3D point clouds generation requires capturing both part-level layout and surface detail while preserving permutation equivariance. Existing latent generative models often encode an entire shape into a single vector, which limits their ability to retain part-level structure. We propose TokenFlow, a hierarchical flow matching framework that represents each shape as a set of latent tokens and couples a rectified flow over these tokens with a conditional flow over points. A bottleneck of M≪N learnable tokens aggregates global context through cross-attention at O(NM) cost. On ShapeNet, TokenFlow achieves the best MMD and coverage across airplane, car, and chair, while obtaining 1-NNA comparable to the strongest baselines. On ModelNet, its learned latent set reaches the best reported linear-evaluation accuracy on ModelNet10. These results show that representing a shape as a set of latent tokens, aggregated at O(NM) cost, provides an effective representation for 3D point cloud generation.
Figures & tables
Figure 1: TokenFlow pipeline. The prior flow transports Gaussian noise to a set of latent tokens over a Transformer encoder with several layers whose output is rescaled by a time-conditioned γ . The conditional point flow then decodes those tokens into a point cloud. A shared per-point MLP embeds each point and feeds two separately projected branches that are added, a code path in which the pooled token set and the time embedding give the scale and shift of an adaptive layer normalization over the point features, and a token path that cross-attends from the points to the latent tokens.
Figure 2: Qualitative comparisons against previous state-of-the-art methods.
Figure 3: Interpolation and extrapolation in the latent space.
Context module
Time
Memory
Transformer [ 48 ]
O(N2C)
O(N2)
PointTransformer [ 66 ]
O(NkC)
O(Nk)
Performer [ 11 ]
O(NC2)
O(NC)
CBA (ours)
O(NMC)
O(NM)
Table 1: Complexity of context aggregation over N points with C channels. CBA uses M≪N latent tokens, so both time and memory are linear in N .
Figure 4: Illustration of CBA block. ”TE” means token embeddings while ”PE” represents point embeddings.
Method
Chair
Airplane
Car
MMD ↓
COV(%) ↑
JSD ↓
MMD ↓
COV(%) ↑
JSD ↓
MMD ↓
COV(%) ↑
JSD ↓
CD
EMD
CD
EMD
–
CD
EMD
CD
EMD
–
CD
EMD
CD
EMD
–
r-GAN
2.57
12.80
33.99
9.97
11.50
0.261
5.47
42.72
18.02
7.44
1.27
8.74
15.06
9.38
12.80
l-GAN (CD)
2.46
8.91
41.39
25.68
4.59
0.239
4.27
43.21
21.23
4.62
1.55
6.25
38.64
18.47
4.43
l-GAN (EMD)
2.61
7.85
40.79
41.69
2.27
0.269
3.29
47.90
50.62
3.61
1.48
5.43
39.20
39.77
2.21
PVD
2.62
–
48.84
50.60
–
0.224
–
48.88
52.09
–
1.10
–
41.19
50.56
–
Table 2: Generation results using MMD, COV and JSD ( ↑ / ↓ as marked). MMD-CD and MMD-EMD are scaled by 103 and 102 ; JSD by 102 . “–” marks unreported entries.
Model
MN10 (%)
MN40 (%)
SPH
68.2
79.8
LFD
75.5
79.9
T-L Network
74.4
–
Vconv-DAE
75.5
80.5
PointGrow
85.7
–
3D-GAN
83.3
91.0
Table 3: Classification results on ModelNet10 (MN10) and ModelNet40 (MN40) datasets. Missing entries are denoted as “–”.
Method
Airplane
Car
Chair
CD
EMD
CD
EMD
CD
EMD
r-GAN
98.40
96.79
94.46
99.01
83.69
99.70
l-GAN (CD)
87.30
93.95
66.49
88.78
68.58
83.84
l-GAN (EMD)
89.49
76.91
71.16
66.19
71.90
64.65
PC-GAN
94.35
92.32
92.19
90.87
76.03
78.37
PointFlow
75.68
70.74
60.65
62.36
62.84
60.57
Table 4: Generation results on Airplane, Car, and Chair compared with baselines using 1-NNA as the metric. Lower is better. For clarity, the table is divided into two splits: the bottom corresponds to results from the past three years while the top corresponds to the earlier methods.
Figure 5: Multi-class results generated by TokenFlow.
Context module
1-NNA-CD ↓
1-NNA-EMD ↓
Transformer [ 48 ]
72.43
68.91
PointTransformer [ 66 ]
71.54
67.96
Performer [ 11 ]
76.23
75.60
CBA (ours)
66.65
60.55
Table 5: Context module ablation on the Airplane category, reported as 1-NNA (%). Lower is better. Only the context module of the encoder is replaced, and everything else is held fixed.
Latent Tokens
1-NNA-CD ↓
1-NNA-EMD ↓
M=1
81.59
80.72
M=8
76.57
73.68
M=32
72.30
67.84
M=64
66.65
60.55
M=128
70.03
66.49
Table 6: Effect of the number of latent tokens M on the Airplane category, reported as 1-NNA (%). Lower is better. M=64 is the default used in the main results.
Point cloud generation creates 3D point sets from noise, images, scans, or other conditions for reconstruction, simulation, and synthetic training data.