights, and optimizes an MF objective on the target domain. This unifies adaptation and acceleration in a single training loop across a broad range of pretrained models. We then introduce Continuous Adversarial MeanFlow, a post-training stage that extends continuous adversarial flow models from instantaneous velocities to MF's finite-interval average velocities. CAMF contrasts changes in a learned potential between real and predicted interval endpoints, recovering fine detail that MF regression averages away, and reduces to the instantaneous criterion in the vanishing-interval limit. Adapting four ImageNet-based source models--DiT (

ε

), SiT (

v

), JiT (

x

), iMF (

u

)--to five target domains, MF-T with CAMF matches or exceeds the fine-tuned teacher in FID and FDD at up to

125\times

fewer Neural Function Evaluations (NFEs), while CAMF improves MF-T's few-step FID by

29\%

on average.

Abstract

Domain Adaptation

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