OT-MeanFlow3D: Bridging Optimal Transport and Meanflow for Efficient 3D Point Cloud Generation

Elaheh Akbari; Shansita Sharma; Ping He; Ahmadreza Moradipari; Kyungtae Han; Hamed Pirsiavash; Yikun Bai; Soheil Kolouri

cs.LGSep 26, 2025

OT-MeanFlow3D: Bridging Optimal Transport and Meanflow for Efficient 3D Point Cloud Generation

Authors: Elaheh Akbari, Shansita Sharma, Ping He, Ahmadreza Moradipari, Kyungtae Han, Hamed Pirsiavash, Yikun Bai, Soheil Kolouri

Organizations: Department of Computer Science, Vanderbilt University · Toyota InfoTech Labs · Department of Computer Science, University of California, Davis · Department of Mathematics, Purdue University

Abstract

Flow-matching models have recently emerged as a powerful framework for generative modeling, including 3D point cloud synthesis. However, their deployment is limited by the need for multiple sequential sampling steps at inference time. MeanFlow enables single-step generation by learning an average velocity field, but its quality depends heavily on the geometry of the training pairs. In this work, we propose an Optimal Transport-enhanced MeanFlow framework (OT-MF3D) for efficient and accurate 3D point cloud generation and completion. Beyond incorporating OT into MeanFlow, our method introduces a latent-conditioned training algorithm that decouples shape-level sampling from point-level matching. This enables exact point-level OT within each conditioned shape while performing shape-level transport in a compact latent space, avoiding the expensive nested OT computation in point-cloud space. Experiments on standard benchmarks show improved generation and completion quality over fast baselines, with substantially reduced training and inference costs compared with diffusion and other flow-based models.

Figures & tables

Figure 1: One-step generated samples for SN and ModelNet-10 generated within 0.04 seconds.

Figure 2: The overall framework for our training and inference process for shape generation and completion. Shape Generation: A pre-trained Encoder is used to train the Shape Gen and Context Gen, and Context Gen is used during inference to condition the Shape Gen model and generate unseen samples. Shape completion: An Encoder is trained jointly and the latent vector is used as conditioning.

Figure 3: Qualitative comparison. Times measured on our GPUs.

Model	ST (s)	Airplane		Chair		Car		Avg
Model	ST (s)	CD	EMD	CD	EMD	CD	EMD	CD	EMD
PointFlow [ 38 ]	0.27	75.68	70.74	62.84	60.57	58.10	56.25	65.54	62.52
DPF-Net [ 19 ]	0.33	75.18	65.55	62.00	58.53	62.35	54.48	66.51	59.52
SoftFlow [ 17 ]	0.12	76.05	65.80	59.21	60.05	64.77	60.09	66.68	61.98
ShapeGF [ 3 ]	0.34	80.00	76.17	68.96	65.48	63.20	56.53	70.72	66.06
DPM [ 27 ]	22.8	76.42	86.91	60.05	74.77	68.89	79.97	68.45	80.55

Table 1: ShapeNet generation results. For 1-NN-CD/EMD, values closer to 50 are better. Bottom-block methods have inference times comparable to our one-step model. Bold and underlined denote the best and second-best results per block. iMF is denoted with (imp). Our method ranks first or second among the fastest methods while training more efficiently than PSF [ 36 ] . PSF* refers to our results generated using the public code and training recipe.

Figure 4: Completion samples using our one-step completion model on the nuScenes dataset.

Method	TT (h)	Memory (GB)
PVD [ 44 ]	107	3.78
LION [ 40 ]	273	32.1
ConTiCoM-3D [ 7 ]	146	37.4
PSF [ 36 ]	85	38.8
OT-MF3D (imp)(Ours)	31	15.7

Table 2: Comparison of training time (TT) and peak GPU memory measured on our GPUs.

Figure 5: Partial point cloud, ground truth, and completed samples using our one-step completion model. Our shape completion model can successfully capture the full shape from a partial view.

		EMD $\downarrow$
Model	ST (s)	Airplane	Chair	Car
SoftFlow [ 17 ]	0.12	1.198	3.295	2.789
PointFlow [ 38 ]	0.27	1.180	3.649	2.851
DPF-Net [ 19 ]	0.34	1.105	3.320	2.318
PVD [ 44 ] (N=1000)	29.98	1.030	2.939	2.146
PSF [ 36 ] (N=1)	0.03	1.004	2.937	2.194

Table 3: Point-cloud completion quality and latency. EMD is scaled by

10^{2}

. Our method achieves the best EMD and fastest inference.

$B$	$P$	CD	EMD
64	256	57.77	52.79
32	256	57.17	53.77
64	128	58.00	53.92

Table 4: Effect of varying number of point clouds (B) vs number of subsampled points (P).

Model	Outer	Inner	ST (s)	CD	EMD
MF ( $N=1$ )	✓	✗	0.03	97.43	93.50
MF ( $N=2$ )	✓	✗	0.06	62.46	63.14
OT-MF3D ( $N=1$ )	✓	✓	0.03	57.77	52.79
MF (imp)	✗	✗	0.03	59.96	60.42
OT-MF3D (imp)	✗	✓	0.03	59.36	55.43
OT-MF3D (imp)	✓	✗	0.03	59.06	60.57

Table 5: 1-NNA comparison on ShapeNet Chairs. Outer and Inner OT denote distribution- and point-level transport, respectively.

Appendix figures & tables8 assets

Supplementary material from the paper’s appendix.

Appendix

Component	Time / step	% of step	Notes
Point-level OT coupling	$\sim$ 89 ms	$\sim$ 15%	$B$ sequential $P{\times}P$ solves
Total training step	$\sim$ 577 ms	100%	fwd + OT + bwd

Appendix

Table 6: Wall-clock overhead of the point-level exact OT coupling, measured per training step on 4-GPU DDP training (

B{=}16

point clouds/GPU,

P{=}256

points/cloud).

Figure 6: Some failure cases of our method across different datasets.

Model	Airplane		Chair		Car		Avg.
Model	CD	EMD	CD	EMD	CD	EMD	CD	EMD
Decoder	71.73	93.70	57.48	77.49	57.10	84.66	62.10	85.29
OT-MF	71.60	64.07	57.40	54.08	58.81	53.98	62.60	57.38

Appendix

Table 7: Shape generation results on ShapeNet-Airplane, Chair, and Car using 1-NN accuracy. Values closer to

50

are better. Best results between the Decoder and OT-MF are shown in bold .

Model	Airplane				Chair				Car
	MMD $\downarrow$		COV $\uparrow$		MMD $\downarrow$		COV $\uparrow$		MMD $\downarrow$		COV $\uparrow$
	CD	EMD	CD	EMD	CD	EMD	CD	EMD	CD	EMD	CD	EMD
Decoder	0.195	0.576	47.65	26.42	2.360	1.743	45.02	33.53	0.814	0.933	42.33	28.69
OT-MF	0.229	0.370	48.40	48.15	2.539	1.487	45.62	52.11	0.910	0.736	46.02	50.57

Appendix

Table 8: Shape generation results on ShapeNet-Airplane, Chair, and Car with MMD and COV scores. CD-MMD is multiplied by

10^{3}

and EMD-MMD is multiplied by

10^{2}

, while COV is reported as a percentage. Best results between the Decoder and OT-MF are shown in bold .

Model	Airplane				Chair				Car
	MMD $\downarrow$		COV $\uparrow$		MMD $\downarrow$		COV $\uparrow$		MMD $\downarrow$		COV $\uparrow$
	CD	EMD	CD	EMD	CD	EMD	CD	EMD	CD	EMD	CD	EMD
1-GAN (CD) [ 1 ]	0.340	0.583	38.52	21.23	2.589	2.007	41.99	29.31	1.532	1.226	38.92	23.58
1-GAN (EMD) [ 1 ]	0.397	0.417	38.27	38.52	2.811	1.619	38.07	44.86	1.408	0.899	37.78	45.17
PointFlow [ 38 ]	0.224	0.390	47.90	46.41	2.409	1.595	42.90	50.00	0.901	0.807	46.88	50.00
SoftFlow [ 17 ]	0.231	0.375	46.91	47.90	2.528	1.682	41.39	47.43	1.187	0.859	42.90	44.60

Appendix

Table 9: Shape generation results on ShapeNet-Airplane, Chair, and Car with MMD and COV scores. CD is multiplied by

10^{3}

and EMD is multiplied by

10^{2}

Figure 7: Additional one-step generation samples on class Chair using our model.

Figure 8: Additional one-step generation samples on class Airplane using our model.

Figure 9: Additional one-step generation samples on class Car using our model.

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Hierarchical Flow Matching for 3D Point Cloud Generation

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Open paper AskPDF arXiv

Generating high-quality 3D point clouds requires capturing both global shape topology and local geometric details. Existing flow-based methods rely on continuous normalizing flows (CNFs) that demand expensive ODE solving and trace estimation during training, while diffusion models require hundreds of iterative denoising steps. Moreover, most approaches adopt single-level generation directly in point space, disregarding the hierarchical structure natural to 3D shapes. We propose Hierarchical Flow Matching (HFM) that extends flow matching to bilevel structure for unconditional 3D point cloud generation. HFM decomposes the task into two levels via optimal-transport flow matching: a Latent Flow Matching models the global shape manifold in a compact latent space, and a Conditional Point Flow Matching reconstructs detailed point clouds conditioned on the latent code. Both flows are trained with simple MSE regression losses. The resulting straight OT paths enable efficient sampling with as few as 15 Euler steps per flow, while the structured latent space supports downstream tasks including classification. Extensive experiments on ShapeNet and ModelNet benchmarks demonstrate that HFM achieves competitive or even best performance compared with prior state-of-the-art methods.

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