Rectified Point Flow: Generic Point Cloud Pose Estimation
Authors: TAO SUN
Liyuan Zhu
Shengyu Huang
Shuran Song
Iro Armeni
Venue: NeurIPS 2025 spotlight ()
Keywords: Point Cloud Registration
Rectified Flow
Multi-Part Assembly
Shape Assembly
Primary area: applications
TL;DR: Rectified Point Flow is a single generative model that turns unaligned point clouds into assembled shapes—unifying pairwise registration and multi-part assembly—and sets new state-of-the-art results across five benchmarks.

Abstract: We present Rectified Point Flow, a unified parameterization that formulates pairwise point cloud registration and multi-part shape assembly as a single conditional generative problem. Given unposed point clouds, our method learns a continuous point-wise velocity field that transports noisy points toward their target positions, from which part poses are recovered. In contrast to prior work that regresses part-wise poses with ad-hoc symmetry handling, our method intrinsically learns assembly symmetries without symmetry labels. Together with an overlap-aware encoder focused on inter-part contacts, Rectified Point Flow achieves a new state-of-the-art performance on six benchmarks spanning pairwise registration and shape assembly. Notably, our unified formulation enables effective joint training on diverse datasets, facilitating the learning of shared geometric priors and consequently boosting accuracy. Our code and models are available at https://rectified-pointflow.github.io/.

Rectified Point Flow: Generic Point Cloud Pose Estimation
Tao Sun" Stanford University
Liyuan Zhu" Stanford University
Shengyu Huang NVIDIA Research
Shuran Song Stanford University
Iro Armeni Stanford University
Abstract
We present Rectified Point Flow, unified parameterization that formulates pair- wise point cloud registration and multi-part shape assembly as single conditional generative problem. Given unposed point clouds, our method learns a continuous point-wise velocity field that transports noisy points toward their target positions, from which part poses are recovered. In contrast to prior work that regresses part- wise poses with ad-hoc symmetry handling, our method intrinsically learns assem- bly symmetries without symmetry labels. Together with an overlap-aware encoder focused on inter-part contacts, Rectified Point Flow achieves new state-of-the trrt performance on six benchmarks spanning pairwise registration and shape assembly. Notably, our unified formulation enables effective joint training diverse datasets, facilitating the learning shared geometric priors and consequently boosting accu- racy. Our code and models are available hutps://rectified pointflow github.io/
Introduction
Estimating the relative poses of rigid parts from 3D point clouds for alignment is core task in computer vision and robotics, with applications spanning pairwise registration [ and complex multi-part shape assembly [2]. In many settings, the input consists of an unordered set of part- level point clouds-without known correspondences, categories, or semantic labels-and the goal is to infer globally consistent configuration of poses, essentially solving multi-part (two more) point cloud pose estimation problem. While conceptually simple, this problem is technically challenging due to the combinatorial space of valid assemblies and the prevalence of symmetry and part interchangeability in real-world shapes
5)
Despite sharing the goal of recovering 6-DoF transformations, different 3D reasoning tasks such as object pose estimation, part registration, and shape assembly- have historically evolved in silos, treat- ing each part independently and relying task-specific assumptions and architectures. For instance, object pose estimators often assume known categories or textured markers 6 7 while part assembly algorithms may require access canonical target shape manual part correspondences [8] This fragmentation has yielded solutions that perform well in narrow domains but fail to generalize across tasks, object categories, or real-world ambiguities.
Among these tasks, multi-part shape assembly presents especially unique challenges. The problem inherently under constrained: parts are often symmetric (9) interchangeable [10], geometrically ambiguous, leading to multiple plausible local configurations. As a result, conventional part-wise registration can produce flipped misaligned configurations that are locally valid but globally inconsistent with the intended assembly. Overcoming such ambiguities requires a model that can
"qqual contribution.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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reason jointly about part identity, relative placement, and overall shape -wihhot relying on strong supervision or hand-engineered heuristics.
In this work, we revisit 3D pose regression and propose a generative approach for generic point cloud pose estimation that casts the problem as learning continuous point-wise flow field over the input geometry, effectively capturing priors over assembled shapes. Our method, Rectified Point Flow, models the motion of points from random Gaussian noise in Euclidean space toward the point clouds of assembled objects. This learned flow implicitly encodes part-level transformations, enabling both discriminative pose estimation and generative shape assembly within a single framework. Rectified Point Flow consists of an encoder that extracts woint-wise features, and flow model that, given the features, predicts the final assembled positions.
To instill geometric awareness of inter-part relationships, we pretrain the encoder on large-scale 3ID shape datasets: predicting point-wise overlap across parts, formulated as binary classification task. While GARF [1] also highlights the value of encoder pretraining for a flow model, relies on mesh-based physical simulation [12] to generate fracture-based supervision signals. contrast, we introduce a lightweight and scalable alternative that constructs pretraining data by computing geometric overlap between parts. Our data generation is agnostic data sources tailored for different tasks fasks-including part segmentation [3] [44 [3], shape assembly 122 [6 [7]. and registration [18]
19
without requiring watertight mesh or simulation, an important step towards scalable pretraining
for pose estimation.
Our flow-based pose estimation departs from traditional pose-vector regression in three ways: (i)
Joint shape-pose reasoning: We cast the registration and assembly tasks as one unified task that reconstructs the complete shape while simultaneously enabling the estimation of part poses; (ii) Scalable shape prior learning: By training to predict the final assembled point cloud, our model learns from heterogeneous datasets and part definitions, yielding scalable training and transferable geometric knowledge across standard pairwise registration, fracture reassembly, and complex furniture assembly tasks; and (iii) Intrinsic symmetry handling: Rather than regressing pose vectors directly in SE(3) space, we operate in Euclidean space over dense point clouds. This makes the model inherently robust to symmetries. part interchangeabblity, and spatial ambiguities that often challenge conventional methods. Our main contributions are summarized as follows:
We propose Rectified Point Flow, a generative approach for generic point cloud pose estimation that addresses both pairwise registration and multi-part assembly tasks and achieves state-of-the- art performances on all the tasks.
We propose generalizable pretraining strategy with geometric awareness of inter-part relation- ships across several 3D shape datasets, and formulate it as point-wise overlap prediction.
We show that our parameterization supports joint training across different registration tasks, boosting the performance on each individual task.
2 Related Work
Parametrization for Pose Estimation. Euler angles and quaternions are the predominant parametrization of rotation in various pose regression tasks (20, 21 22 23
24 25 26 due
to their simplicity and usability. As Euler angles and quaternions are discontinuous representations, Zhou et al. [27] proposed to represent 3D rotation with a continuous representation for neural net- works using 6D and 7D vectors. In contrast to directly regressing pose vectors, other methods train networks to find sparse correspondences between image pairs point cloud pairs and extract pose vectors using Singular Value Decomposition (SVD) 28 29
31 32 More recently, RayDif- fusion K3 proposed to represent camera poses as ray bundles, naturally suited for coupling image features and transformer architectures. Huang et al. 34 adopted a point cloud generative model for policy learning in robot pick- mack-and-place tasks. then recovered relative poses between the object and gripper via SVD. DUSt3R (35] directly regresses the pointmap of each camera in a global reference frame and then extracts the camera pose using RANSAC-PIP 33 37]. Our proposed Rectified Point Flow, extends the dense point cloud or point map representation for learning generalizable pose estimation on point cloud registration and shape assembly tasks.
Learning-based 3D) Registration. 3D registration aims to align point cloud pairs in the same reference frame by solving the relative transformation from source target. The first line of work

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Condition Point Clouds
Noised
Estimated Point Clouds (X(0))
Recovered
Point Clouds
Poses (Tiken
{Xthee
(X())
Anchored
Estimated
Per:aar SVD
Shape Assembly
Condition
Port
Rectified Point Flow
Anchored
P Part SVD
Condition Part
Estimated
Pairwise Registration
Rectified Point Flow's Pose-from-Shape Pipeline. Our formulation supports shape assembly (first row) and pairwise registration (second row) tasks single framework. Given of unposed part point clouds [Xi Rectified Point Flow predicts each part's 's point cloud at the target assembled state X (0)) Subsequently, we solve Procrustes problem via SVD between the condition point cloud X; and the estimated point cloud ((()) to recover the rigid transformation T] for each non-anchored part.
Figure 1:
that first extract correspondences between point clouds, followed by robust estimators recover the transformation. Subsequent works 29 42 32) advance the performance by learning more powerful features with improved architecture and loss design. The second line of work comprises direct registration methods [I] 43 30 [2 that directly compute a score matrix and apply differentiable weighted SVD to solve for the transformation. Correspondence-
focuses on correspondence-bssse methods 38
39 40
methods can fail in extremely low-overlap scenarios shape assembly and direct methods fall short in terms of pose accuracy. Our method, which directly regresses the coordinates of each point in the source point cloud, agnostic and more generalizable varying overlap ratios compared to direct methods.
Multi-Pare Registration and Assembly. Multi-part registration and shape assembly generalize pairwise relative pose estimation to multiple parts, with applications in furniture assembly [17] and shape reassembly 12). Methods 44
46 47 tackle the multi-part registration problem by estimating the transformation for each rigid part in the scene (multi-source and multi- target). Multi-part shape assembly differs task from registration because it has multi-source input and a canonical target, and each part has almost 'zero' overlap w.r.t. each other. Chen et al. [48] adopt an adversarial learning scheme to examine the plausibility for different shape configurations. Wu et al. [49 leverage SE(3) equivariant representation to handle pose variations in shape assembly. leverage diffusion models predict the transformation for each part. GARF [I]] combines fracture-awan pretraining with flow matching model to predict per-part transformation. These methods, however, not handle interchangeability and symmetry as well as ours does. Moreover, Rectified Point Flow is the first solution for furniture assembly of 3D shapes on the PartNet-Assembly [15] and IKEA-Manual [1 datasets.
45
26
Diff DiffAssembly [50] and PuzzleFusion 24 25
3 Pose Estimation via Rectified Point Flow
Rectified Point Flow addresses the multi-part point cloud pose estimation problem, defined in Sec. 3.1
The overall pipeline consists of two consecutive stages: overlap-aware point encoding (Sec. 3.2
and conditional Rectified Point Flow (Sec. (S3c.3.3). Finally, we explain how our formulation inherently addresses the challenges posed by symmetric and interchangeable parts in Sec. E

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Multi-part Point Clouds
Overlap Points Prediction
Overlap Points Target
Encoder
Overlap
Head
Figure 2: Encoder pre-training via overlap points prediction. Given unposed multi- point clouds, encoder with point-wise overlap prediction head performs binary classification identify overlapping points. Predicted overlap points are shown in blue. For comparison, the ground- truth overlap points visualized the assembled object for clarity (target overlap).
3.1 Problem Definition
Consider set of unposed point clouds of multiple object parts, {X; E R3xN: heg, where the part index set, ! := [S2] is the number of parts, and N; is the number of points in part i. The goal to solve for set of rigid transformations {T, SE(3) hen that align each part the unposed multi-part point cloud X to form single, assembled object Y in global coordinate frame, where
X = U E Y Y = U T,X, E R and N Σ N IEN
(1)
iEQ
To eliminate global translation and rotation ambiguity, we the first part (i 0) as the anchor and define its coordinate frame as the global frame. All other parts are registered to this anchor.
3.2
Overlap-aware Point Encoding
Pose estimation relies geometric cues from mutually overlapping regions among connected parts 229 32 In our work, we address this challenge through a pretraining module that develops task-agnostic, overlap-aware encoder capable of producing pose-invariant point features. As illustrated in Fig. R we train an encoder F to identify overlapping points in different parts. Given a set of unposed parts Jen. we first apply random rigid transforms Tç E SE(33 and compose transformed point clouds X, = T;XX; as input to the encoder. These data augmentations enable the encoder learn more robust pose-invariam ins-invariant features. The encoder then computes per-point features Ci, E Rd for the j-th point on part after which an MIPP overlap prediction head estimates the overlap probability Pi.j The binary ground-truth label p..j is if point X. falls within radius e of least one point in other parts.
We train both the encoder and the overlap head using binary cross-entropy loss. For objects without predefined part segmentation, we employ off-the-shelf 3D part segmentation methods to generate the necessary labels. The features extracted by our trained encoder subsequently serve as conditioning input for our Rectified Point Flow model.
3.3 Generative Modeling for Pose Estimation
The overlap-aware encoder identifies potential overlap regions between parts but cannot determine their final alignment, particularly in symmetric objects that allow multiple valid assembly configu- rations. To address this limitation, we formulate the point cloud pose estimation as conditional generation task. With this approach, Rectified Point Flow leverages the extracted point features to sample from the conditional distribution of all feasible assembled states across multi-part point clouds, generating estimates that maximize the likelihood of the conditional input point cloud. By recasting pose estimation generative problem, we naturally accommodate the inherent ambiguities arising from symmetry and part interchangeability in the data.
score-free generative modeling framework that learns to transform sample X (0) from source distribution, into (1) from target distribution. The forward process defined as linear interpolation between them with timestep as
Preliminaries. Rectified Flow (RF) 511 52
X x)x + +1)(),, te [0.
(2)

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Multi-Part Point Clouds
Encoder
Noised
Points
(Xthea
Flow Mudel
Assembled State
Positional Encoding
[Xo(O), ... (x)
Noised
Velocity Field
Point Clouds (Xx(t)
dX
dX
di
di
Figure 3: Learning Rectified Point Flow. The input to Rectified Point Flow are the condition point clouds (ii Jees and noised point clouds (X) at timestep I. They are first encoded by the pre-trained encoder and the positional encoding, respectively. The encoded features are concatenated and passed through the flow model, which predicts per-point velocity vectors (l)d.()) and defines the flow used predict the part point cloud in its assembled state.
The reverse process modeled as a velocity field V V.X (t), which is parameterized as a network (tt, X (t) X) conditioned on X and trained using conditional flow matching (CFM) loss [53].
LCFM = Ex,x [IV X (t) x) V.X(0))]
Rectified Point Flow. In our method, we directly apply RF to the 3D Euclidean coordinates of the multi-part point clouds. Let (t) E a M; denote the deeeddepndentt point cloud for part i, where M; is number of sampled points. At t = 0, {X, (0)) hen is uniformly sampled from the assembled object Y. while at / = 1, points on each part are independently sampled from a Gaussian, i.e., (1(1) ~ ~O, I). Then, we define the continuous flow for each part as straight-line interpolation in 3D Euclidean space between the points in noised and assembled states. Specifically, for each part
(t) (1 x)) + x1),1), t [0.
(4)
The velocity field of Rectified Point Flow is therefore,
dt, x1(1) X²()).
(5)
dt
We fix the anchored part (i 0) by setting Xo(1) = (0) for all [0, implemented via mask that zeros out the velocity for its points. Once the model predicts the assembled point cloud of each part (O),, we recover its pose T; in a Procrustes problem,
ñ, arg min || (0))l.
(6)
7,ES(()
Solving poses 7; for all non-anchored parts via SVD completes the pose estimation task in Eq.
Learning Objective. We train flow model to recover the velocity field in Eq. taking the noised point clouds (X.()) Jien and conditioning unposed multi-part point cloud X, as shown Fig- 3 First, we encode using the pre-trained encoder F., For each noised point cloud, we apply a positional encoding to its 3D coordinates and part index, concatenate these embeddings with the point features, and feed the result into the flow model. We denote its predicted velocity field by the flow model for all points by (t,, (X, (t) X) E R3x M We optimize the flow model V by minimizing the conditional flow matching loss in Eq.
3.4 Invariance Under Rotational Symmetry and Interchangeabilityy
In our method, the straight-line point flow and point-cloud sampling, while simple, guarantee that every flow realization and its loss in Eq. remain invariant under assembly symmetry group G: Theorem (G-invariance the learning objective). For every element g E G. we have the learning (()))))
objective in Eq. following LCFM
(CCMM(g(VV
The formal definition of G and the proof of Theorem I appear in the supplementary material. As result, the flow model learns all the symmetries in & during training, without the need for additional hand-made data augmentation heuristics symmetry and interchangeability.
5

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Experiments
Implementation Details. We use PointTransformerV3s (PTv3) 54 as the backbone for point cloud encoder, and use Diffusion Transformer (DiT) [55] as our flow model. Each DiT layer applies two self-attention stages: (i) part-wise attention to consolidate part-awareness, and (ii) global attention over all part tokens to fuse information. We stabilize the attention computation by applying RMS Normalization [56, 57 to the query and key vectors per head before attention operations. We sample the time steps from U-shaped distribution following [58]. We pre-train the PTv3 encoder all datasets with an additional subset of Objaverse [14] meshes, where we apply PartField [33 to obtain annotations. After pretraining, NVIDIA A 100 80GB GPUs for 400k iterations with an effective batch size of 256. We use the AdamW [59] optimizer with an initial learning rate 5 10-4 which is halved every 25k iterations after the first 275k iterations.
freeze the weights of the encoder. We train our flow model on
Table Dataset statisties. We train our flow model on six datasets with varying sizes, part definitions, and complexities. The encoder is pre-traine pre-trained on these datasets with an extra Objaverse dataset.
Train & Val
Test
Dataset
Task
Part Definition
Samples
Parts
Samples
Parts
IKEA-Manual 17
Assembly
Reusability and packing
84
[2. 19]
18
[2. 19]
TwoByTwo [6
Assembly
Insertable parts
308
[2, 2]
144
[2. 2]
Assemey
Assembly
Semantics and functions
23755
[2. 64]
261
[2, 64]
BreakingBad
12
Assembly
Fracture simulation
35114
[2]
265
[2, 49]
TUD-L [8
Registration
RGB-D sensor scans
19138
[2. 2]
300
[2.
ModeINet-40 19
Registration
Random partition
19680
[2, 2]
260
[2,
Objaverse 1.0
14
Pre-training
From PartField
63199
[3, 12]
6794
[3, 12]
4.1 Experimental Setting
Datasets. For the multi-part shape assembly task, we experiment the BreakingBad [2)
TwoByTwo [16], PartNet [5], and IKEA-Manual [17] datasets. The PartNet dataset has been processed for the shape assembly task following the same procedure [17] but includes all object categories; we refer to this version as PartNet- Assembly Evaluation of the pairwise registration is performed the TUD-L [18] and ModelNet-40 [19] datasets. We follow [22 for prepossessing the TUD-L dataset. We split all datasets into train/val/tess sets following existing literature for fair comparisons. These datasets define parts at distinct levels, ranging from random partitions (e.g., ModelNet-40 and Breaking Bad) to human-labeled (e.g., semantically meaningful parts in PartNet and IKEA-Manual). The statistics and information of all datasets are summarized Tab. I
Evaluation Protocols. We evaluate the pose accuracy following the convention of each benehmark. with Rotation Error (RE), Translation Error (TE), Rotation Recall 5 (Recall @ 5"), and Translation Recall at cm (Recall @ cm). For the shape assembly task, we measure Part Accuracy (Part Acc) by computing per object the fraction of parts with Chamfer Distance under cm, and then averaging those per-object scores across the dataset, following 25
30
Following [11,
select the largest- largest-volume volume part the anchor and fix it during inference. However, this effectively provides the model with anchor pose in the object's CoM (center of mass) frame, an unrealistic assumption for real-world assembly applications. Therefore, anchor-free setting (see Appendix B Anchor-free Models), and argue that anchor-free evaluation should be the standard protocol for shape assembly tasks.
also train our model in an
Baseline Methods. We evaluated our method against state-of of-the--rrtt methods for pairwise registra- tion and shape assembly. For pairwise registration, we compare against DCPNet [II, RPMNet (0). GeoTrassformer [32]. and Diff- RPMNet (22). For shape assembly, we compare against MSN 48
SE(3)-Assembly 49 Jigsaw 660, PuzzleFussion++ (25), and GARF [.. We report our per-
formances under two training configurations: dataset-specific training where models are trained
independently for each dataset (denoted Ours (Single)), and joint training where a single model trained across all datasets (denoted Ours (Joint)).

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parts
7 parts
parts
12 parts
24 parts
48 parts
Input
GARF
Ours
G7
Figure Qualitative Results on PartNet-Assemblle Columns show objects with increasing number of parts (left to right). Rows display (1) colored input point clouds of each part, (2) GARF outputs (dashed boxes indicate samples limited 20 by GARF's design, selecting the top parts by volume), (3) Rectified Point Flow outputs, and (4) ground bouund-truth assemblies. Compared to GARF, our method produces more accurate pose estimation on most parts, especially as the number of parts increases.
Table Multi-Part Assembly Results. Rectified Point Flow (Ours) achieves the best performance across all metrics on BreakingBad-Everyyee Everyday, TwoByTwo and PartNet-Assembiy datasets.
Breaking Bad Everryay 222
TwoByTwo
[6
PartNet-Assembly
Methods
RE | [deg]
TE [em]
Part Acc
RE
RE [deg]
TE.
Part Acc
ddgg]
[em]
[em]
[%]
MSN
48
85.6
15.7
16.0
70.3
28.4
49
73.3
14.8
27.5
52.3
23.3
Jigsaw 60
42,3
10.7
68.9
53.3
36.0
PuzzleFusion++
25
38.1
8.0
76.2
58.2
34.2
GARF
9.9
2.0
93.0
22.1
7.1
66.9
21.9
25.7
Ours (Single)
9.6
93.5
18.7
4.1
24.8
15.4
50.2
Ours (Joint)
7.4
91.1
13.2
3.0
21.8
14.8
53.9
4.2
Evaluation
We report pose accuracy for shape assembly and pairwise registration in Tab. and Tab. re- spectively. Our model outperforms all existing approaches by substantial margin. For multi-part assembly, the closest competitor is GARF [1I, which formulates per-part pose estimation as 6-DoF pose regression; see Figs. 4 aand5 5 We attribute our superior results to two key advantages of Rectified Point Flow: (i) in contrast to our closest competitor GARF [1]] which performs 6-DoF pose regres- sion, our dense shape-and- pose parametrization helps the model learn better global shape prior and fine- fine-grained geometric details more effectively; and (ii) generative formulation natively handles
"We found that the BreakingBad benchmark 12 the RMSE of Euler angles, which not a proper metric SO(3). To ensure consistency, we re-evaluate all baselines using the geodesic distance between rotation matrices via the Rodrigues formula [61 31 29 32 For Ours (Single) on TwoBy Two, we used encoder pretrained in the Ours (Joint) setting but trained the flow model only TwoByTwo, due to its limited size.
originally computed rotation
(RE) using

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ModelNet
TUD-L
BaaakkingBd-vveryddde
Input
GARF
Ours
GT
Figure 5: Qualitative Results Across Registration and Assembly Tasks. From left to right: pairwise registration on ModelNet 40 and TUD-L., shape assembly on BreakingBad- From top to bottom: Colored input point clouds, GARF results, ours, and ground truth (GT). Our single model performs the best across registration and assembly tasks.
Table 3: Pairwise Registration Results. Rectified Point Flow (Ours) outperforms all baselines on both TUD-L and ModelNet 40, achieving the highest accuracy and lowest errors across all metrics.
TUD-L [8]
ModelNet 40
I9
Methods
Recall @5 f
Recall Icm" f
RE 1 [deg]
TE [unit]
[%]
[%]
DCPNet
23.0
11.98
0.171
RPMNet 30
73.0
89.0
1.71
0.018
Geo Transssoommrr
32
88.0
97.5
1.58
0.018
GARF II
53.1
52.5
42.5
0.063
Dift-RPMNG
22
90.0
98.0
Ours (Single)
97.0
98.7
1.37
0.003
Ours (Joint)
97.7
99.0
0.93
0.002
part symmetries and interchangeabilityy For pairwise registration, GARF-despite heing retrained on target datasets-faile to generalize beyond the original task. In contrast, method achieves state-of-the-art performance on registration benchmarks, outperforming methods designed solely for registration (e.g., GeoTransformer (32) and Diff-RPMNet (22]) and demonstrating strong generaliza- tion across different datasets (Fig 5 We also achieve the strongest shape assembly performance on IKEA-Manual [7 for more details evaluation and visualizations, see supplementary.
Joint Training. By recasting pairwise registration as two-part assembly task, our unified for- mulation enables joint training of the flow model on all six datasets-innlludngg very small sets like TwoByTwo (308 samples) and IKEA-Manual (84 samples) and the additional pretraining data from Objaverse. Ours (Joint) consistently matches or outperforms the dataset-specific (Ours (Single)) models. For example, on TwoByTwo the rotation error drops from 18.7 to 13.2 (=30%), and on BreakingBad from 9.6 7.4 (x23%), while on ModelNet40, the rotation error is reduced from 1.37 to 0.93%. These results demonstrate that joint training enables the model to learn shared geomet- ric priors from datasets with diverse part segmentation, symmetries, and common pose distributions, which substantially boosts performance, particularly on datasets with limited training samples.

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Symmetry Handling. We demonstrate our model's ability to handle symmetry (Sec. IKEA- Manual [17] dataset with symmetric assembly configurations. As shown Fig. 6 while being only trained on single configuration (left), Rectified Point Flow samples various reasonable assembly configurations (right), conditioned on the same input unposed point clouds. Note how our model permutes the 12 repetitive vertical columns and swaps the middle baskets, yet always retains the non-intrrchangeable top and footed bottom baskets their unique positions.
Prediction
GT
Training
Generated
Example
Results
Figure 6: Learning from symmetric assembly. Left to right: (1) a single training sample from IKEA-
Figure 7: Two common failure types. First columm: Assemblies that are geomet- rically plausible but mechanically non- functional. Second column: Objects with high geometric complexity.
Manual [17), and (2-4) three independent samples gen- erated, conditioned on the same inputs. Parts are color- coded consistently across plots. (Best viewed color.)
Table 4:
Ablation on Encoder Pre-training, We ablate the impact of different pre-training tasks on the shape assembly performance. Our overlap detection pre-training yields the best results.
RE L [deg]
TE J [cm]
Part Acc
Dataset
Encoder
Pre-training Task
[%]
MLP
Pre-training
41.7
12.3
68.3
PTv3
Pre-training
18.5
4.9
79.5
BreakkngBaal-Eeerrdday
12
PTv3
Instance Segmentation
16.7
4.4
80.9
PTv3
54
Overlap Detection (ours)
9.6
1.8
93.5
Point-BERT 62
Point Cloud Completion
27.4
23.3
45.2
PartNet-Assembly 15
PTv3
54
Overlap Detection (ours)
24.8
15.4
50.2
Ablation Overlap-aware Pretraining. The first block of Tab. 4 compares four pretraining strategies for our flow-based assembly model on Breeerng [12]. The first two encoders (MLP and PTv3 without pre-training) trained jointly with the flow model. The last encoders are PTv3 pretrained on instance segmentation and our overlap-aware prediction tasks, respectively, Their pretrained weights are frozen during flow model training. We find that PTv3 is more powerful feature encoder compared to the MLP, and pretraining on instance segmentation can already extract useful features for pose estimation, while our proposed overlap-awar pretraining leads the best accuracy. We hypothesize that, although the segmentation backbone provides strong semantic features, only our overlap prediction task explicitly encourages the encoder to learn fine-grained part interactions and rre-assemlly cues, critical for precise assembly and registration.
To further compare against autoencoder-baase
pretraining, we substitute our encoder with Point- BERT (62)' s encoder, which is pre-trained on ShapeNet [63], superset of PartNet. We then train the flow model on PartNet under the same protocol. As reported in Tab. Point-BERT encoder reduces the Part Accuracy from 50.2% to 45. 15.2%, and worsens the accuracy in both TE and RE. We attribute this performance drop (i) Coint-BERT' pre-trained for masked point cloud completion, which does not explicitly encourage the encoder to capture inter-part relations (c.g., contacts) that our overlap-aware pretraining targets; and (ii) PointBERT's s default 64-group tokenization aggregates points into relatively coarse groups, losing fine lie-ggained geometric details for accurate pose estimation.

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Shape Prior Learning. To probe whether our model learns the shape priors of assembled objects better than pose-vector methods, we construct a cylindrical toy dataset. We train using a single part partition scheme and then evaluate on the same cylinder shapes but with different partition schemes.
Table 5: Part Accuracy [%] on Test- ing Part Schemes. Our model shows much less drop on OOD partitions.
Partition Scheme
GARF
Ours
Specifically, we generated 6,000 training cylinders with heights and diameters uniformly sampled from [0.2, 1.0] m, each cut into two parts by horizontal plane at random height. For testing, 600 new cylinders were cut under three schemes: (i) Horizontal (in dindistribution, ID), (ii) Axial: through the cen- tral axis at random orientation cuu-off-dsstrbbue
Horizontal (ID)
99.5
100.0
Axial (OOD)
89.5
97.0
Random (OOD)
87.5
97.8
All
92.1
98.3
OOD), and (iii) Random: through random 3D plane (OOD). As shown in Tab. 5 our method achieved part accuracies of 100.0%, 97. 97.0%, and 97.8% on three partition schemes, respectively. While GARF has comparable performance on the II) scheme, degrades on two OOD schemes, verifying that our model learns a transferable shape prior over the whole assembled object rather than overfitting to the part partition-specific patterns.
Table 6: Zero-shot Evaluation on the Unseen FRACTURA Testset. We report Part Accuracy (%) for GARF and ours and include the supervised performance for reference.
Setting
Method
Leg
Hip
Rib
Vertebra
Pig Bones
All
Supervised
GARF
89.7
80.8
74.8
60.8
79.0
77.3
GARF
70.5
72.8
62.9
37.7
53.4
57.7
Zero-shot
Ours
79.9
63.4
76.2
42.0
63.2
64.4
Generalization to Unseen Dataset. We evaluated the out-of-domain generalization of our model by performing zero-shot tests on unseen bone fracture on the test split of the FRACTURA dataset [II] covering human bones (Leg, Hip, Vertebra, Rib) and pig bones. We report Part Accuracy for our method and GARF [I]] in Tab. 6 Our model achieves strong zero-shot performance, surpassing GARF in most categories, especially Leg and Rib, and higher overall accuracy. While there remains gap to fully supervised training, we expect that pretraining and/or fine-tuning on medical datasets will further improve our model by instilling bone-specific shape priors and fracture geometry cues.
5 Conclusion
We introduce Rectified Point Flow, a unified flow-based framework for point cloud pose estimation across registration and assembly tasks. By modeling part poses velocity fields, it captures fine geometry, handles symmetrics and part interchangcabiiity, and scales to varied part counts via joint training 100K shapes. Our two-stage pipeline-overlap-ae -verlap-aware encoding and rectified flow training-achieve achieves state-of-the-al results on six benchmarks. Our work opens up new directions for robotic manipulation and assembly by enabling precise, symmetry- motion planning.
Limitations and Future Work. While our experiments focus on object-centric point clouds, real- world scenarios often involve cluttered scenes and partial observations. Moreover, while our model can generate multiple plausible assemblies, some of these may not be mechanically functional; see Fig. 7 (first column). Also, our model cannot handle objects that exceed certain geometric complexity: see Fig. (second column). Another limitation arises from the number of points our model can handle, which may restrict its usage large-scale objects. Future work will extend Rectified Point Flow to robustly handle occlusion, support scene-level and multi-body registration, incorporate object-function reasoning, and scale to objects with larger point clouds.
Broader Impact. Rectified Point Flow makes easier to build reliable 3D alignment and assembly systems straight from raw scans, benefiting robotics, digital manufacturing, AR, and heritage recon- struction. Given its performance and speed, it reduces the barrier for applying 3D part reasoning in resource-constrained settings. However, the model can still produce incorrect, hallucinated, or nonfunctional assemblies. For safety, further work on assembly verification and assembly error recovery will be essential.
10

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Acknowledgments and Disclosure of Funding
Tao Sun is supported by the Stanford Graduate Fellowship (SGF). Liyuan Zhu partially supported by SPIRE Stanford Student Impact Fund Grant. Shuran Song is supported by the NSF Award #2037101. We appreciate the authors of GARF [I] for providing the FRACTURA dataset. We also thank Stanford Marlowe Cluster [64] for providing GPU resources.
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Rectified Point Flow: Generic Point Cloud Pose Estimation
Supplementary Material
In this supplementary material, we provide following:
Model Details A): Description of the DiT architecture and positional encoding scheme.
Additional Evaluation (Sec. B
Runtime analysis.
Evaluation on the preservation of rigidity at the part level.
Comparison against category-speciff assembly models on PartNet and IKEA- -anual. Analysis of different generative formulations,
Evaluation of the anchor- free version of our model.
Randomness in Assembly Generation (Sec. C): Investigation of the assemblies generated through noise sampling and linear interpolation the noise space.
Generalization Ability (Sec.D) D): Qualitative results on unseen assemblies with same- or cross-
category parts test the model's generalization ability.
Proof of Theorem 1 (Sec. Ep: Formal definition of the assembly symmetry group and complete proof of the flow invariance under the group G.
Generalization Bounds (Sec. F Derivation of the generalization risk guarantees and comparison with that of existing 6-DoF methods.
A
Model Details
Condition Point Clouds
X
Assembled State
Nossed Points
[Xo(0)
Xz(0)
Xi [8o.
Ada LagerNorm
Part-wise Atccation
Ada LayerNorm
Global Attetion
Ada LayerNorm
MLP
MLP
Noised Point Clouds
Flow
Pos.
dXo
dX N
[X (x.6))
N
DIT Blocks
Velocity Field
Figure 8: Details of the DiT Block. Our flow model consists of an Encoder and a position embedding (Pos. Emb.), and sequential DiT blocks (N 6). Each block comprises Part-wine wise Attention, Global Attention, MIP, and AdaLayerNorm layers.
DIT Architecture. Our flow model consists of sequential DiT [55] blocks, each with a hidden dimension of 512. For the multi-head self-attention in the DiT block, set the number of attention heads to 8, resulting in a head dimension of 64. As illustrated in Figure 8) inspired by [73), we apply separated Part-wise Attention and Global Attention operations in each DiT block capture both intra intra-part and inter-part context:
Points within each part independently undergo a self-attention operation, improving the model's ability capture local geometric structures.
Part-wise Attention:
Global Attention: Subsequently, global self-attention operation is applied to all points across parts, facilitating inter-part information exchange.
we apply RMS normalization individually to the query and key features in each attention head before both attention operations to enhance numerical stability during training. Additionally, every DiT block employs Adal Adal ayerNorm, a layer normalization whose scaling and shifting parameters modulated by the time step following [55].
As discussed Sec. 4
14

---

Positional Encoding. We adopt multi-frequeen Fourier feature mapping 770, to encode spatial information in both the condition and noised point clouds. For the j-th point the i-th part in the condition point cloud, x X, we construct 10-dimensional vector, which comprises:
The 3D absolute coordinates of X..i
The 3D surface normal ni. at that point X.j in the condition point cloud.
The 3D absolute coordinates of the noised point cloud X (1) at the index (i,j).
The scalar part index 6.
Each of these vectors mapped through sinusoidal embeddings at multiple frequencies and then concatenated with the point-wise feature output of encoder F.
Inference. At inference time, recover the assembled point cloud of each part by numerically integrating the predicted velocity fields (t,, (X,(t))en X) from t = to t = 0. In practice, we perform K uniform Euler steps as,
{ A/) (1) (V. (x,(())))) X) where At 1/K.
After K iterations, the resulting (0) approximates the point clouds of all parts in the assembled state. For all evaluations, we set K 20.
B Additional Evaluation
Runtime Analysis. The number of sampling steps of the flow model is an important factor that affects both accuracy and runtime. In Tab. we vary the sampling steps and report the Part Accuracy, Chamfer Distance, and the runtime per sample in AastNet-Assembly, measured GPU. Increasing steps consistently improves accuracy and geometric precision, with diminishing returns beyond 20 steps. We K 20 sampling steps for all evaluations in the paper. In this setting, our model achieves 4.3 samples per second, making practical for robotic assembly and localization tasks that require frequent online inference.
single RTX 4090
Table 7: Trade-offs of Sampling Steps between Accuracy and Runtime. Metrics and runtime evaluated on PartNet-Assembll dataset with a single NVIDIA RTX 4090 GPU.
Sampling steps
10
20
Part Accuracy [%] f
25.2
38.1
46.7
52.1
53.9
54.6
Chamfer Distance [em]
3.23
1.70
0.90
0.75
0.73
0.71
Runtime sample [s]
0.072
0.081
0.108
0.148
0.232
0.483
Part-level Rigidity Preservation. As a dense point map prediction framework, Rectified Point Flow is not explicitly trained preserve the rigidity of each part. To quantify how well preserves the rigidity of the parts, we first align each predicted part (0) with the part assembled state (0) using the Kabsch algorithm.
We then measure over all points and (2) the Overlap Ratio (OR) over all points at varying thresholds 7 E (0.1,
rigidity preservation errors using (1) the Root Mean Square Error (RMSE)
00.1, 0.2, 1,2) em. Specifically, for part i with Mj points, compute
1 M.
RMSE
(0)l? and T
M
1 (6 ||T',, x0,( < <
OR (T)
M,
Here, T/ E SE(3) denotes the optimal rigid transform returned by Kabsch; x, and &;, denote the j-th point on (0) and on (O), respectively. Because each part is first rigidly aligned to the ground-truth assembled state, these metrics intentionally ignore pose errors, and only measure the shape difference between the predicted and ground truth point parts. To factor in the variations in
15

---

Table 8: Part-level Rigidity Preservation Evaluation. Rectified Point Flow demonstrates low shape discrepancy between condition and predicted part point clouds, measured by the Root Mean Square Error (RMSE), Relative RMSE, and Overlap Ratios (ORs) across datasets. represents the average object scale of each dataset. (Abbr: BreakingBad-F Breaking -aradddayyyyy: PartNet-A PartNet-Assembly IKEA-M IKEA-Manual.)
Shape Assembly
Pairwise Registration
Metric
BreakingRad-F
TwoByTwa Two
PartNet-A
IKEA-M
TUD-L ModelNet-40
Object Scale D
[em]
52.
107.7
89.0
61.4
40.8
70.0
RMSE
[em]
0.76
2.46
1.04
0.66
0.16
0.30
Relative RMSE
[%]]
1.5
2.3
1.2
1.1
0.4
0.4
OR (T 0.1 cm)
[%]] f
52.3
63.8
33.1
46.7
96.9
95.0
OR (T 0.2 cm)
[%]]
61.7
70.8
48.6
57.7
97.1
96.0
OR (T 0.5 cm)
[%]
74.9
76.8
66.8
69.8
97.4
96.3
OR (T = cm)
[%]] 1
81.4
78.7
77.9
81.0
97.7
96.6
OR (T cm)
[%]]
89.5
81.9
87.4
92.0
98.2
97.1
object size across datasets, compute the average scale of an object, denoted by D, twice the average distance from the object's center of gravity to all its points. Then, we define the Relative RMSE RMSE/ / D, i.e., the RMSE normalized by the average object scale. We report these metrics averaged for all parts in each dataset in Tab.
For the pairwise registration task, Rectified Point Flow demonstrates strong rigidity preservation. On TUD-L, we obtain Relative RMSE of 0.4% and ORs above 96.9% even at the strictest T 0.1 cm threshold; on ModelNet-40, we achieve the same Relative RMSE of 0.4% with similar high ORs above 95.0%. Specifically, on TUD-L we record ORs of 96.9% (r = 0.1 cm), 97.1% 1% (r = 0.2 cm), 97.4% (T 0.5 cm), 97.7% (r cm) and 98.2% (r = 2 cm); on ModelNet-40 the corresponding ORs are 95.0%, 96.0%, 96.3%, 96.6% and 97.1%, %, demonstrating consistently strong rigidity preservation.
In the more challenging shape assembly task, rigidity errors remain low. Across the four datasets, the Relative RMSE ranges from 1.1% to 2.3%. At strict threshold of r = 0.1 cm, overlap ratios (ORs) span 33.1 % (PartNet-Assemble up to 63.8 % (TwoByTwwo); By r = cm, the ORs exceed 77.9% in the four datasets (77.9% -1.4%..) increasing further to 81. 31.9%% in the more relaxed r 2 cm. The highest Relative RMSE and lower averaged ORs are observed in TwoByTwo, probably due to its limited training samples and lower shape similarity to other datasets, and the fact that TwoBy Two has the largest overall object scale of 107.7 cm among all datasets. In contrast, IKEA-Manual, despite having fewer training samples, benefits from shared priors in furniture objects in joint training, delivering the lowest RMSE and high ORs at all thresholds. These results demonstrate robust rigidity preservation Rectified Point Flow even in complex shape assembly scenarios.
Furthermore, please note that the subsequent pose recovery stage in Rectified Point Flow further refines part poses via an SVD-based global optimization, which fits optimal poses under noises. Overall, we empirically confirm that Rectified Point Flow generates point clouds that reliably respect the rigid structure the conditioning parts.
Comparison with Category-specffic Models. We compare against category-specific point-cloud assembly methods in Tab. 9 All baselines are trained separately for each category, and the category labels are assumed to be known at inference time. RGL-Net (66) additionally assumes top-to-bottom bottom ordering of the input parts. In contrast, Rectified Point Flow is class-agnostic and performs inference without any class label or part ordering. We evaluated both shape Chamfer Distance (CD) and Part Accuracy (PA) in PartNet-Assembly and IKEA-Manual, following the protocol of Huang et al. [47).
Without category or ordering assumptions like the baseline methods, our joint model still achieves the lowest CD and matches exceeds the PA of category speciffc baselines optimized for each category (chair, table, lamp). In particular, we observe a relative improvement 110.2% on Lamps PA over the strongest baseline. In IKFA-Manual, we observe that all category-specific models collapse to PA S 6.9% for the Chair category. We hypothesize that the baselines' architecture and hyperparameter largely tailored to PartNet. In contrast, our joint model achieves 29.9% PA for the Chair category
16

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Table 9: Comparison with Category-specifie Models. We report Shape Chamfer Distance (CD) and Part Accuracy (PA) on the PartNet-Assembly and AKEA-Manual, All baselines are trained per category, whereas Rectified Point Flow trained over all categories. ("RGI.-Net additionally requires a top-to-bottom part ordering.)
PartNet-Assembly
IKEA- Manual 17
Known Category
Chair
Table
Lamp
All
Chair
All
Method
CD 4
PA
PA
CD L
PA
CD J
PAT
CD
1
CD
PAT
[em]
[%]
[em]
[%]
[em]
[%]
[em]
[%]
[em]
[%]
[em]
[%]
B-LSTM
66
1.31
21.8
28.6
0.77
20.8
3.5
B-Global 65
1.46
15.7
1.12
15.4
0.79
22,6
1.95
0.9
RGL-Net* 66
0.87
49.2
0.48
54.2
0.72
37.6
5.08
4.0
Huang of al.
0.91
39.0
0.50
49.5
0.93
33.3
1.51
6.9
Ours (Joint)
0.71
44.1
0.36
49.4
0.49
70.0
0.48
53.9
1.49
29.9
0.48
33,2
Table 10: Generative Formulation Comparison. We compare Rectified Flow (RF) with Denoising Diffusion Probabilistic Model (DDPM) in our method, with both using the same DiT architecture and pretrained encoder. RF achieves superior performance on Rotation Error (RE) and Translation Error (TE) across all datasets. (Abbr: BreakingBad-F. = BreakingBad-Fverrydyy PartNet-A = PartNet- Assembly; IKEA-M = IKFA-Manual)
Generative Formulation
Shape Assembly
Pairwise Registration
Metric
BreakingBad-F
TwoByTwo
PartNet-A
IKEA-M
TUD-L
ModeINet-40
DDPM
13.0
17.2
29.5
21.4
2.6
RE [deg] J
RF
7.4
13.2
21.8
10.8
1.4
DDPM
3.5
10.1
21.3
19.2
0.5
0.7
TE [em]
RF
2.0
3.0
14.8
17.2
0.3
0,2
and 33.2% PA for all categories, over times higher than any baselines. Those observations confirm that our category-agnosti cross-dataset training improves the learning of shared geometric priors far beyond any single category or dataset.
Ablation on Generative Formulation. As an alternative to the generative formulation of Rectified Flow (RF) in our method, we also evaluate Denoising Diffusion Probabilistic Model (DDPM) [68 using an identical DIT architecture and the pre-trained encoder. In this setup, the forward noising process employs constant variances (8) that increase linearly from 10-4 to 0.02 over T = 1000
timesteps. As shown in Tab. [0] the RE-based model consistently outperforms the DDPM variant on both shape assembly and pairwise registration tasks, with 35.3% lower rotation error (RE) and 11.63% lower translation error (TE). This result is in line with the findings of GARF .T]. We hypothesize that the straight- line flow in RF reduces the learning difficulty in our tasks. DDPM's frequency-barr based generation which works well for images may not be as effective as RF for 3D point cloud synthesis in Euclidean space.
Anchor-free Models. In the anchor-free setting, we do not fix the anchor's pose. Instead, during training, we treat the anchor exactly like any other part the conditioning: point cloud is centered to its own CoM frame and then randomly rotated. The model, therefore, never receives the true anchor pose from condition. The flow target is defined in the anchor frame: we put the completed assembly point cloud in the anchor's frame and then re-center the whole assembled point cloud. At inference, we first estimate the rigid transform between the predicted anchor and the ground-truth anchor point cloud via ICP, and then apply this transform to all predicted parts. Metrics (RE, TE, and Part Acc.) are computed after this anchor alignment.
Across shape assembly datasets (Tab. IT and pairwise registration (Tab. 12). anchor-free (average) underperforms anchor-fixed as expected due to (i) error propagation from anchor misalignment and (ii) ambiguity induced by symmetric anchor parts. However, despite the lower absolute performance, our anchor-free ffree model preserves the same relative ordering among baselines on all shape-assembly datasets; the only exception is GARF, which is evaluated in the anchor-fixe fixed protocol. In particular,
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Table 11: Evaluation the Anchor-free Model on Shape Assembly Datasets.
Anchor-fixed
Anchor-free (Average)
Anchor-free (Best-of- 3)
Dataset
RE [deg]
f [%]
RE [deg]
PA f
RE 4 [deg]
TE
[cm]
[cm]
[%]
[em]
[%]
BreakingBad-F
12
93.5
17.4
90.2
13.0
5.9
92.2
TwoByTwo T6
13.2
3.0
15.2
24.2
9.0
16.7
PartNet-Assembly
15
21.8
14.8
53.9
47.3
40.5
45.3
38.2
32.9
54.3
IKEA-Manual [17
20.7
24.7
33.2
54.7
51.5
19.5
39.0
40.5
28.6
Table 12: Evaluation of the Anchor-free Model on Pairwise Registration Datasets.
ModeINet-40 19
TUD-L (18]
Setting
RE $
TE L
Recall 5
Recall @ lem f
[deg]
[unit]
[%]]
[%]
Anchor-fixed
0.93
0.002
97.7
99.0
Archor-free (Average)
2.05
0,012
96.6
96.3
Anchor-free (Best-of-3)
1.18
0.007
97.3
97.3
our model significantly improves anchor-free SOTA on Brakkiggaad-vveryday Part Accuracy from 76.2% (PuzzleFussion++ (251) 90.2%. For pairwise registration, our model is also achieving the lowest TE on ModelNet and the highest Recall@5" on TUD-L among baselines, while remain competitive on other metrics.
Furthermore, we observe that the anchor-free (best-of-3) evaluation, which selects the best prediction of different random seeds per sample, largely narrows the gap anchor-fixed. This indicates that a small stochastic budget may find more reliable anchor-free prediction. The effect is most pronounced on datasets with higher part count and weaker geometric cues (c.g., PartNet-Assembly and IKEA-Manual) where anchor ambiguity is stronger and small anchor errors propagate severely.
Generated Results by Different Z
Figure 9: Sampling in Noise Space. For each fixed condition input point clouds, we sample four independent Gaussian noise vectors to generate distinct assembly outputs (shown in columns 2-5). While all samples preserve the object's 's structure, they show meaningful variation in part placement, orientation, and overall geometry, particularly for symmetric parts (e.g., armrests and chair bases). For comparison, the first column shows the ground-truth assemblies.
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C Randomness in Assembly Generation
Diversity via Noise Sampling. To evaluate the diversity of assembly configurations generated by Rectified Point Flow, we sample the Gaussian noise vector Z multiple times for the same conditional (unposed) point cloud inputs. inference time, we X (1) Z and run the model to obtain single final assembly: the first column
prediction (0). In Figure each row corresponds shows the ground-truth assembly, and the next four columns display outputs produced by four different Gaussian noises. All generated assemblies preserve the part structure, yet exhibit meaningful variations in the parts' placement and orientation, and overall geometry of the object. As expected, the model produces diverse configurations for symmetric or interchangeable parts, such as the armrests and the chair base. This shows that Rectified Point Flow effectively captures a diverse conditional distribution valid assemblies.
I Linear Interpolation in Noise Space. We illustrate Rectified Point Flow's learned mapping from random Gaussian noise to plausible assembly configurations. same condition (unposed) point cloud, with the left and right columns showing the outputs of two randomly sampled noise vectors Zo and Z, respectively. The three columns in between display results generated by Zss) which linearly interpolates between Zg and Z₁ in noise space, i.c.,
Figure TO each row uses the
(s) = (1 2o + sZi, where E {0.25, 0.5, 0.75).
At each interpolation step s, we run inference with X(1) (s)). As increases, the predicted shapes smoothly morph from the configuration induced by Zo toward that of Zi. As shown in the first rows in Figure 10 we observe smooth transitions among interchangeable parts in both examples. The 2 bottom rows in Figure TO visualize the transitions in the overall structure of objects. In the table example, we observe a gradual reduction in overall height, a lowering of the horizontal beams, and more centralized positioning where the four legs meet. In the shelf example, the transformation
Noise
Interpolated Noise Z(s) (1 Z) + aZ
Noise Z
Part Interchanging
Structural Changing
Figure 10: Linear Interpolation in Noise Space. For different objects in each row, we fix the same conditional input and decode two independently sampled Gaussian noise vectors, Zo (leftmost) and Zi (rightmost), into plausible part configurations. The three center columns show outputs from the linearly interpolated noises between Zo and Z,. We observe continuous, semantically meaningful mapping from Gaussian noise to valid assemblies.
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Object
Object 2
Generated Results
Figure 11: Generalization to Unseen Assemblies Within the Same Category: We select parts from two objects of the same category the PartNet-Assembly test set. Parts from Object are shown in blue, and parts from Object 2 in red; unselected parts shown in gray. The results demonstrate that the model comprehends the underlying geometric structure of the category and can re-target parts to construct the final shape.
more drastic: two vertical boards become horizontal and two diagonal cables are rearranged to new vertical configuration. The above transitions across various assemblies confirm that Rectified Point Flow learns continuous mapping from Gaussian noise semantically meaningful geometry space, Note that most of the interpolated configurations are physically plausible assemblies, creating functional objects that can stand in real-world.
D Generalization Ability
We test the generalization ability of our model for novel assemblies under two different settings: between objects from the same (in-category) and different (cross-category) categories. Given two objects in PartNet-Assembby. we select certain parts from each of them the input Rectified Point Flow to test the model can generate novel and plausible assemblics.
In-category Test. As shown in Fig. parts selected from Object 1 rendered in blue and those from Object 2 in red. Our model then synthesizes novel assemblies that blend and reconfigure these parts in coherent and category-consistett manner. For example, in the chair category (first two rows), the model successfully retains a functional and plausible seat-back-leg structure while creatively mixing parts. In the lamp category (third row), even though the base and shade style differ significantly between objects, generated results exhibit sensible combinations that maintain structural integrity. Similarly, the table category (last row), our method combines parts from flat-top table and lattice-ste styll base to produce hybrid yet coherent table designs.
Cross-category Test. Fig. highlights Rectified Point Flow's ability to generalize unseen part combinations across categories. This is particularly challenging test, since such part combination
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Object
Object 2
Generated Results
Figure 12: Generalization to Unseen Assemblies Across Categories: We select parts from two objects of different categories in the PartNet-Assembly test set. Parts from Object are shown in blue, and parts from Object 2 in red; unselected parts shown in gray. The results demonstrate that the model can reason about part compositionality and re- re-target parts to construct a plausible final shape even if some of them originate in completely different objects.
may not even be possible to be assembled into meaningful object. Nevertheless, our method still demonstrates certain degree of generalization. We show two input objects from different categories, for example, a monitor and a chair, a chair and lamp, or a wall sconce and spray bottle. The results on the right demonstrate that our model reconfigure these parts into plausible new assemblies, preserving geometric coherence. This suggests that the model has learned strong understanding of part relationship, allowing it to reason about compositionality across category boundaries.
E Proof of Theorem 1
key advantage of Rectified Point Flow is that it learns both rotational symmetrics of individual parts and the interchangcability of set of identical parts, without any labels of symmetry parts. Below, we first formally define an assembly symmetry group G that characterizes the symmetry and interchangeability of the parts in the multi -art point cloud.
Definition 1 (Assembly symmetry group). For each part E Ω, let G, S SO(3) be the (finite) stabilizer of its assembled shape, i.c. RX2(0)= X2(0) for all R E G.. Let Bin be the set of permutations that only permute indices of identical parts. We define the assembly symmetry group as the semidirect product
g = (G1 ... x Gja) S.
(8)
A group element g = (RI,.... Rgy σ) E G acts on every realization of the Rectified Point Flow by (()((t)) = R, X, 160 and on network outputs of the i-th part (denoted as V.)
by g( (V.(t, (X))) : R, (tt,
Now, we show the following result that single point's flow distribution is invariant under any g E G. Lemma I (G-invariance of the flow distribution). For every element g G and given multi-part point cloud X, we sample a flow realization:
x(t) tx(1) + (1 t)x(0)), where x(1) ~ NO0, ~ X.
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then, we have
r(lg x(1))e(0.1) = p((((1))ee)
Proof. Recall that, in Rectified Point Flow, flow of single point is x(t) == (1 =)x(() tx(1),
where x()) ~ X is drawn uniformly from the assembled shape and x(1) ~ 00, I). Because the
(0,
end-points of the linear interpolation are sampled independently, the PDF of the path distribution
factorizes as
p p((x())eeo.1) - =x((()))(((0))
which indicates the randomness resides by the states / and / only. Because the perturbation x(1) (0, I) is isotropic, ((x(1)) is invariant under every rotation R E SO(3). For p(x(0)) we distinguish two cases:
Rotational symmetry: If R G,, then RX = (() point-wise, so p(x(0)) = p(Rx(O)).
Interchangeability If parts and j are identical, sampling first a part index with probability p(t) = N,/N and then point uniformly inside it implies p(x(0) E Xx(O)) p(x(0) (
Therefore exchanging the indices (a = j. o = i) leaves p(x(0)) unchanged.
By composing the above two properties for all parts, we complete the proof.
Lemma [ can directly lift from single points to the full multi part flow (X:(t) This leads us the Theorem [ For every element G, we have the learning objective Eq. following RCFM(V) LCFM(g(V (()))))
F Generalization Bounds
While the Rectified Point Flow predicts a much ligher-dimensional space (3M, coordinates per part), we find that its Rademacher complexity scales exactly the same rate as the 6-DoF methods, 0(1//m), where is the number of samples in the training set.
Below, compute their Rademacher complexities and empirical risks, respectively. Without loss of generality, we use the reconstruction error for the evaluation of poses, i.e., E(R, E; Rt t*) [| (((R-R*)) X - fl First, we define hypothesis classes for both methods:
Our Rectified Point Flow:
F. = (C (0:00) where X;(0;0) = X,(1) Vi(1;C,0)d.
Pose vector-based flow:
G. (C. to
Rademacher Complexity of Rectified Point Flow. With i.i.d. training objects D
{(C(k) (k)k), (*(k),(*())))) k= we write the population risk R(h) = =E [(((h(C), t*)] and empri- cial risk
RD( - 1 m
Σ (((CO)) R((1) (())
Since our Rectified Point Flow method estimates the part pose by the Procrustes operator, i.e., (R, f) = Pr( (0; f)), where Pr R3N + SE(3) is the Procrustes operator, we have following Lipschitz contracting property.
Property (Lipschitz Contracting). Let X ER3N be the centralized ground-truth point set of single part, and denote Guin mmin ( (X* solution (R, P(X(0) (0)) satisfies
X*). x() X* the optimal Procrustes
(I(R R¹ i- t*)l
(10)
Vomin
22

---

This property directly follows from Davis Davis-Kahan perturbation bounds [67 for the Top-3 singular vectors. Crucially, min [(N]) for well-spread point clouds, so Pr is VN
Lipschitz map.
Let (H) denote the empirical Rademacher complexity on S. Because composition with L-Lipschitz map contracts Rademacher complexity
Lev3N
of
Lo
Rm FP I
Rm(FF &
(11)
mm
Rademacher Complexity of 6DoF-based Methods. For the baseline we need only regress d numbers, hence
Lovd
of
L vm
Nmm (9) S vm
(12)
Comparison of Generalization Bounds. Applying Bartlett Theorem and using 10 with probability at least 5 over the samples from D,
obtain,
log(2/6)
R(Pof) s (P((of) + 2 ( + +31
(FLoww)
2m
log(2/6)
R(O) & RD(g) + 2. +
(6DoF)
2m
where fEF and EGG are the empirical-risk minimizers on S.
In conclusion, while Rectified Point Flow predicts much higher-dimensional space, the contraction of the SVD stage cancels this apparent over- wer-parameterizzaion, producing a complexity term that scales at the same rate of ((1//m) (1/mm) as the 6-DoF baseline; (FL.W (DDFF).
As result, method enjoys least same generalization risk guarantees despite operating in over wver-parameterized prediction space, while retaining the G-invariance benefits proven in Sec. E
References
[67] Chandler Davis and William Morton Kahan. The rotation of eigenvectors by perturbation. iii. SIAM Journal on Numerical Analysis, 7(1):1-46, 1970.
[68] Jonathan Ho, Ajay Jain, and Pieter Abbeel. Denoising diffusion probabilistic models. Advances in neural information processing systems, 33:6840- 1116600-551,,,, 2020.
[69] Shengyu Huang, Zan Gojeic, Jiahui Huang, Andreas Wieser, and Konrad Schindler. Dynamic 3d scene analysis by point cloud accumulation. ECCV, 2022.
[70] Ben Mildenhall, Pratul Srinivasan, Matthew Tancik, Jonathan Barron, Ravi Ramamoor- thi, and Ren Ng. Nerf: Representing scenes as neural radiance fields for view synthesis. Communications of the ACM, 65(1):99-106, 2021.
[71] Abhinav Narayan, Rajendra Nagar, and Shanmuganathan Raman. Rgl-net: A recurrent graph learning framework for progressive part assembly. WACV, 2022.
[72] William Peebles and Saining Xie. Scalable diffusion models with transformers. arXiv preprint 1rXiv:2212.099 097448, 2022.
[73] Jianyuan Wang. Minghao Chen, Nikita Karaev, Andrea Vedaldi, Christian Rupprecht, and David Novotny. Vggt: Visual geometry grounded transformer. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2025.
Here, (2-) denote the asymptotic rate, instead of part index set.
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Reviews:
[{"review_id": "ODFTYdnVwn", "reviewer": "Reviewer_oaRr", "summary": "This paper introduces point-cloud registration and part assembly at the object level. The authors propose the Rectified Point Flow to achieve a generalizable point cloud pose estimation scheme and show good results across multiple benchmarks.", "questions": "1) How efficient is the overlapping training strategy? All successful results in the paper seem to involve relatively simple parts to be assembled, e.g., the dining table, lamp, etc. However, in the failure case, when the parts become less determinative (e.g., the Wassily Chair), the method fails to assemble them.\n2) Is there any performance evaluation on out-of-domain data? I understand that the authors trained across different datasets and used a train/test split, yet there is no demonstration of how distinct the train and test sets are. Especially, there is no out-of-domain evaluation.", "limitations": "Yes.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths:\n1) The numerical results are good; the proposed method achieves better performance than other counterparts on different datasets.\n2) The idea of considering point cloud registration and multi-part shape assembly as a conditional generative problem seems to work on sythentic object-level datasets.\n\nWeaknesses:\n1) Method: The overlapping training strategy seems to work only for objects with clear and determinative parts to be assembled, which may be suitable for synthetic toy datasets but not sufficient for most in-the-wild real objects. The claimed 'generic' nature of the method should be toned down.\n2) Evaluation: The current evaluation scheme does not fully support the claimed 'generic' performance, as all evaluations are conducted on an in-domain basis. This setup only demonstrates that the Rectified Flow performs better than other baselines in terms of 'remembering' the dataset, rather than validating the proposed method's generalization capability.", "was_revised": true, "final_justification": "Thank you for responding to my questions. The rebuttal addresses most of my concerns, and I am inclined to accept this paper. I recommend that the authors include these discussions and experiments in the final version to further strengthen the work.", "rebuttal": "We sincerely thank the reviewer for the thoughtful feedback, and particularly for highlighting our \"novel formulation of pose estimation as a conditional generative process\" and recognizing our \"strong numerical performance.\" We appreciate the constructive suggestions, which help us improve the quality of our paper. Below are our responses to the comments.\n\n---\n\n> **Q1**: The overlapping training strategy seems to work only for objects with clear and determinative parts to be assembled, which may be suitable for synthetic toy datasets but not sufficient for most in-the-wild real objects. The claimed \"generic\" nature of the method should be toned down.\n\nWe appreciate this insightful comment and agree that it is important to address both **(1)** the applicability to real-world meshes and **(2)** the handling of objects with less clearly defined boundaries or overlapping regions.\n\nFirst, please note that our evaluation in the main paper already includes the TUD-L \\[18] dataset, which features real-world 3D scans obtained from depth camera, including partial observations and sensor noise.\n\nTo further stress-test our method in this challenging setting of real-world meshes, we conducted additional zero-shot experiments on the **3RScan** \\[A] dataset, following the protocol of LivingScenes \\[26]. 3RScan consists of room-scale scans captured with real-world RGB-D sensors, and involves relocating objects in a secondary scan, introducing  real-world distributions of noisy points and overlapping regions. Notably, both the dynamic range and noise levels in 3RScan are significantly higher than those in TUD-L. Following \\[26], we report the Registraion Recall (%, higher is better) and mean Rotation Error (degree, lower is better). Plus, we report the Translation Error (cm, lower is better).\n\n| Method           | Registration Recall [%] | Rotation Error [deg] | Translation Error [cm] |\n|------------------|:-----------------------:|:--------------------:|:----------------------:|\n| *LivingScenes*    |           *61.1*          |          *7.9*         |            -           |\n| GARF, zero-shot |           0.2          |         38.4         |          26.2          |\n| Ours, with PointBERT encoder, zero-shot |           14.1          |        23.4         |           7.9          |\n| Ours, zero-shot |           **58.9**          |         **11.3**         |           **2.0**          |\n\nFrom the table, we observe that not only does our method substantially outperform the previous strong baseline, GARF, but it also approaches SOTA performance as established by LivingScenes, without ad-hoc test-time optimization as in LivingScenes. \n\nTo further highlight the effectiveness of our overlap-aware encoder and pretraining strategy, we conducted an ablation study where we replaced our encoder with PointBERT's encoder; details in our response to **Reviewer haCE** (Q2). Importantly, in this setting, the flow model is still trained jointly across all datasets, just as in our full model. Nonetheless, performance drops significantly across all metrics, clearly demonstrating that our overlap-aware pretraining design is critical for robust performance in diverse inter-part boundaries and overlap regions.\n\n\nRegarding the term \"generic,\" we acknowledge the need for clarity that we use \"generic\" to refer to the generic nature of our overlap-aware pretraining across **a wide spectrum of part definitions**. In fact, we train and test our method on six datasets, each with different part definition, specifically:\n\n1. **TUD-L** \\[18\\]**:** Part segmentation obtained from real-world 3D scans, which include partial observation and noise.   \n2. **ModelNet** \\[19\\]**:** Parts segmented by randomly posed planes.\n3. **BreakingBad** \\[12\\]**:** Parts are fractured with physical simulation by applying external forces to the object surface;  \n4. **PartNet** \\[15\\]: Segmentation based on expert-defined hierarchical taxonomies focused on part reusability across objects;  \n5. **IKEA-Manual** \\[17\\]: Part segmentation defined by functional roles in furniture;  \n6. **TwoByTwo** \\[16\\]**:** Segmentation annotated for robotic insertion tasks;\n\nThis generic encoder features joint training across varied datasets and part definitions, further enhancing performance.\n\nFinally, we will update the manuscript to more clearly scope and define our use of \"generic\", which is different from \"general\" and \"generalizable\".\n\n\n**Reference**\n\n\\[A] Johanna Wald, et al. \"RIO: 3D object instance re-localization in changing indoor environments.\" ICCV, 2019.\n\n---\n\n> **Q2**: How efficient is the overlapping training strategy? All successful results in the paper seem to involve relatively simple parts to be assembled, e.g., the dining table, lamp, etc. However, in the failure case, when the parts become less determinative (e.g., the Wassily Chair), the method fails to assemble them.\n\nAs shown in Table 4 of the main paper, we present an ablation study comparing our overlap-aware pretraining strategy against alternatives, including random initialization and pretraining with a semantic segmentation task, where our pretraining yields the best performance. Additionally, as detailed in our response to **Reviewer haCE** (Q2), we substituted our encoder with PointBERT’s encoder (pretrained on ShapeNet) and observed that our overlap-aware pretraining still outperforms this baseline, demonstrating both efficiency and effectiveness in learning part-aware representations.\n\nThe assembling of 3D shapes remains a highly challenging problem, particularly for objects with ambiguous or weak geometric cues. On furniture assembly tasks (e.g., PartNet, IKEA-Manual), prior methods such as B-LSTM [66] and RGL-Net [65] struggle with performance and require the object category as part of the input, while our method outperforms them **without** such category input. On fracture reassembly (e.g., BreakingBad), our method is competitive with state-of-the-art methods such as GARF.\n\nFor challenging cases like the Wassily Chair, the core difficulty is not just the part definition or overlap points detection, but the inherent lack of discriminative geometric cues. This ambiguity means that the same parts could be plausibly assembled into entirely different objects, making the task under-constrained from geometry alone. We acknowledge this limitation and will include it in the paper that assembly in such cases likely requires additional context information, which is an open problem in the field. \n\nIn summary, while all geometric shape assembly methods (including ours) are limited in severely under-constrained cases, our unified point flow formulation, generic pretraining, and symmetry handling advance state-of-the-art performance in real-world scenarios. We appreciate the reviewer highlighting this important direction for future research.\n\n---\n\n> **Q3**: Is there any performance evaluation on out-of-domain data? I understand that the authors trained across different datasets and used a train/test split, yet there is no demonstration of how distinct the train and test sets are. Especially, there is no out-of-domain evaluation.\n\nWe agree that out‑of‑domain (OOD) zero-shot evaluation is valuable. In addition to the zero-shot results on 3RScan [A], in our response to **Reviewer yLRg** (Q2), we also performed zero-shot evaluation on the unseen **Fractura** [11] dataset for the shape assembly task, which includes bone scans from various body parts. Consistent with previous findings, our model outperforms GARF in the zero-shot setting.\n\nWe would like to clarify, however, that our paper does **not** claim universal cross-domain generalization or a foundation 3D assembly model. Rather, our focus is on a generic formulation across diverse part definitions, tasks, and symmetries within the domains studied. Generalization to arbitrary OOD data or developing a foundation assembly model remains an open challenge for future work."}, {"review_id": "x4HY68DLad", "reviewer": "Reviewer_haCE", "summary": "This paper presents a unified formulation of point cloud registration and multi-part shape assembly as a conditional generative modeling problem. To address this, the authors propose Rectified Point Flow, a flow-based model that explicitly handles symmetry and part interchangeability—challenges commonly faced in assembly tasks. The method demonstrates strong performance on both shape assembly and registration benchmarks, outperforming prior approaches that rely on deterministic or SE(3)-based optimization.", "questions": "- Chamfer Distance in Main Results: Could the authors include the shape Chamfer Distance (CD) in Tables 2 and 4, alongside pose metrics? This would provide a more comprehensive evaluation aligned with the method’s stated goals.\n- Comparison with Self-supervised Pretraining: In Table 4, only no pretraining and supervised methods are compared. Please consider including results with standard self-supervised methods (e.g., PointBERT or similar baselines) to contextualize the benefit of the proposed overlap-aware pretraining.\n- Overlap Label Symmetry: The overlap supervision seems to assign binary labels to points based on spatial proximity (e.g., only the top region of chair legs is marked as overlapping in Fig. 2). Given that parts like chair legs are symmetric and can be assembled in reverse, does the current labeling overlook valid symmetrical configurations? How does the model handle such ambiguity?\n- Anchor Part Selection: Line 118 states that the anchor part is chosen as the first part in the input. Could the authors clarify how the input order is determined? If the order is based on part size or another heuristic, is the assembly result sensitive to different anchor choices?", "limitations": "Yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 4, "strengths_and_weaknesses": "**Strengths**\n- Originality: The paper is the first to model point cloud registration and multi-part shape assembly under a shared conditional generation framework. This is a notable departure from prior works that treat the two tasks separately. In contrast to methods like GARF, Rectified Point Flow can naturally handle ambiguous or interchangeable parts.\n- Quality & Clarity: The proposed model is thoroughly evaluated through multiple ablations and visualizations. For instance, Figure 4 illustrates how the model scales to larger assemblies, and Table 2 compares both per-task and joint training strategies, clearly showing the benefits of joint learning. Supplementary experiments (e.g., Fig. 11 on cross-category generalization) further strengthen the motivation for using generative modeling for assembly.\n- Significance: Addressing part ambiguity and interchangeability is central to robust 3D assembly. This work provides a practical solution through generative modeling in Euclidean space, potentially influencing downstream applications such as robotic assembly or 3D scene synthesis.\n\n**Weaknesses**\n- Clarity: While the paper proposes a pretraining approach using overlap prediction, it does not compare this to standard self-supervised pretraining techniques (e.g., PointBERT), leaving unclear whether the proposed strategy is necessary or optimal.\n- Clarity: Although the method is motivated by ambiguity and interchangeability, most evaluation metrics in the main paper focus on pose accuracy. Measuring the Chamfer Distance (CD) of the assembled shape would better reflect success under these challenges. While CD is reported in the supplementary (Tab. 5), it is missing from the main tables (Tabs. 2 and 4), making comparisons less complete.", "was_revised": true, "final_justification": "After reading the rebuttal and the other reviews, my concerns on the evaluation metrics and pre-training are resolved. Therefore, I recommend to accept this paper.", "rebuttal": "We would like to sincerely thank the reviewer for their constructive feedback and suggestions. We are particularly grateful for highlighting our method as \"the first to model point cloud registration and multi-part shape assembly under a shared conditional generation framework,\" which is \"a notable departure from prior works.\" We also appreciate for the comments that our model \"explicitly handles symmetry and part interchangeability—challenges commonly faced in assembly tasks,\" and for noting its potential to \"influence downstream applications such as robotic assembly or 3D scene synthesis.\" Below are our response to the comments.\n\n---\n\n> **Q1**: Chamfer Distance in Main Results: Could the authors include the shape Chamfer Distance (CD) in Tables 2 and 4, alongside pose metrics? This would provide a more comprehensive evaluation aligned with the method’s stated goals.\n\nBelow is the Chamfer Distance (CD, cm, lower is better) metric between our method and GARF over all datasets we evaluated. Our method is consistently better than or on par with the best-performing baseline, GARF across different datasets. We will include the CD numbers in both Tables 2 and 4.\n\n| Task                  | Dataset       | GARF [CD]   | Ours [CD]         |\n|-----------------------|---------------|:-------:|:------------:|\n| Pairwise Registration | TUD-L         |  0.042   | **0.016**     |\n|                       | ModenNet-40   |  0.109   | **0.023**    |\n| Shape Assembly        | BreakingBad-Everyday| **0.025**    | 0.029    |\n|                       | PartNet    |  1.82   | **0.73**     |\n|                       | TwoByTwo   |  2.38   | **0.32**     |\n|                       | IKEA-Manual|  3.28   | **1.96**     |\n\nPlease note that the CD values in Table 5 of the Supplementary Material differ due to a different averaging scheme. For a valid comparison with pose-graph methods \\[65, 66], we average CD following their convention of assigning each part with the same number of points, whereas in our approach and GARF, the number of points per part is proportional to surface area.\n\n---\n\n> **Q2**: Comparison with Self-supervised Pretraining: In Table 4, only no pretraining and supervised methods are compared. Please consider including results with standard self-supervised methods (e.g., PointBERT or similar baselines) to contextualize the benefit of the proposed overlap-aware pretraining.\n\nThanks for this insightful suggestion. We have tested PointBERT [D]’s encoder (dVAE) as a substitute for our own pretrained feature encoder. Following PointBERT’s configuration, we used their encoder weights pre-trained on ShapeNet meshes. Note that ShapeNet and PartNet share the same meshes; PartNet only adds part annotations to a subset of ShapeNet's objects. Using this setup, we trained our flow model on PartNet. The evaluation results are presented in the table below.\n\n| Encoder | Part Acc. \\[%\\] | Chamfer Dist. \\[cm\\] | Rot. Err. \\[deg\\] | Trans. Err. \\[cm\\] |\n| :---- | :---: | :---: | :---: | :---: |\n| PointBERT Encoder | 45.2 | 1.92 | 27.4 | 23.3 |\n| Our Pretrained Encoder | **53.9** | **0.73** |  **21.8** | **14.8** |\n\nWe observe that when using PointBERT’s encoder, the Part Accuracy drops to 45.2%, whereas our pretrained encoder achieves 53.9%, reflecting a 16% relative improvement. Furthermore, localization metrics deteriorate significantly with PointBERT’s encoder — for instance, Chamfer Distance increases from 0.73 cm to 1.92 cm (a 2.6x increase). We attribute these differences to two main reasons:\n\n1. PointBERT’s encoder is trained for reconstruction on ShapeNet point clouds but is not explicitly optimized for capturing inter-part relationships as our encoder, e.g., overlapping regions.  \n2. The grouping mechanism inside PointBERT’s encoder (with 64 groups by default) limits its ability to preserve fine-grained local geometric details, leading to higher localization errors.\n\nWe will include this experiment in Table 4.\n\n**Reference**\n\n[D] Xumin Yu, et al. \"Point-bert: Pre-training 3d point cloud transformers with masked point modeling.\" in CVPR, 2022.\n\n---\n\n> **Q3**: Overlap Label Symmetry: The overlap supervision seems to assign binary labels to points based on spatial proximity (e.g., only the top region of chair legs is marked as overlapping in Fig. 2). Given that parts like chair legs are symmetric and can be assembled in reverse, does the current labeling overlook valid symmetrical configurations? How does the model handle such ambiguity?\n\nThis is a good point. Our overlap labels are based on spatial proximity, which may not capture all symmetrical configurations. However, the flow model itself is designed to account for symmetries based on the per-point feature during training and inference, which can model multiple valid symmetrical configurations beyond what the overlap supervision specifies. More explanation and experiment of the generalization w.r.t. symmetry configurations can be found in our response to **Reviewer JGmh** (Q4).\n\n---\n\n> **Q4**: Anchor Part Selection: Line 118 states that the anchor part is chosen as the first part in the input. Could the authors clarify how the input order is determined? If the order is based on part size or another heuristic, is the assembly result sensitive to different anchor choices?\n\nDuring training, part order is randomly shuffled at each iteration for all tasks, so the anchor part is selected randomly. During inference, for the shape assembly task, we select the part with the largest volume as anchor, which is a standard approach for shape assembly, following GARF. For the pairwise registration task, we follow the datasets' pre-defined `target` point cloud as the anchor."}, {"review_id": "89KmTQGue8", "reviewer": "Reviewer_q4io", "summary": "This paper proposes Rectified Point Flow (RPF), which is a unified framework for 3D point cloud pose estimation, addressing both pairwise registration and multi-part shape assembly problems as a single conditional generative task. RPF learns a continuous point-wise velocity field to transport noisy points to their target positions, from which poses are then recovered. This approach inherently learns and handles assembly symmetries without explicit labels. Coupled with a self-supervised encoder that focuses on overlapping points, RPF achieves state-of-the-art performance across six benchmarks.", "questions": "Experiments: \n- The trade-off between time complexity and quality. What the results will be with different iterations of conditional generation.\n- The size of the point cloud. Are the point clouds sampled to the same fixed number of point clouds? What is the value of M_i? Will it be different for parts?\n- Baseline. Do the baselines also use the pre-trained dataset used in RPF?\n- The straight-line interpolation is used for each part (line 153). Does this linear interpolation matches the flow process, which is unlikely to be linear?\n- It would be good to see the denoising intermediate results in the main text.\n- What is the effect of the overlap self-supervised pre-training? It would be good to see the results with and without the self-supervised task in the main text.", "limitations": "Yes. The failure cases were discussed (Fig. 7).", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths\n\n- Both pairwise registration and multi-part assembly tasks are tackled in a unified framework of per-part pose estimation with the proposed point flow based point cloud pose estimation method.\n- A explicit function of overlap prediction between parts is formulated to facilitate the learning of inter-part relationships.\n- The comparison with state-of-the-art shows performance improvement across the evaluated metrics.\n\nWeaknesses\n\n- The experimental comparison against baselines may be biased due to the usage of the pre-trained dataset.\n- time consumption. Time complexity comparison is missing. \n- others as listed in the questions.", "was_revised": true, "final_justification": "The authors added further analysis and experimental result to address my concerns. They promise to include those in the revised manuscript.", "rebuttal": "We sincerely thank the reviewer for their insightful and constructive feedback and greatly appreciate the recognition of our \"unified framework for both pairwise registration and multi-part assembly tasks.\" Please find our responses to the comments below.\n\n---\n\n> **Q1** The experimental comparison against baselines may be biased due to the usage of the pre-trained dataset. Do the baselines also use the pre-trained dataset used in RPF?\n\nWe would like to point out that in all baseline methods, only GARF proposed pretraining in their method and GARF is the strongest baseline. Other baselines do not require or include pretraining in their methods. For GARF, we use the same pretraining dataset as in RPF for a fair comparison. As shown in Tables 2 and 3, our method outperforms GARF across the board. In our ablation study (Table 4), we also show the effectiveness of our proposed pretraining task. \n\n---\n\n> **Q2**: The trade-off between time complexity and quality. What the results will be with different iterations of conditional generation.\n\nWe thank the reviewer for highlighting this important trade-off. As suggested, the primary variable affecting both runtime and accuracy is the number of sampling steps (iterations). Below, we provide a table summarizing Part Accuracy, Chamfer Distance, and runtime per sample at different sampling steps on PartNet dataset. All tests were performed on a single RTX 4090 GPU. \n\nWe find that performance nearly saturates for steps greater than 50, and that the best trade-off balancing speed and accuracy is at 20 steps, which has already been used in all evaluations in the paper.\n\n| Sampling steps               | 1 | 2 | 5 | 10 | 20 | 50 |\n|----------------------|------|-------|-------|--------|--------|--------|\n| Part Accuracy \\[%]    |  25.2  | 38.1    | 46.7   | 52.1    |   53.9   |  54.6    |\n| Chamfer Distance \\[cm] |  3.23  |  1.70   |  0.90   |   0.75   |  0.73   | 0.71  |\n| Runtime per sample \\[s] | 0.072  | 0.081 |  0.108   | 0.148    | 0.232    | 0.483    |\n\nFor reference, below is the detailed runtime breakdown for the 20-step setting: most of the runtime is attributed to the flow model, as expected.\n\n| Stage                          | Runtime per sample \\[s] | Percentage \\[%] |\n|------------------------------- |-----------------------|---------------|\n| Point cloud encoder            | 0.055                 | 23.7          |\n| Flow model with 20 sampling steps    | 0.169                 | 72.8          |\n| Rigid transformation fitting by SVD   | 0.008                 | 3.5           |\n| **Total**                      | **0.232**             | 100.0           |\n\nWe will include these results in the revised manuscript.\n\n---\n\n> **Q3**:  The size of the point cloud. Are the point clouds sampled to the same fixed number of point clouds? What is the value of M_i? Will it be different for parts\n\nIn our experiments, we sample 5000 points per object, over all its parts. The number of sampled points $M_i$ for the $i$-th part is proportional to that part’s surface area. This sampling ensures that the flow is equivalent with respect to the assembly symmetry group. Further details can be found in Section E of the Supplementary Material.\n\n---\n\n> **Q4**: The straight-line interpolation is used for each part (line 153). Does this linear interpolation matches the flow process, which is unlikely to be linear?\n\nWe have visualized the flow process of each point at inference time and found that most of the point trajectories are close to straight lines. It is true that, during inference, the generated flows may indeed be nonlinear. This drift (i.e., error accumulation) during inference is a well-known issue for flow-based models \\[B, C]. While test-time optimization techniques may help mitigate this, we leave this to future work. \n\n**Reference**\n\n\\[B] Liu, Xingchao, Chengyue Gong, and Qiang Liu. \"Flow straight and fast: Learning to generate and transfer data with rectified flow.\" in ICLR 2023.\n\n\\[C] Zhou, Zhengyu, and Weiwei Liu. \"An Error Analysis of Flow Matching for Deep Generative Modeling.\" Forty-second International Conference on Machine Learning.\n\n---\n\n> **Q5**: It would be good to see the denoising intermediate results in the main text.\n\nThanks for the suggestion. We will include additional flow trajectories and denoising states visualizations to illustrate the intermediate results in the revised manuscript.\n\n---\n\n> **Q6**: What is the effect of the overlap self-supervised pre-training? It would be good to see the results with and without the self-supervised task in the main text.\n\nWe provide this ablation in Table 4 of the main paper, comparing our overlap-based pretraining against no pretraining (random initialization) and semantic segmentation pretraining. Additionally, we also substituted our encoder with PointBERT's pretrained encoder in our response to **Reviewer haCE** (Q2). We found that our overlap-aware pretraining remains the most effective one among all these alternatives evaluated. \n\nMoreover, our pretrained encoder demonstrates particularly strong out-of-domain performance in challenging real-world scenarios such as the 3RScan dataset; see our response to **Reviewer oaRr** (Q1) for details. We will further highlight these results in the revision to clarify the contribution and effectiveness of our pretraining strategy."}, {"review_id": "FU2Ohieuz9", "reviewer": "Reviewer_yLRg", "summary": "This paper proposes rectified point flow, a framework that can treat point cloud registration and multi-part shape assembly in a unified manner. The key idea is to adopt the recently popular flow matching technique into the classic point cloud pose estimation problem, which remarkably accommodates both pair-wise and multiple components settings. Overall the idea is interesting, and the experimental validation suggests sufficient advantage over the competing baselines.", "questions": "- The reported models are mainly trained on instance-level man-made datasets. Some important applications of shape assembly come from medical tasks. I am wondering 1) the current method relies on an overlap estimation module, which requires semantic segmentation. can the framework deal with more random segments such as bone fragments due to fracture? 2) following 1), if one generates some bone fragments, which are likely unseen by the models, how well the models can generate in assembling bones? 3) if one has to train from scratch, is there any insight on the minimal requirements of training set? \n\n- Another challenging scenario (also with strong medical background) is non-rigid shape assembly. Is there any insight on how the proposed framework can be extended to the more challenging setting?", "limitations": "Yes.", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 4, "originality": 4, "strengths_and_weaknesses": "Strengths: \n\n1. Point pose estimation task is fundamental in processing 3D data. The reported method demonstrates promising results on rather challenging setting, e.g., shown in the last two columns of Fig. 4, which is potentially of great utility in various down-stream applications. \n\n2. The proof of Thm. 1 looks reasonable to me. It provides good basis from the theoretical perspective. \n\n3. The idea of incorporating rectified flow framework into point pose estimation is interesting, and I appreciate the authors' efforts to make this seemingly intuitive idea work in practice (e.g., the conditioning design as well as the ablation in Tab.4 suggest the efforts). \n\nWeaknesses: \n\nI have some questions, please refer to the *Question* part.", "was_revised": true, "final_justification": "I am happy with the response from the authors, and thus would maintain my initial score.", "rebuttal": "We thank the reviewer for finding our idea \"interesting,\" noting that the method \"remarkably accommodates both pair-wise and multiple components settings,\" and \"demonstrates promising results on rather challenging settings.\" We also appreciate the reviewer's recognition of the theoretical proof as \"reasonable and providing a foundation from theoretical perspective\". Please find our responses to the comments below.\n\n---\n\n> **Q1**: The reported models are mainly trained on instance-level man-made datasets. Some important applications of shape assembly come from medical tasks. I am wondering the current method relies on an overlap estimation module, which requires semantic segmentation. can the framework deal with more random segments such as bone fragments due to fracture?\n\nOur framework is designed to accommodate various definitions of part segmentation, not only semantic ones. Specifically, we have demonstrated support for:\n\n1. **Random fragmentation**: as in ModelNet-40, where parts are generated via random plane cuts.\n2. **Physically simulated fracture**: as in BreakingBad, where parts are created using physical simulations of breakage when external forces are applied on object surface.\n3. **3D scanning**: As in TUD-L, where part point clouds are acquired from real sensors, including partial occlusions and noise.\n4. **Instance (semantic) segmentation**: As in Objaverse, PartNet, and IKEA-Manual, where parts are defined by semantic instance labels.\n\nThis flexibility suggests that our method could potentially handle irregular or random segmentations, such as bone fragments from fractures, provided that the input parts are reasonably represented as point clouds, discussed below.\n\n---\n\n> **Q2**: Following Q1, if one generates some bone fragments, which are likely unseen by the models, how well the models can generate in assembling bones?\n\nWe  agree that bone fragments are an important application of 3D shape assembly. To evaluate our method in this context, we conducted zero-shot tests on bone scans from the test split of the newly-released **Fractura** \\[11] dataset, which includes human bones (`Leg`, `Hip`, `Vertebra`, `Rib`) and pig bones (`Pig Bones`). Below, we report Part Accuracy (%) for both our model and GARF:\n\n\n| Setting      | Method |    Leg   |    Hip   |    Rib   | Vertebra | Pig Bones |    All   |\n|--------------|-------|:--------:|:--------:|:--------:|:--------:|:---------:|:--------:|\n| *Supervised* | *GARF*  |   *89.7*   |   *80.8*   |   *74.8*   |   *60.8*   |    *79.0*   |   *77.3*   |\n| Zero-shot    | GARF  |   70.5   | **72.8** |   62.9   |   37.7   |    53.4   |   57.7   |\n| Zero-shot    | Ours  | **79.9** |   63.4   | **76.2** | **42.0** |  **63.2** | **64.4** |\n\n\nOur model demonstrates stronger zero-shot performance on previously unseen bone fragments, outperforming GARF in most categories, particularly for Leg, Rib, and Pig Bones. However, there remains a gap compared to fully supervised training. We expect that training on relevant medical datasets would further improve accuracy of our model, as it would allow the model to better learn bone-specific shape priors and fracture geometries.\n \n\n---\n\n> **Q3**: If one has to train from scratch, is there any insight on the minimal requirements of training set?\n\nThis is an excellent question. From our experience, successful training requires a dataset with:\n\n1. **Shape prior**: A sufficient number of objects covering the final (assembled) shape distribution, and \n2.  **Overlap geometry**: Informative geometry of the overlapping region, such as fracture region or joints.\n\nFor specialized domains, e.g., medical or paleontological reconstructions, collecting a domain-relevant dataset with hundreds to thousands of objects and their fragmentations will be necessary for strong generalization. We will release our model weights, training code, and scripts for fine-tuning on custom datasets to support the community.\n\n---\n\n> **Q4**: Another challenging scenario (also with strong medical background) is non-rigid shape assembly. Is there any insight on how the proposed framework can be extended to the more challenging setting?\n\nOur current framework is designed for rigid shape assembly, and extending it to handle non-rigid or deformable assembly would require substantial conceptual and methodological changes, such as defining overlap points and learning shape priors over the distribution of all possible non-rigid deformations. We acknowledge this limitation and highlight non-rigid assembly as an important and challenging direction for future research, with broad applications for fields such as robotic manipulation, medical reconstruction, and material reuse."}, {"review_id": "aYRdEvaITE", "reviewer": "Reviewer_JGmh", "summary": "This paper is addressing the problem of registration of point clouds. More specifically, the main focus is registration of multiple point clouds to each other resulting in an assembled object. This problem is not solving generic multi point cloud registration, but rather a specific problem, of part assembling, where the input are object parts in arbitrary poses and they can be aligned to make an object. A side problem the paper addresses, is a registration of two scans. The problem  addressed in this paper is interesting and relevant.\n\nThe paper approaches this problem using generative modelling, notably, it leverages a diffusion model. The diffusion model is basically conditioned on the unposed object parts and outputs a vector field for each point in each part, pointing towards its location in the target or assembled object. The rigid transformations are easily computed from known dense point correspondences using a SVD. For such generative models to work reasonably it is necessary to train them on a large amount of data. Authors use Objaverse dataset for initialisation, where the objects were segmented into the parts using available off the shelf methods. Later their diffusion model is trained specifically on each dataset they use in evaluation, resulting in one model per dataset. Alternatively, they trained a single model for all available datasets they use in the evaluation.", "questions": "The questions below are related to weaknesses, so when addressing them, please refer to corresponding weaknesses.\n1) Generalization. The question is if the objects from the test split belong to the same classes as those used for training. What would be the results if the model was trained on one dataset and evaluated on the other.\n\n2) Self-supervision. It would be good to get more details here and explain, why the authors call pre-training approach self-supervised.\n\n3) Related work especially wrt. symmetry handling. It would be good to give an intuition about this intrinsic symmetry handling. My feeling is that the diffusion model “memorises” how to from different parts to the canonical shape, even in case of symmetries. I would be surprised if a new object with novel type of symmetry can easily be handled.", "limitations": "Not applicable", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths: The paper proposes an interesting approach for multi part registration. I find  it clearly formulated and presented. I find using a diffusion model for addressing this problem intriguing, but the formulation is nice and appealing. Experimental evaluation is substantial and contains a number of datasets and related works the paper compares too. Finally, I find the discussion useful and appreciate showing failure cases and their causes.\n\nWeaknesses: Even though I like the approach and the formulation, I think it has several weaknesses. \n1) Questionable generalisation capablities. Primarily, generative models, like diffusion models, are still bound to the datasets they are trained on. They excel in the generative tasks, like generating new shapes, interpolated between the existing one from the training. However, for the registration, they are bound to the datasets they use for training. Unlike, classical methods, e.g. keypoint matching based, which can handle any objects in any configurations, generative models, cannot be applied to completely new objects. I believe that the same applies here. The model is bound to the datasets they are trained on, even if they are trained on all datasets used in this paper. For example, the paper, follows, train/validation/test splits. This means that part of the dataset has been seen during the training of the diffusion model. \n\n2) Self-supervised pretraining. Training the encoder and overlap head on a large dataset, as Objaverse, using cross entropy loss, where all object parts and their overlaps are known, doesn’t seem to be self-supervised, but rather supervised. Generating labels(object part IDs) and their overlaps automatically, cannot be considered as past of self-supervision. I would appreciate your comment on this.\n\n3) Related works. The discussion about the related work is valid and well structured. However, it is hard to see how different the proposed approach is from the related diffusion models:DiffAssembly, PuzzleFusion and GARF. Claiming that others handle symmetries in an ad-hoc manner, while the proposed approach does it intrinsically is not clear. \n\n4) Experimental evaluation. Even though the evaluation is exhaustive, I would like to see comparisons, where test objects have never been used for training. For example, a cross validation kind of evaluation would be interesting: the model is trained on all datasets except one, on which it is tested. Why there is no comparison to DiffAssembly, which seems to be quite related to the current approach? Symmetry handling example in Figure 6 is not sufficient. It would be great to have a cylindrical toy object, e.g. bottle, and show how multiple symmetric scans could be registered. Training on one set of cylindrical objects and testing on  completely different one would be beneficial to see if the method generalises in case of symmetries.", "was_revised": true, "final_justification": "I appreciate the authors' rebuttal, where they addressed my concerns. Taking into account other reviews and provided answers, I am raising my score to 5.", "rebuttal": "We sincerely thank the reviewer for finding our approach \"interesting\" and \"clearly formulated\", and for describing our formulation as \"nice and appealing\", along with recognizing our \"substantial experimental evaluation\". We also greatly appreciate the constructive and insightful feedback. Below is our response to the comments.\n\n---\n\n> **Q1**: Generalization. The question is if the objects from the test split belong to the same classes as those used for training. What would be the results if the model was trained on one dataset and evaluated on the other.\n\nWe have conducted zero-shot out-of-domain evaluation and find that our method demonstrates better generalization abilities, compared to the state-of-the-art method GARF. Please refer to our response to **Reviewer oaRr** (Q1), where we report zero-shot evaluation on the **3RScan** \\[A] dataset (pairwise registration under noisy real-world 3D scanning with partial observations), and to **Reviewer yLRg** (Q2) for our zero-shot evaluation on the **Fractura** \\[11] dataset (shape assembly of various types of bone scans).\n\n---\n\n> **Q2**: Self-supervision. It would be good to get more details here and explain, why the authors call pre-training approach self-supervised.\n\nOur overlap-aware pretraining uses various part segmentations, including random planar partitions (e.g., ModelNet-40). However, we agree that our Objaverse pretraining uses automatically extracted part segmentation labels by PartField, which technically falls under supervised learning or distillation. To better reflect this, we will rename this stage to \"Overlap-aware Pretraining\" and update Section 3.2 to clarify the distinction from fully unsupervised approaches.\n\n---\n\n> **Q3**: Why there is no comparison to DiffAssemble, which seems to be quite related to the current approach? \n\nThanks for the suggestion. DiffAssemble [49] applies denoising diffusion to a graph neural network (GNN) for SE(3) pose vector generation, which differs from our flow-based generative formulation. For completeness, we compared our method with DiffAssemble on the BreakingBad-Everyday, evaluating rotation error (degrees, lower is better), translation error (cm, lower is better), and part accuracy (%, higher is better):\n| Method  | Rotation Error \\[deg] | Translation Error \\[cm] | Part Accuracy \\[%]|\n| :---: | :---: | :---: | :---: |\n| DiffAssemble | 73.3 | 14.8 | 27.5 |\n| Ours | **7.4** | **2.0** | **91.1** | \n\nAs shown, our method achieves substantial improvements over DiffAssemble across all metrics. We will include these results in Table 2.\n\n---\n\n> **Q4**: Symmetry handling example in Figure 6 is not sufficient. It would be great to have a cylindrical toy object, e.g. bottle, and show how multiple symmetric scans could be registered. Training on one set of cylindrical objects and testing on completely different one would be beneficial to see if the method generalises in case of symmetries.\n> It would be good to give an intuition about this intrinsic symmetry handling. My feeling is that the diffusion model “memorises” how to from different parts to the canonical shape, even in case of symmetries. I would be surprised if a new object with novel type of symmetry can easily be handled.\n\nThanks for the insightful comments on symmetry generalization. \n\nWe would like to emphasize that our method fundamentally handles symmetry more robustly than prior pose-vector approaches, such as DiffAssembly, PuzzleFusion, and GARF. These methods define their per-part target pose in SE(3) space, which inherently loses geometric symmetry information without explicit data augmentation. For example, consider a table with four identical cylindrical legs. Prior pose-vector approaches [11,25,41] require first annotating equivalence classes of symmetric parts (e.g., grouping legs A=B=C=D and specifying each leg’s rotational symmetry axis) and then using ad-hoc augmentations (such as swapping part locations and random rotations around those axes) during training to cover the symmetry modes. Note that those methods are originally developed for the BreakingBad dataset where there is nearly no identical fractures and only one possible way to reassemble them. Consequently, these methods often fail to generalize to other assembly tasks involving significant symmetry or part equivalence, e.g., furniture and mechanical objects.\n\nIn contrast, our method requires only a single configuration (with no swapping or rotating needed) during training and can learn the full distribution over the corresponding symmetry group. Intuitively, this is because (1) our flow formulation operates in the continuous Euclidean space where the geometric symmetry information is preserved in the learning target, and (2) our point flow formulation holds equivalence over an assembly symmetry group. We provide a formal proof of this equivalence in Section E of the Supplementary Material. This property is also demonstrated in Figure 9 in the Supplementary Material, where the diversity among test samples arises mainly from symmetric part placements.\n\nBeyond generalization within the assembly symmetry group, our method also demonstrates strong generalization to **unseen** symmetry types.  To further illustrate this, we constructed a cylindrical toy dataset, as suggested. We generated 6,000 cylinders with heights uniformly sampled from \\[0.2, 1.0\\] m and diameters from \\[0.2, 1.0\\] m. Each cylinder in the training set was cut into 2 pieces only by a **horizontal** plane at a random height parallel to the cylinder's faces. For testing, we generated 600 new cylinders and applied three cut configurations:\n\n1. **Horizontal**: by a plane at a random height parallel to the cylinder's faces, same as training,  \n2. **Axial**: by a plane through the cylinder's central axis at random orientation, and   \n3. **Random**: by an arbitrary 3D plane. \n\nNote that **Axial** and **Random** cuts have never been seen during training. The results are shown in the table below. Our method achieved high part accuracy of 100.0%, 97.0%, and 97.8% on the three configurations, respectively. While GARF shows similar results in the horizontal cut, its performance on out-of-domain (OOD) configurations is worse. This demonstrates our model’s ability to generalize to previously unseen symmetry types, rather than simply memorizing them. \n\n| Method | Horizontal | Axial (OOD) | Random (OOD) | All Cuts |\n| :---: | :---: | :---: | :---: | :---: |\n| GARF | 99.5 | 89.5 | 87.5 | 92.1 |\n| Ours | **100.0** | **97.0** | **97.8** | **98.3** |\n\nWe will include this experiment and discussion of symmetry handling in the revised manuscript."}]

Author rebuttal:

Meta-review: This paper received positive ratings from all reviewers; all reviewers agree that the paper tackles an important problem, proposes an interesting approach, and shows significant improvement over previous SOTA. The rebuttal also addresses most of the reviewer’s concerns, in particular, the generalization to unseen datasets. The AC also appreciates the scientific contribution of unifying registration and assembly in a novel conditional generative task, and thus recommends accepting this work.
Decision: Accept (spotlight)