VDOT++: Unified Few-Step Video Generation via Unbalanced Optimal Transport Distillation

Yutong Wang; Xingtong Ge; Enhuai Liu; Yunke Wang; Tianfan Xue; Yu Qiao; Yaohui Wang; Xinyuan Chen

cs.CVOct 2, 2026

VDOT++: Unified Few-Step Video Generation via Unbalanced Optimal Transport Distillation

Authors: Yutong Wang, Xingtong Ge, Enhuai Liu, Yunke Wang, Tianfan Xue, Yu Qiao, Yaohui Wang, Xinyuan Chen,

Organizations: University of Sydney · Hong Kong University of Science and Technology · Shanghai AI Laboratory · Chinese University of Hong Kong

Abstract

Video creation spans text-to-video (T2V), image-to-video (I2V), and condition-based generation, yet video diffusion models remain costly because they repeatedly evaluate large backbones during sampling. Distribution matching distillation (DMD) reduces this cost, but its reverse Kullback--Leibler (KL) objective can provide unstable or incomplete guidance when the student and teacher distributions have limited overlap. VDOT addressed this issue by adding optimal transport distillation (OTD), whose explicit coupling supplies geometric directions for condition-based generation. Balanced OTD, however, performs full-mass matching between the spatial tokens of each corresponding student--teacher frame pair. This assumption weakens for T2V and I2V, where one condition admits many valid outputs and spatial content need not align across different realizations. We present VDOT++, a unified distillation framework that applies the same training recipe separately to generators for the three task families. It makes OTD robust to output diversity through an asymmetric unbalanced formulation that allows unreliable student tokens to carry less mass while maintaining coverage of the teacher tokens. An $\ell_1$ ground cost further replaces mean-based aggregation with a more mode-preserving weighted median that limits the influence of distant transport targets. The two changes respectively determine whom to match and how the selected targets should be aggregated. We additionally combine distribution matching and adversarial refinement through sequential backward passes, and exploit the decoupled score networks for cross-scale distillation, where larger score networks improve a compact generator. Experiments on UVCBench, VBench, VBench-I2V, and the VACE benchmark show that the resulting four-step generators are competitive with many-step teachers and strong few-step baselines across all three task families.

Figures & tables

Fig. 1 : Reverse-KL failure modes and the role of OT. When the student and teacher distributions are initially separated, reverse KL can neglect uncovered teacher modes or produce unstable gradients on unsupported student samples. An OT coupling supplies explicit transport directions that guide the student toward the teacher support. Adapted from the conference version [ 5 ] .

Fig. 2 : Symmetric versus asymmetric unbalanced OT. Under balanced OT, the hard student marginal gives $r_{i}/u_{i}=1$ for every token, producing a uniformly yellow map that cannot distinguish reliable from unreliable student tokens. With the frames, latent features, and ground costs fixed, symmetric UOT relaxes both marginals using $(\tau_{s},\tau_{t})=(0.1,0.1)$ (left), whereas our asymmetric variant uses $(\tau_{s},\tau_{t})=(0.1,10)$ (right) to relax the student side while preserving teacher coverage. Colored anchors and lines connect selected teacher tokens to their mass-weighted student matches under $\bm{T}^{*}$ . The heat maps show relative student-token mass $r_{i}/u_{i}$ , where $r_{i}=\sum_{j}T^{*}_{ij}$ : red, yellow, and green indicate suppressed, near-uniform, and emphasized mass, and red contours mark $r_{i}/u_{i}<0.5$ . Asymmetric relaxation preserves teacher coverage while selectively downweighting unreliable student regions.

Fig. 3 : Overview of VDOT++ . Top: Given the conditioning signal, the few-step generator is jointly optimized by the DMD score-difference loss, frame-wise optimal-transport matching, and an adversarial loss through two sequential backward passes followed by one optimizer step. Bottom: The OT diagrams show one paired temporal frame. For clarity, the diffusion-time and frame indices $(t,q)$ are omitted. DMD provides a score-difference signal at corresponding spatiotemporal coordinates; balanced OTD explicitly couples spatial tokens within each paired frame but enforces rigid full-mass matching; and symmetric UOT relaxes both marginals. Our asymmetric UOT instead uses a loose student-side penalty and a tight teacher-side penalty, selectively suppressing unreliable student-token mass while retaining coverage of teacher tokens.

Symbol	Meaning
$G_{\theta}$ ; $F_{\psi},F_{\phi}$	generator; teacher and fake score networks
$p_{\mathrm{fake}},p_{\mathrm{real}}$	student and teacher video distributions
$\bm{A}_{t,q},\bm{B}_{t,q}$	spatial-token sets in temporal frame $q$ at diffusion time $t$
$\bm{u},\bm{\mu}$	prescribed student and teacher marginals
$\bm{C}$	pairwise ground-cost matrix
$\bm{T}_{t,q},\bm{T}^{*}_{t,q}$	within-frame transport plan and its optimum

TABLE I : Core notation. The complete list is in Appendix A .

Panel of Table 5 — TABLE II : Quantitative comparison on representative single-condition tasks of UVCBench . We bold the best results and underline the second-best results .

Panel of Table 6 — TABLE III : Quantitative evaluations on VBench (T2V) . We compare VDOT++ with the many-step teacher and few-step baselines. We bold the best results and underline the second-best results .

Panel of Table 7 — TABLE IV : Quantitative evaluations on VBench-I2V . We compare VDOT++ with the many-step teacher and few-step baselines. We bold the best results and underline the second-best results .

Fig. 4 : Qualitative comparison on controllable video generation. We compare the 100-NFE VACE teacher with 4-NFE VDOT and VDOT++ on (a) flow-conditioned video-to-video generation, (b) video outpainting, and (c) multi-reference image-to-video generation. The top row shows the input conditions, and each method row shows frames at 0, 2.5, and 5 seconds.

Fig. 5 : Qualitative comparison on text-to-video generation. Each row shows the first, middle, and last frames of the generated video. Zoom in for more details.

Fig. 6 : Qualitative comparison on image-to-video generation. Each row shows the first, middle, and last frames of the generated video. Zoom in for more details.

Matching	Cost	VACE (strong) $\uparrow$	T2V (loose) $\uparrow$
Balanced	$\ell_{2}$	78.31	77.62
Balanced	$\ell_{1}$	78.08	80.41
Partial	$\ell_{2}$	78.11	79.47
Partial	$\ell_{1}$ (ours)	78.56	81.59

TABLE V : Controlled objective factorial with adversarial refinement : matching (balanced vs. partial)

\times

cost (

\ell_{2}

vs.

\ell_{1}

), evaluated on the strongly-conditioned VACE tasks and the loosely-conditioned T2V (UVCBench and VBench normalized average).

Fig. 7 : Qualitative ablation of matching and ground cost on T2V. Balanced and partial matching are compared with squared- $\ell_{2}$ and $\ell_{1}$ costs for the panda-on-a-surfboard prompt shown below the panels. Each variant shows three sampled frames from left to right. The example complements the controlled factorial in Table V .

Relaxation	$(\tau_{s},\tau_{t})$	Dynamic $\uparrow$	Imaging $\uparrow$	Avg. $\uparrow$
Balanced	$(\infty,\infty)$	45.84	70.73	80.41
Symmetric	$(0.1,0.1)$	29.75	72.95	78.26
Target relaxed	$(10,0.1)$	35.89	69.49	77.84
Source relaxed (ours)	$(0.1,10)$	54.91	72.83	81.59

TABLE VI : Effect of marginal-relaxation direction on T2V under the controlled protocol of Table V .

\tau_{s}

and

\tau_{t}

penalize deviations from the student and teacher marginals, respectively. Dynamic Degree measures motion freedom, while Imaging Quality measures visual degradation.

Fig. 8 : Qualitative ablation of marginal-relaxation direction. Three sampled frames are shown for each T2V variant under the library prompt. The settings are balanced OT, symmetric relaxation $(\tau_{s},\tau_{t})=(0.1,0.1)$ , target-side relaxation $(10,0.1)$ , and source-side relaxation $(0.1,10)$ , corresponding to Table VI .

	VACE		T2V
Training	Imaging $\uparrow$	Aesthetic $\uparrow$	Imaging $\uparrow$	Aesthetic $\uparrow$
No GAN	64.56	61.99	69.80	70.25
Alternating	65.59	62.71	69.85	68.44
Joint (ours)	65.76	62.02	72.83	69.14

TABLE VII : Effect of adversarial refinement and its update schedule on VACE and T2V. We report Imaging Quality and Aesthetic Quality, the two dimensions most directly targeted by adversarial refinement.

Method	Generator	Scores	#NFE $\downarrow$	VBench Avg. $\uparrow$
Wan2.1 (teacher)	14B	–	50 $\times$ 2	77.70
Wan2.1 (original)	1.3B	–	50 $\times$ 2	76.70
DMD2	1.3B	1.3B	4	77.87
DMD2	1.3B	14B	4	78.15
VDOT ++	1.3B	1.3B	4	79.98
VDOT ++ (Ours)	1.3B	14B	4	80.51

TABLE VIII : Same-scale and cross-scale distillation on T2V, evaluated by the VBench normalized average.

Fig. 9 : Qualitative comparison of same-scale and cross-scale distillation on T2V. The top row shows the original Wan2.1 models; the middle and bottom rows show the DMD2 baseline and VDOT++ , respectively. In distilled variants, $A\!\rightarrow\!B$ denotes the score-network and generator sizes: all generators are 1.3B, with 1.3B scores on the left and 14B scores on the right. Each variant shows three sampled frames for the guitar-playing prompt below the panels.

Appendix figures & tables4 assets

Supplementary material from the paper’s appendix.

Appendix

Symbol	Meaning
Networks and generation
$G_{\theta}$	few-step generator (deployed at inference)
$F_{\psi}$ / $F_{\phi}$	frozen teacher (real) / trainable fake score network
$D_{\omega}$	discriminator head embedded in $F_{\phi}$
$\bm{z}$ , $\bm{\xi}$	generator-input noise; re-noising noise
$\bm{c}$	heterogeneous generation condition

Appendix

TABLE IX : Main notation used throughout the paper.

Panel of Table 19 — TABLE X : Additional single-condition results on UVCBench . We bold the best results and underline the second-best results .

Panel of Table 20 — TABLE XI : Quantitative evaluations of composite tasks on UVCBench . We compare the automated score metrics of our VDOT with VACE on the dimensions of video quality and video consistency.

Panel of Table 21 — TABLE XII : Quantitative evaluations on VACE-Benchmark . We compare the automated score metrics of our VDOT++ with VACE on the dimensions of video quality and video consistency.

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Few-step distillation for video diffusion models has attracted significant attention, driven by the urgent demand for efficient deployment in real-world scenarios. However, Distribution Matching Distillation (DMD), a leading paradigm, tends to degrade under limited NFE budgets, manifesting in video generation as layout instability, oversaturation, and broken motion dynamics. We trace this failure to a structural limitation: standard DMD is an intra-sample distribution-matching objective with coordinate-wise gradients, and thus imposes no explicit constraint on the relational geometry across batch elements or temporal frames, leaving the underlying copula largely unregulated. Combined with the mode-seeking tendency of its reverse-KL objective, this absence of relational guidance makes DMD prone to collapsing into local optima in the few-step regime. Motivated by this insight, we propose Copula-aware DMD (CoDMD), a lightweight relational regularizer that reuses score estimates already produced by the frozen teacher and the online fake model to construct pairwise relation matrices across samples and frames. These are matched through a supplementary distributional objective that requires no additional networks, datasets, or sampling trajectories. On the Wan-2.1-T2V model series at 1.3B & 14B scales, CoDMD distills 50-step teachers into 4-step students, achieving an approximate 25

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