RFMPose: Generative Category-level Object Pose Estimation via Riemannian Flow Matching
Authors: Wenzhe Ouyang
Qi Ye
Jinghua Wang
Zenglin Xu
Jiming Chen
Venue: NeurIPS 2025 poster ()
Keywords: 6D Pose Estimation
Riemannian Flow Matching
Generative Modeling
Primary area: applications

Abstract: We introduce RFMPose, a novel generative framework for category-level 6D object pose estimation that learns deterministic pose trajectories through Riemannian Flow Matching (RFM). Existing discriminative approaches struggle with multi-hypothesis predictions (e.g., symmetry ambiguities) and often require specialized network architectures. RFMPose advances this paradigm through three key innovations:
(1) Ensuring geometric consistency via geodesic interpolation on Riemannian manifolds combined with bi-invariant metric constraints;
(2) Alleviating symmetry-induced ambiguities through Riemannian Optimal Transport for probability mass redistribution without ad-hoc design;
(3) Enabling end-to-end likelihood estimation through Hutchinson trace approximation, thereby eliminating auxiliary model dependencies.
Extensive experiments on the Omni6DPose demonstrate state-of-the-art performance of the proposed method, with significant improvements of $\textbf{+4.1}$ in $\mathrm{\textbf{IoU}_{25}}$ and $\textbf{+2.4}$  in $\textbf{5°2cm}$ metrics compared to prior generative approaches. Furthermore, the proposed RFM framework exhibits robust sim-to-real transfer capabilities and facilitates pose tracking extensions with minimal architectural adaptation.

RFMPose:
Generative Category-level Object Pose Estimation via Riemannian Flow Matching
Wenzhe Ouyang', Jinghua Wang', Zenglin Xu Jiming Chen', Qi Ye Zhejiang University, Harbin Institute of Technology, Shenzhen, 3 Fudan University, Shanghai Academy of Al for Science
Abstract
We introduce RFMPose, novel generative framework for category-level 6D object pose estimation that learns deterministic pose trajectories through Riemannian Flow Matching (RFM). Existing discriminative approaches struggle with multi- hypothesis predictions (e.g., symmetry ambiguities) and often require specialized network architectures. RFMPose advances this paradigm through three key innova- tions: (1) Ensuring geometric consistency via geodesic interpolation on Riemannian manifolds combined with bi-invariant metric constraints; (2) Alleviating symmetry- induced ambiguitics through Riemannian Optimal Transport for probability mass redistribution without ad-hoe design; (3) Enabling end-to-end likelihood estima- tion through Hutchinson trace approximation, thereby eliminating auxiliary model dependencies. Extensive experiments the-art performance of the proposed method, with significant improvements of +4.1 in 1oU25 and +2.4 in 5 2em metrics compared prior generative approaches. Furthermore, the proposed RFM framework exhibits robust sim-to-real transfer capabilities and facilitates pose tracking extensions with minimal architectural adaptation. Code is available at https://github.com wwwptttthu.ooooeeeeommmmeoeeoe wtt.l/ooo//shoaece http://...om//babbouannn///ea Shabiouyang/RMFPos...
the Omni6DPose demonstrate state-of-
Introduction
6D object pose estimation, which entails predicting the 3D rotation R E SO(3) and 3D translation t E Is of observed objects, stands as a fundamental yet pivotal task within computer vision due to its diverse applications in augmented reality (26 32 robotic manipulation 4 24 and hand- object interaction 22
29], etc. Prior works have predominantly focused on instance-level object Although these methods, particularly recent progress (38) empowered by the Large Language Models(LLMMs), have demonstrated promising performance, instance-level object pose estimation methods still suffer from limited generalization capabilities stemming from the dependency on the 3D models or RGB images for each instance. To address these limitations, category-level object pose estimation has garnered considerable attention for its generalization advantages, which eliminates the need for instance-level 3D models or RGB images during both the training and inference phases.
pose estimation methods 15
21 [2].
Existing category- methods [3 20 27
28 can be categorized into two distinct groups: the correspondence-basee methods and the direct regression-based methods. The former ap- proaches [36, 20 37 28 aim to extract features from the camera coordinate space and subsequently establish correspondences within a predefined category-specins canonical templates, including 3D NOCS [36). key-points (20]. or implicit 3D embeddings [37]. However, these methods often en- counter difficulties due to the non-differentiable nature of correspondence process. contrast,
33
10
*Corresponding author: Qi Ye (qi eju.cdu.cn). This work was supported in part by NSFC under Grants (No.62233013, 62088101, 62293511, I, 621 72285),, Key Research and Development Program of Zhejiang Province (No.2025C01064) and Shenzhen Science and Technology Program (Project No.GXWD 20231 20125551001),
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

---

the latter approaches [9 18 19 [0] strive to directly regress the 6D pose in an end-to-end manner.
These approaches mainly focus on learning pose-sensitive features and various specialized networks, such as 3D Graph Convolution
and Spherical convolutions 19
10
leveraging for the learning.
Stage
Symmetric Ground Truths
r (t) u(t)
Score-based
Model
Riemannian Metric
Riemannian
OT
A/ douas
Pose Candidates
e ( soa
Riemannian Flow-matching Model
((t) g+
tx (J,)
Stage
P P
Energy- based Model
ODE Solver
P3
RR, Th, log P:
[Retses Tetad) log Petar
Likelihood
Pose Candidates
(4) Score-matching pipeline(Two-stager
(b) Our Riemannian Flow-matching (inelinn((En-tooend))
Figure 1: Existing Score matching pipeline and our proposed Riemanian Flow Matching
pipeline. The Score matching pipeline proposed in [43] employs two-stage framework: the first stage generates pose candidates, while the second stage estimates likelihood scores for these candidates. In contrast, our Riemannian Flow matching method models the object pose probability distribution Riemannian manifolds ensure geometric consistency, and simultaneously enables end-to-end likelihood estimation via trace estimation tr(Je). Moreover, our approach leverages Riemannian Optimal Transport to address the challenge of multiple feasible discrete poses induced by object symmetry. Continuous pose evolution from to & + A is governed by the learned velocity field vn in Riemannian space with the aid of ODE solver.
While the aforementioned methodologies have demonstrated efficacy, their fundamental conceptual- ization remains anchored in the discriminative paradigm, thereby inheriting two cardinal limitations: 1) difficulties in resolving the multi- holtii-hypothesis prediction problem(c.g. symmetry-induee multiplicity) and 2) reliance on tailored pose-sensitive feature extraction networks. Particularly regarding the second limitation, this constraint substantially hinders the flexibility of integration into thriving Lgiion-Languag-Acttiin (VLA) models [6] 2 for robot learning applications. To cir- cumvent the limitations above, advocate embracing the probabilistic methods in pose estimation, which inherently accommodates multi-hypothesis problem through probabilistic modeling while offering architectural flexibility in network design. As seminal attempt, GenPose (43) utilized score matching framework (31] to learn the distributions of 6D pose. However, due to the computa- tional intractability of normalization constants in high-dimensional domains, GenPose 43 requires auxiliary training of an Energy-based model to estimate the likelihood of generated samples, as shown in Fig. a). This two-stage framework inevitably introduces model complexity and sacrifices the simplicity of end-to-end training. Furthermore, score matching estimates the score function of single-sample distribution via gradient approximation, which struggles to address the multi-target optimization in pose estimation caused by object symmetry.
pose
To address the limitations, in this paper, we present a novel geometrically consistent framework that learns deterministic pose trajectories Riemannian manifolds for category- object pose estimation, termed RFMPose. The proposed RFMPose directly learns pose trajectories through Probability Flow ODEs derived from the continuity equation, which regulate probability density evolution. Our RFM framework rigorously preserves geometric constraints via two key mechanisms: (1) Geodesic-based interpolation on SO(3) via Lie algebra transformations for rotations, coupled with Euclidean interpolation in R for translations; (2) A bi-invariant Riemannian metric combining the Killing form SO(3) with Euclidean distances in R By coalescing these components, RFM framework guarantees physically plausible pose evolution in the SE(3) manifold.
Furthermore, we specifically address two critical challenges identified in prior works: 1) effective likelihood estimation for generative models and 2) multi-hypothesis predictions from object symmetries. To eliminate the requirement for auxiliary energy networks, we introduce an efficient likelihood estimation strategy for the RFM framework using Hutchinson trace estimation, thereby

---

enabling efficient divergence computation and end-to-end training. For symmetry- pose multiplicityy we propose Riemannian Optimal Transport formulation, which minimizes the weighted geodesic cost while facilitating adaptive redistribution of probability mass across equivalent poses, as shown in Fig. b)) This manifold-based geometric approach resolves ambiguities by exploiting the first principles of manifold geometry, instead of relying on symmetry-speciffe network architectures.
Comprchensive experiments on the challenging Omni6DPose dataset demonstrate the proposed method's superiority, outperforming previous generative approaches by +4,1 in 1oU25 and +2.4 in 592mm. Additionally, the proposed method also achieves 42.1 in ToU25 under real-world scenarios without domain adaptation, verifying its inherent sim-to-real transfer capability. Moreover, the proposed method permits direct extension to object pose tracking through marginal architectural adjustments and demonstrates competitive performance accuracy on object pose tracking.
The principal contributions of this work can be summarized as follows:
We establish a Riemannian Flow matching framework that leverages Riemannian interpola- tion and metric ensure manifold-consistent trajectory learning for 6D pose estimation;
We propose end-to-end likelihood estimation with the Hutchinson trace estimation on 6D pose estimation, which eliminates the requirement for auxiliary models.
We design Riemannian Optimal Transport to resolve symmetry-induced pose multiplicity in 6D pose estimation.
Extensive experiments on the challenging Omni6DPose dataset verify the superior perfor- mance the proposed method compared to state-of-the-ar approaches and demonstrate the great potential of the proposed RFM framework in object pose estimation.
2 Related Works
Correspondence-bsss based Category-leve Pose Estimation. This family of methodologies [36] 20
37 (28 seeks establish the correspondence between camera coordinate space and the predefined category-specific canonical templates, subsequently recovering poses via optimization-base fitting algorithms (e.g., Umeyama alignment (355). As a seminal advancement, NOCS (36) introduced unified canonical representation to align intra-category object instances geometrically. Build- ing upon this foundation, SpherePose (28] utilizes spherical feature interaction mechanisms to achieve enhanced correspondence precision through geodesic-aware feature matching. Besides, AG- Pose (20] advocated geometry-driven keypoint detection as an alternative correspondence paradigm, while Query6DoF (37 developed implicit shape priors through learnable sparse query matching, circumventing explicit template constraints. SAR-Net [17] and RBP-Net [44] focused on symmetry- correspondence to mitigate the symmetry-induced pose multiplicity. Notwithstanding these advance- ments, the correspondence process is inherently non-differentiable and cannot be integrated into the learning process. Consequently, inaccuracies in generating predefined category-speciff canonical templates exert a significant influence on the accuracy of pose estimation, as error propagation remains unmitigated through gradient-based optimization.
Direct Regression-based Category-level Pose Estimation. This category of approaches D
18
19 10
aims to regress the object pose in an end-to-end manner directly. FS-Net [9] proposes to decouple the rotation into two perpendicular vectors, simplifying prediction, and utilizes 3D Graph Convolution autoencoder for feature extraction. VI-Net 19 leverages spherical representations to decouple the rotation into viewpoint rotation and an in-plane rotation, thereby simplifying the challenge of rotation estimation. Based on the decoupled representation. SecondPose [10] proposed to extract SE33)-consistent semantic and geometric features enhance pose estimation accuracy. However, these methods struggle with the pose- pose-sensitive feature learning due to the non-linearity of SE(3). Furthermore, excessive reliance on specialized pose-sensitive feature extraction networks undermines model simplicity, impeding seamless integration with contemporary VLA frameworks.
Generative Modeling for Object Pose Estimation. Recently, generative modeling has emerged as promising paradigm for various tasks far beyond classic generation tasks, such as classification [6]. perception [39), and robotics action planning 41 As a pioneering work, GenPose [3] proposed to learn 6D pose distribution by score matching. However, score matching struggles to estimate probabilities in high-dimensional manifolds like SE((3 and fails to resolve pose ambiguity caused by object symmetry. As a comparison, flow matching (3] learning deterministic trajectories via
Probability Flow ODEs. Recent advances in Riemannian manifolds [8] 3 [4] have demonstrated the
3

---

capacity of flow matching to model complex geometric transformations. In this paper, we pioneer the application of Riemannian Flow matching to category-level 6D pose estimation, systematically addressing the geometric constraints inherent in the object pose estimation.
3 Methodology
We will first introduce the core mechanism of learning pose distributions via Riemannian Flow Matching. Subsequently, we will detail how we address the challenge of object symmetries using Riemannian Optimal Transport. Finally, we explain our end-to-end likelihood estimation technique, which employs Hutchinson trace estimation to obviate the need for auxiliary models.
3.1 Preliminaries
Problem Formulation. The 6D pose estimation task aims to estimate 6D object pose [R,, T:], where R E R is a rotation matrix and T E R. is translation vector, using the given multi-modal sensory inputs: partially observed point cloud O E RR3N and a cropped RGB image 1 E 3xxxx* Therefore, the learning agent is given a training set with a paired dataset D = (IR; Til. 0,
Conditional Continuous Normalizing Flows for Pose Generation. To model target conditional distribution ((R, T)cc) for a given condition variable c, we transform a prior conditional distribution
po( (c) with velocity fields conditioned c. This transformation is guided by the following
Ordinary Differential Equations (ODEs):
d dt 06 (t, c, [R,
c,,
where are trainable parameters and & [0, 1]. This ODE equation generates a flow and a conditional probability density path pr Pr[ Tlcc.. In this paper, the condition variable represents a partially observed point cloud O and cropped RGB image L. The target distribution q( TT) corresponds to the distribution of 6D poses of the ground truth in the datasets.
3.2 Learning Pose Distribution via Riemannian Flow Matching
Conditional flow paths in Eq. ( are designed primarily under the assumption of Euclidean geometry, resulting in linear interpolations. However, this can be particularly restrictive for tasks such as trajectory inference, where straight paths might lie outside the data manifold, thus failing to capture the underlying dynamics giving rise to the observed marginals.
In this paper, we tackle the aforementioned issue by learning the 6D pose distribution within Riemannian space, which facilitates geodesie-based interpolations using minimal-length curves under Riemannian distance [8. Prior to delving into the method, we first delineate the Riemannian structure inherent in the 6D pose estimation task. Conventionally, a pose matrix [R, T in Euclidean space can be transformed into SE(3) manifolds. According to 31, the disintegration of measures posits that every SE(3)- invvarrat measure can be decomposed into an SO(3) measure proportional to the Lebesgue measure on IR3. This enables us simplify the construction of independent flows on SO(3) and R' for simplicity. To construct a conditional vector field from Rg to Rj on the Riemannian space SO(3), we leverage the Lie algebra (3), which is comprised of skew- symmetric matrices acting as tangent vectors at the identity of SO(3). The geodesic interpolation at f. in SO(3) can be formulated as:
measure and a
u()soa = R(() = Ro exp (L log RT Ri)).
where log SB(3) - sc(3) is the Lie algebra transformation, and exp se(3) + SE(3) is the Lie group transformation. Ro and R₁ are orthogonal rotation matrices in the initial and target states. Constructing a conditional vector field for translation on Rd can be simplified via Euclidean interpolation:
u(t)= = T(t) = (1 - t)To + tTi,
where To to Ti are the translation vector in the initial state and target state. Capitalizing on the above Riemannian interpolation, we can derive the Riemannian flow matching framework for 6D pose distribution through the following formulation:
CRCFM (0) (. ([R [oo c, [R,T)) u(t, [R, TDI
Herein, we can model the target distribution q(RR, T|(c) by sampling from a predefined prior distri- bution Po([ RR Tlcc) and evolving these initial samples along a Riemannian flow over [0, 1]. as
depicted in Fig. 2

---

0
0.25
= 0.5
Po T
Pass [R, T
Pua A (R.T))))
0.75
1.0
Ground Truth
Pare 7)
PLo( [R. c)
( o)
Figure 2: The illustration of object pose generation Process with Riemannian flow matching. We leverage geodesic interpolation on SO(3) and Euclidean interpolation R to derive deterministic pose trajectories, ensuring geometric consistency across rotational and translational components.
3.3 Riemannian Optimal Transfer For Symmetry
Building upon the aforementioned Riemannian flow matching framework, we construct conditional probability paths to learn 6D pose distributions from given datasets. However, a critical challenge in 6D pose estimation lies in handling symmetric objects (e.g., bottles), where multiple feasible ground truths exist for single object pose. In addressing the coexistence of heterogeneous asymmetric and symmetric objects in the 6D pose estimation task, we divide the construction of conditional probability paths into two distinct scenarios: single-hypothesis and multi-hypothesis.
First, consider the scenario source pose to the single target pose via the unique shortest path. Therefore, the objective of Optimal Transport(OT) 34 in Riemannian manifolds is akin SE(3) geodesic interpolation, as both aim to find the shortest path. For scenarios involving multiple-hypothesss. there exist multiple feasible ground truth poses. Assuming continuous source distribution Po 6iR., Ta) and target distribution P1 ŌiR, T.). where 6()) denotes the Dirac measures. The general form of the Riemannian OT 3 for constructing the optimal conditional probability paths is given by:
The optimal transformation must map the single
inf / IEC SE(3)
OT p1)
[1 (RR,, T2))) Po([Re, (a))du([RR,, Tal);
where is the set of admissible transport plans on SE(3), ([R,,, Tz]) represents the transformed pose via (-),, and du is the Haar measure on SE(3). this paper, the function e([Ri, ti), [R2, to]) is defined on Riemannian manifolds, more specifically, the SE(3) manifold:
a( RR, tı), [R2, t2)) loo (I t.) " t2)) (lac
Because the target distribution #I 61R,TT: has multiple feasible ground truth poses, Pi can be rewritten as a discrete distribution P1 = E, B, 8, mn.s:TTss? Subsequently. the objective simplifies to minimizing the weighted average cost over target poses:
OT(po: = inf Σ 33 |llo (RRo, t ty))) DEC
where 8, the coefficient for j-th discrete distribution. In the field of 6D pose estimation, it is commonly assumed that multiple ground-truth poses are attributable to object symmetries. Con- sequently, these poses have equal occurrence probabilities, leading to identical coefficients for discrete distributions. This formulation allows the transport map Φ(-) to distribute "probability mass" from the single pose to multiple poses, guided by the SE(3) Riemannian metric.
5

---

3,4 Likelihood Estimation for Pose Candidates
Although the Riemannian flow matching model enables conditional sampling from pose distributions, the 6D pose estimation task often necessitates deterministic and numerically accurate output. To address this challenge, we must develop strategy for selecting or aggregating a final output estimation from multiple generated samples. Due to the vanilla mean pooling of 6D pose samples typically leading to significant statistical bias induced by outliers in the distribution tails, GenPose [ trained a decoupled Energy-based model [3] that performs likelihood estimation for its generating candidates, However, this Energy-base approach deprives the model of the advantages of end-to-end training.
To achieve end-to-end training, we estimate the likelihood of generated samples in flow matching using Hutchinson trace estimation [13,, which eliminates the need for auxiliary likelihood estimation models. As depicted in Fig. [Tb), the evolution of wiglliielhooo for Riemannian flow matching log Pe ( Ti)) depends on a continuous ODE equation:
alog pr (lR,, T.ll) - (vo((Re, T:),
Ot The Log-likenn log-likelihood can be computed by integrating
where V7.) denotes a divergence operation. e [0, 1]: log (Vo 7())) log Moggooooo[[RA) Tol)) = V (no([Re, T())) di
To calculate the divergence of the velocity field V (vo ([Re, Til)) is equivalent to solving the trace of its Jacobian matrix:
Ov, ( T.l,t)
V ([R, tr()))
(10)
Oxg
where (J)) represents the trace of the Jacobian matrix. Calculating the trace of the Jacobian matrix in nigh-dimenssioal spaces involves significant computational complexity, which is infcasible for real-time applications. To tackle this issue, we utilize the Hutchinson trace estimator [I3, which enables us to approximate the divergence using an unbiased estimation. Specifically, we first generate a random vector with the same dimension as vo[[R, T.D)), typically sampled from the standard normal distribution (N, 1). Then, we calculate the Jacobian-Vedee which can efficiently calculated using automatic differentiation tools in PyTorch. Finally, we repeat the this operation N times to obtain the expectation of JVP, which can be regarded as an approximate estimation of divergence:
Product (JVP), Ju, ( (RR
tr (J.)) = E|E J&E]
(11)
After obtaining the integration term in Eq. 9.. we still need to calculate log (v
( R,, Tt))). Since
the initial state [R, 2]] follows a standard normal distribution (0, with density function po(x) =
(2m)a/a exp (-3 2 x), the ligeliiklooodd at the initial time step can be computed as follows:
1 1 Tol [Ro, Tol logpo(vo((Ro Tbl)) - [R.
d
2 log(2x),
(12)
where d denotes the dimension of 6D pose. After acquiring the likelihood values for each pose candi- date, we discard candidates with likelihoods below the threshold 8. Finally, the retained candidates then aggregated by computing the weighted average of rotations in SO(3) and translations in R. respectively.
3.5 Discussion
Why RFM Enables Cooometri--Cossstennee Score matching aims to learn the noise in the denoising process, which inherently lacks physical outputs as a post-processing step to ensure its physical legitimacy). contrast, flow matching directly learns a velocity vector field vp(l, c, RR, TJ) that governs the evolution of poses, endowed with explicit physical interpretability. This enables enforcing geodesic constraints on the Riemannian manifold, thereby ensuring geometric consistency throughout the pose generation process.
is only applied to the final

---

Why RFM Enables End-to-End Likelihood Estimation. Score matching learns score functions (probability gradients) rather than the probability distribution itself, thereby suffering from the calcu- lation of the intractable normalization constant, especially in high-dimensional spaces. In contrast, flow matching explicitly models deterministic probability flows through velocity fields derived from the continuity equation, inherently ensuring probability conservation, reversible trajectories, and stable trace computation via Jacobian determinants. Moreover, flow matching's 's direct optimization of velocity fields mitigates the instability of score matching in low-density regions, where score gradients become ill-defined due to sparse sampling.
Experiments
4.1 Experimental Setup
Datasets. Since our generative modeling framework does not require any category- speciffc canonical priors, this obviates the need for an effortless extension of the framework to datasets containing numerous object categories. Therefore, we conduct experiments on Omni6DPose [42], novel yet challenging benchmark dataset for 6D pose estimation. This comprehensive dataset comprises 807K synthetic and real images with over 6.5 million annotations spanning 149 object categories. Notably, the diversity and scale of Omni61Pose 442 significantly surpass prevailing datasets like REAL2275 36), which contains only 7K images restricted to 6 common object categories. We train our models exclusively on synthetic data for all experiments and evaluate performance across both synthetic and real-world data.
we employ RGB and point cloud modalities dual input streams for both training and inference phases. For RGB image input, pre-trained, frozen DINOv2 model is utilized to extract semantic feature representations. For the point cloud input, leverage Farthest Point Sampling (FPS) subsample 1,024 points, followed by global feature extraction via PointNet++. During the feature aggregation stage, the RGB features are spatially concatenate with corresponding point coordinates to construct cross-modal fused representations. Please refer to the Supplementary Materials for more implementation details.
Implementation Details. Following the baseline established in Omni6DPose 42
4.2 Comparison with State-of-the-art Methods
Results on Simulation Datasets. We first compare the proposed method with other existing methods under simulation settings. The Omni6DPose 442 contains the synthetic data based on three classic datasets: ScanNet++ [40), IKEA [.. and Matterport3D [5].
comparative evaluations of the proposed method against state-of-the-ar methods on the Omni6DPose ScanNet+ test-set. As shown in Table [ our approach surpasses all deterministic methods by large margin across all evaluation metrics, which demonstrates the potential of conditional generative modeling for category- level object pose estimation. Notably, even when compared with the state-of-the-ar generative method GenPose++ [42] our solution maintains a sigmificant performance advantage. Specifically, the proposed method leads by over +4.1 in IoU25 and +3.4 in 5'2cm.
Results on Real-world Datasets. To further validate the efficacy of our approach, we also evaluate our approach on real-world datasets. Notably, we still train our models exclusively on the aforementioned synthetic data. Table shows the comparison of our method with state-of-the- of-the-art methods on the Omni6DPose ROPE set. As shown Table the proposed method significantly outperforms existing solutions across all quantitative metrics, demonstrating the sim-to-real transfer capability of our
Table I: Quantitative comparison of category-level object pose estimation on Omni6DPose ScanNet++ test-set. The results are averaged over all 149 categories.
End-to-End Training
Input Modality
IoU
AUC
Method
loU To
10U50
1oU
75
5.2em 5 5'5em 10-2cm 5cm
Deterministic:
HS--Pse
45
Point Clouds
31.1
12.0
1.7
3.4
6.1
7.9
13.4
AG-Pose
20
RGB-D
29.9
10.6
1.1
2.2
4.3
6.2
10.1
SecondPose
10
RGB-D
31.5
12.2
2.0
3.1
7.9
11.3
16.7
Probabilistic:
GenPosc++
42
X
RGB-D RGB-D
43.9
24.7
3.3
10.4
13.2
21.7
28.5
Ours
48.0
28.9
5.0
12.8
16.2
25.2
31.6
7

---

Table 2: Quantitative comparison of category-level object pose estimation Omni6DPose ROPE set. The results are averaged over all 149 categories.
Input Modality
IoU
AUC
Method
IoU25
IoUs0
IoU75
5'2cm
5cm
10m 10
Deterministic:
NOCCS [36
RGB-D
0.0
0.0
0.0
0.0
0.0
0.0
0.0
SGPA 77
RGB-D
10.5
2.0
0.0
4.3
6.7
9.3
15.0
IST--Net
RGB-D
28.7
10.6
0.5
2.0
3.4
5.3
8.8
HS-Pose
45
Point Clouds
31.6
13.6
1.1
3.5
5.3
8.4
12.7
AG-Pose
20
RGB-D
29.3
10.9
0.7
2.1
3.5
6.7
9.2
SecondPose
10
RGB-D
33.6
15.4
2.0
5.0
7.3
10.4
15.1
Probabilistic:
GenPose |43
Point Clouds
6.6
9.6
13.1
19.3
GenPose++
RGB-D
39.0
19.1
2.0
10.0
15.1
19.5
29.4
Ours
RGB-D
42.1
21.0
2.2
10.4
15.7
21.0
30.8
(a) Ground truth
(b) GenPose++ 42
(c) Ours
Figure 3: Visualization comparison on Omni6DPose [42. As shown in the zoomed area of the
figure above, our approach has achieved better performance than GenPose++ 442
proposed Riemannian flow matching framework. F detailed comparative visualization results of our model against GenPose++ [42] and the ground truths.
Results on Category-level Object Pose Tracking. The closed-loop generative architecture inherent in the flow matching framework enables seamless adaptation of the proposed method the object pose tracking task with minimal modification. Technically, we perturb the pose input R,T; of ODE Solver in Fig. with a Gaussian noise, while initializing the imput as ts E (0, 1). By default, we set the to 0.55 in this paper. Moreover, we employ the same likelihood estimation and aggregation strategy with single-frame pose estimation framework to obtain the estimation of the current frame. The comparison of category- object pose tracking the Omni6DPose ROPE set is presented
in Table 3 As demonstrated Table 3 our method maintains a leading position in the object pose tracking task. Notably, the proposed Riemannian flow matching framework not only enables end-to-end training but also offers faster inference speed compared to GenPose++
Table 3: Comparison of category-level object pose tracking on Omni6DPose ROPE. The results averaged over all 149 categories.
Method
Input
FPSt
5 f
mloUt
Reyr
4
T (cm)
GenPose
43
Point Clouds
11.7
13.3
19.3
1.2
-GenPose++
42
RGB-D
8.7
15.9
53.4
17.6
1.2
-Ours
RGB-D
11.3
16.1
54.1
15.9
1.2

---

Table 4: Ablation studies on the Riemannian Interpolation and Metric.
Table 5: Ablation studies on the Likelihood Esti- mation and Samples Aggregation.
Ahlation
1oU2st
5-2emf
5'5emt
Ablation
IoU25 t
5 5'2em"
5 5'5emt
Vanilla Euclidean Interp.
43.4
9.7
13.9
Maximum likelihood
29.7
6.6
9.3
+ Riemannian Interp.
45.1(+1.7)
(0.4(+0.7) (5.1(+1)7)1100440+7)
14.7(+0.8)
with Averaging
46.8
10.8
15.5
++ Riemannian Metrie 48.0(+4.6)
12.8(+3.11
16.2(+2.3)
Weighted Averaging
48.0(+1.2)) 12.8(+2.0) 18.024
(6.2(+0.7)
4.3 Ablation Studies
We conduct ablation studies on the Scannet++ test set of Omni6DPose 42 from three perspectives: (I) the effectiveness of Riemannian interpolation and metric; (2) the impact of likelihood estimation and sample aggregation; (3) the role of Riemannian OT for symmetric objects.
Effectiveness of the Riemannian Interpolation and Metric. In this paper, we introduce Riemannian interpolation and Riemannian metric enable pose distributions. To this end, we first conduct an ablation study on the roles of these two core components, Table[4preseet ablation results for the Riemannian interpolation and metrie. As shown in T the Riemannian interpolation design effectively improves performance in IoU25 by +1.7 and 592em by +0.7. The Riemannian Metric further boosts he 6D pose estimation performance by +4.6 in IoU25 and +3.1 in 5e2mm
efficient modeling of and learning from 6D
Ablation studies on the Likelihood Estimation and Samples Aggregation. Table presents ablation results for the proposed likelihood estimation method and different sample aggregation strategies. As shown in Table 5 the multiple sample aggregation strategy (2nd and 3rd columns) surpasses the single sample obtained by maximum likelihood estimation by large margin, verifying the superiority of generative models reducing pose estimation error through multiple samplings. Moreover, the weighted averaging strategy outperforms standard averaging with improvement +1,2 in 1oU25 and +2.0 in 5 2em, validating the effectiveness of the proposed likelihood estimation method.
Effectiveness of the Riemannian OT for Symmetric Objects. In this pa- per, we introduce Riemannian OT to address the challenge posed by mul- tiple feasible poses of symmetric ob- jects in 6D pose estimation. To ex-
Table 6: Ablation studies on the Riemannian Optimal Trans- fer(ROT) for Symmetric Objects.
Method
IoU2s
5'2em
5'5emt
GenPose++ (Symmetric)
41.5
11.1
12.5
Ours(wlo (ST)mymmeri
43.4
12.1
15.2
perimentally validate the effective- ness of Riemannian OT, we incorpo- rated the half-symmetric property into Omni6DPose 42 for comparative experiments. As demonstrated in Table 6
Ours(with (OT)mSymetrric)
(8.5(45.1)
13.7(+1.6)
17.1(+1.9)
Riemannian OT
successfully alleviates this issue, leading to significant performance improvements compared to configurations without it. Notably, the proposed method is independent of symmetry network architectures or custom loss designs.
Conclusion
In this paper, we present the Riemannian Flow Matching (RFM) for category-level 6D pose estimation, which learns deterministic pose trajectories via geodesic interpolations while explicitly preserving geometric constraints. The key contributions of our work are threefold: 1) a Riemannian manifold- based probabilistic path modeling for 6D pose estimation; probability mass redistribution for symmetry-induced pose multiplicity through Riemannian Optimal Transport; 3) an efficient likelihood estimation strategy with trace estimation for end-to-end training. Comprehensive evaluations on the challenging Omni6DPose dataset demonstrate that RFM significantly outperforms state-of of-the-art baselines. With its simple architecture and compatibility with advanced generative models, our approach offers a robust foundation for integrating into unified robot learning frameworks.
Limitations and Future Works: Although our RFM model has achieved promising performance, its accuracy remains unsatisfactory on articulated objects (e.g., laptops). Given the prevalence of such articulated objects in hand-object interactions, our future work will focus on two key aspects: 1 E)Enancigg the RFM framework to improve pose estimation accuracy for articulated objects; 2) exploring integration of the RFM framework into emerging vision- languallanuaee-ccoo (VLA) models. enabling end-to-end perception- coan-to-mannnn to-manipulation pipelines.

---

References
[1] Yizhak Ben-Shabat, Xin Yu, Fatemeh Salch, Dylan Campbell, Cristian Sadriguzz-Opazo Hongdong Li, and Stephen Gould. The ikea asm dataset: Understanding people assembling furniture through actions, objects and pose. In Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision (WACV), pages 847-859, January 2021.
[2] Kevin Black, Noah Brown, Danny Driess, Adnan Esmail, Michael Equi, Chelsea Finn, Niccolo Fusai, Lachy Groom, Karol Hausman, Brian Ichter, Szymon Jakubczak, Tim Jones, Liyiming Ke, Sergey Levine, Adrian Li-Bell, Mohith Mothukuri, Suraj Nair, Karl Pertsch, Lucy Xiaoyang Shi, James Tanner, Quan Vuong, Anna Walling, Haohuan Wang, and Ury Zhilinsky, To. A vision-language-actiin flow model for general robot control, 2024.
[3] Joey Bose, Tara Schound-Sadegll Guillaume Huguet, Kilian FATRAS, Jarrid Rector-Brooks Cheng-Hao Liu, Andrei Cristian Nica, Maksym Korablyov, Michael M. Bronstein, and Alexan- der Tong. SE(3)-stcchastic flow matching for protein backbone generation. In The Twelfth International Conference on Learning Representations, 2024.
[4] Wen Bowen, Lian Wenzhao, Bekris Kostas, and Schaal Stefan. You only demonstrate once: Category-level manipulation from single visual demonstration. In Robotics: Science and Systems, 2022.
[5] Angel Chang, Angela Dai, Thomas Funkhouser, Maciej Halber, Matthias Niessner, Manolis Savva, Shuran Song, Andy Zeng, and Yinda Zhang. Matterport3d: Learning from rgb-d data in indoor environments. International Conference on 3D Vision (3DV), 2017.
[6] Huanran Chen, Yinpeng Dong, Shitong Shao, Zhongkai Hao, Xiao Yang, Hang Su, and Jun Zhu. Diffusion models are certifiably robust classifiers. In The Thirty-eighth Annual Conference Neural Information Processing Systems, 2024.
[7] Kai Chen and Qi Dou. Sgpa: Structure-guided prior adaptation for category-level 6d object pose estimation. In 2021 IEEE/CVF International Conference Computer Vision (ICCV), pages 2753-2762 2021.
[8] Ricky T. Q Chen and Yaron Lipman. Flow matching on general geometries. In The Twelfth International Conference on Learning Representations, 2024.
[9] Wei Chen, Xi Jia, Hyung Jin Chang, Jinming Duan, Linlin Shen, and Ales Leonardis. Fs-net: Fast shape-based network for category-level 6d object pose estimation with decoupled rotation mechanism. In Proceedings of the IEEE/CVF Conference on Computer Vision and Putlern Recognition (CVPR), pages 1581-1590, June 2021.
[10] Yamei Chen, Yan Di, Guangyao Zhai, Fabian Manhardt, Chenyangguang Zhang, Ruida Zhang, Federico Tombari, Nassir Navab, and Benjamin Busam. Secondpose: Se(3)-consistent dual- stream feature fusion for category-level pose estimation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 9959-9969, June 2024.
[11) Cheng Chi, Zhenjia Xu, Siyuan Feng, Eric Cousineau, Yilun Du, Benjamin Burchfiel, Russ Tedrake, and Shuran Song. Diffusson policy: Visuomotor policy learning via action diffusion. The International Journal of Robotics Research, 2024.
[12) Zheng Dang. Lizhou Wang, Yu Guo, and Mathieu Salzmann. Match normalization: Learning- based point cloud registration for 6d object pose estimation the real world. IEEE Transactions on Pattern Analysis and Machine Intelligence, 46(6):449944533, 2024.
[13] Will Grathwohl, Ricky T. Q. Chen, Jesse Bettencourt, and David Duvenaud. Scalable re- versible generative models with free-form continuous dynamics. International Conference on Learning Representations, 2019.
[14] Guillaume Huguet, James Vuckovic, Kilian FATRAS, Eric Thibodeau-Laufen Pablo Lemos, Riashat Islam, Cheng-Hao Liu, Jarrid Brooks, Tara Akhound-Sadest Michael M. Bronstein, Alexander Tong, and Joey Bose. Sequence-augmenter SE(3)-flow matching for conditional protein generation. In The Thirty-eighth Annual Conference on Neural Information Processing Systems, 2024.
10

---

[15] Xiaoke Jiang, Donghai Li, Hao Chen, Ye Zheng, Rui Zhao. and Liwei Wu. Uni6d: A unified enn framework without projection breakdown for 6d pose estimation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Puttern Recognition (CVPR), pages 11174- 11184, June 2022.
[16] Moo Jin Kim, Karl Pertsch, Siddharth Karamcheti, Ted Xiao, Ashwin Balakrishna, Suraj Nair, Rafael Rafailov, Ethan P Foster, Pannag R Sanketi, Quan Vuong, Thomas Kollar, Benjamin Burchfiel, Russ Tedrake, Dorsa Sadigh, Sergey Levine, Percy Liang, and Chelsea Finn. Openvla: An open-source vision-lagguage-action model. In Pulkit Agrawal, Oliver Kroemer, and Wolfram Burgard, editors, Proceedings of The 8th Conference Robot Learning, volume 270 of Proceedings of Machine Learning Research, pages 2679-2713 PMLR, 06-09 Nov 2025.
[17] Haitao Lin, Zichang Liu, Chilam Cheang, Yanwei Fu, Guodong Guo, and Xiangyang Xue. Sar-net: Shape alignment and recovery network for category-level 6d object pose and size estimation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 1707-6717, June 2022.
[18] Jiehong Lin, Zewei Wei, Zhihao Li, Songcen Xu, Kui Jia, and Yuanqing Li. poalpesenet: Category-level 6d object pose and size estimation using dual pose network with refined learning of pose consistency. In Proceedings of the IEEE/CCV International Conference on Computer Vision (ICCV), pages 3560-35600000 (0003,6,,000 October 2021.
[19] Jiehong Lin, Zewei Wei, Yabin Zhang, and Kui Jia. Vi-net: Boosting category-level 6d object pose estimation via learning decoupled rotations on the spherical representations. In Proceedings of the IEFE/CVF International Conference on Computer Vision (ICCV), pages 14001-14011, October 2023.
[20] Xiao Lin, Wenfei Yang, Yuan Gao, and Tianzhu Zhang. Instance-adaptive and geometric-aware keypoint learning for category-level 6d object pose estimation. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 11040-210444 June 2024.
[21] Yongliang Lin, Yongzhi Su, Praveen Nathan, Sandeep Inuganti, Yan Di, Martin Sundermeyer, Fabian Manhardt, Didier Stricker, Jason Rambach, and Yu Zhang. Hipose: Hierarchical binary surface encoding and correspondence pruning for rgb-d 6dof object pose estimation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 00148-10158, June 2024.
[22] Zhifeng Lin, Changxing Ding, Huan Yao, Zengsheng Kuang, and Shaoli Huang. Harmonious feature learning for interactive hand-object pose estimation. In 2023 IEEF/VV Conference on Computer Vision and Pattern Recognition (CVPR), pages 12989-12998, 2023.
[23] Yaron Lipman, Ricky T. Q. Chen, Heli Ben-Hamu, Maximilian Nickel, and Matthew Le. Flow matching for generative modeling. In The Eleventh International Conference on Learning Representations, 2023.
[24] Jian Liu, Wei Sun, Chongpei Liu, Xing Zhang, and Qiang Fu. Robotic continuous grasping system by shape transformer-guided multiobject category- 6-d pose estimation. IEEE Transactions on Industrial Informatics, 19(11)11171-1113 2023.
[25] Jianhui Liu, Yukang Chen, Xiaoqing Ye, and Xiaojuan Qi. Ist-net: Prior-free category-level pose estimation with implicit space transformation. In 2023 IEEE/CVF International Conference Computer Vision (ICCV), pages 13932-13942, 2023.
[26] Eric Marchand, Hideaki Uchiyama, and Fabien Spindler. Pose estimation for augmented reality: A hands-on survey. IEEE Transactions on Visualization and Computer Graphics, 22(12):2633-263 2016.
[27] Sida Peng. Yuan Liu, Qixing Huang, Xiaowei Zhou, and Hujun Bao. Pvnet: Pixel-wise voting network for 6dof pose estimation. In Proceedings of the IEFF/CVF Conference on Computer Vision and Pattern Recognition (CVPR), June 2019.
11

---

[28] Huan Ren, Wenfei Yang. Xiang Liu, Shifeng Zhang, and Tianzhu Zhang. Learning shape- independent transformation via spherical representations for category- object pose estima- tion. In The Thirteenth International Conference Learning Representations, 2025.
[29] Alireza Rezazadeh, Snehal Dikhale, Soshi Iba, and Nawid Jamali. Hierarchical graph neural networks for proprioceptive 6d pose estimation of in-hand objects. In 2023 IEEE International Conference on Robotics and Automation (ICRA), pages 2884 2890, 2023.
[30] Tim Salimans and Jonathan Ho. Should EBMs model the energy or the score? In Energy Based Models Workshop ICLR 2021, 2021.
[31] Yang Song, Jascha Sohl-Dickstein, Diederik P Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole. Score-based generative modeling through stochastic differential equations. In International Conference on Learning Representations, 2021.
[32] Yongzhi Su, Jason Rambach, Nareg Minaskan, Paul Lesur, Alain Pagani, and Didier Stricker. Deep multi-state object pose estimation for augmented reality assembly. In 2019 IEEE Interna- tional Symposium Mixed and Augmented Reality Adjunct (ISMAR-Adjunct), pages 222-227, 2019.
[33] Yongzhi Su, Mahdi Saleh, Torben Fetzer, Jason Rambach, Nassir Navab, Benjamin Busam, Didier Stricker, and Federico Tombari. Zebrapose: Coarse to fine surface encoding for 6dof object pose estimation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 6738-6748, June 2022.
[34] Alexander Tong, Kilian FATRAS, Nikolay Malkin, Guillaume Huguet, Yanlei Zhang, Jarrid Guy Wolf, and Yoshua Bengio. Improving and generalizing flow-based genera- tive models with minibatch optimal transport. Transactions on Machine Learning Research, 2024. Expert Certification.
[35] S. Umeyama. Least-squares estimation of transformation parameters between two point patterns. IEEE Transactions on Pattern Analysis and Machine Intelligence, 13(4))376-380, 1991.
[36] He Wang, Srinath Sridhar, Jingwei Huang, Julien Valentin, Shuran Song, and Leonidas J. Guibas. Normalized object coordinate space for category-level 6d object pose and size estimation. In Proceedings of the IEEE/CVF Conference Computer Vision and Pattern Recognition (CVPR), June 2019.
[37] Ruiqi Wang, Xinggang Wang, Te Li, Rong Yang. Minhong Wan, and Wenyu Liu. Query6dof: Learning sparse queries as implicit shape prior for category-level 6dof pose estimation. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), pages 14055-14064, October 2023.
[38] Bowen Wen, Wei Yang, Jan Kautz, and Stan Birchfield. Foundationpose: Unified 6d pose estimation and tracking of novel objects. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 17868-17879, June 2024.
[39] Fei Xie, Zhongdao Wang, and Chao Ma. Diffusiontrack: Point set diffusion model for visual object tracking. In Proceedings of the IEEE/CVF Conference Computer Vision and Pattern Recognition (CVPR), pages 19113-19120 June 2024.
[40] Chandan Yeshwanth, Yueh-Cheng Liu, Matthias Nießner, and Angela Dai. Scannet++: A high-fidelity dataset of 3d indoor scenes. In Proceedings of the International Conference on Computer Vision (ICCV), 2023.
[41] Yanjie Ze, Gu Zhang, Kangning Zhang, Chenyuan Hu, Muhan Wang, and Huazhe Xu. 3d diffusion policy: Generalizable visuomotor policy learning via simple 3d representations. In Proceedings of Robotics: Science and Systems (RSS), 2024.
[42] Jiyao Zhang, Weiyao Huang, Bo Peng, Mingdong Wu, Fei Hu, Zijian Chen, Bo Zhao, and Hao Dong. Omni6dpose: A benchmark and model for universal 6d object pose estimation and tracking. 2024.
12

---

[43] Jiyao Zhang, Mingdong Wu, and Hao Dong. Generative category-lever -evell object pose estimation via diffusion models. volume 36, 2024.
[44] Ruida Zhang, Yan Di, Zhiqiang Lou, Fabian Manhardt, Federico Tombari, and Xiangyang Ji. Rbp-pose:
Residual bounding box projection for category-level pose estimation. In Computer Vision ECCV 2022: 17th European Conference, Tel Aviv, Israel, October 23-27, 2022, Proceedings, Part I. page 655-672. Berlin, Heidelberg, 2022. Springer- Verlag.
[45] Linfang Zheng, Chen Wang, Yinghan Sun, Esha Dasgupta, Hua Chen, Aleš Leonardis, Wei Zhang, and Hyung Jin Chang. Hs-pose: Hybrid scope feature extraction for category-level object pose estimation. In Proceedings of the IEEE/CVF Conference Computer Vision and Puttern Recognition (CVPR), pages 17163-17173, June 2023.
13

---

NeurIPS Paper Checklist
1. Claims
Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
Answer: [Yes]
Justification: The abstract and introduction explicitly outline the core contributions (Rie- mannian flow matching for deterministic 6D pose trajectories, symmetry handling via Riemannian Optimal Transport, end-to-end likelihood estimation via Hutchinson trace ap- proximation), with experimental results validating these claims across synthetic/real datasets.
Guidelines:
The answer NA means that the abstract and introduction do not include the claims made in the paper.
The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. A No or
NA answer to this question will not perceived well by the reviewers.
The claims made should match theoretical and experimental results, and reflect how much the results
be expected to generalize other settings.
is fine to include aspirational goals as motivation as long is clear that these goals are not attained by the paper.
2. Limitations
Question:
Does the paper discuss the limitations of the work performed by the authors?
Answer: [Yes]
Justification: We explicitly discusses limitations in handling articulated objects (e.g., laptops) and outlines plans to integrate the framework into Vision-Language-AAee (VI.A) models for broader applicability.
Guidelines:
The answer NA means that the paper has no limitation while the answer No means that the paper has limitations, but those are not discussed in the paper.
The authors are encouraged to create separate "Limitations" section in their paper.
The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e.g., independence assumptions, noiseless settings, model vell-specificattin, asymptotic approximations only holding locally). The authors should reflect on how these assumptions might be violated in practice and what the implications would be.
The authors should reflect on the scope of the claims made, e.g., if the approach was only tested few datasets with few runs. In general, empirical results often depend on implicit assumptions, which should be articulated.
The authors should reflect on the factors that influence the performance of the approach. For example, facial recognition algorithm may perform poorly when image resolution is low or images are taken in low lighting. Or speech-to-text system might not be used reliably to provide closed captions for online lectures because it fails handle technical jargon.
The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size.
If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and faimess.
While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, worse outcome might be that reviewers discover limitations that aren't acknowledged the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play an impor- tant role in developing norms that preserve the integrity of the community. Reviewers will be specifically instructed to not penalize honesty concerning limitations.
15

---

3. Theory assumptions and proofs
Question: For each theoretical result, does the paper provide the full set of assumptions and a complete (and correct) proof?
Answer: [Yes]
Justification: We have rigorously proven our theoretical results and cited relevant works to support them.
Guidelines:
The answer NA means that the paper does not include theoretical results.
All the theorems, formulas, and proofs in the paper should be numbered and cross- referenced.
All assumptions should be clearly stated or referenced the statement of any theorems.
The proofs can either appear in the main paper or the supplemental material, but they appear in the supplemental material, the authors are encouraged to provide short proof sketch to provide intuition.
Inversely, any informal proof provided in the core of the paper should be complemented by formal proofs provided in appendix or supplemental material.
Theorems and Lemmas that the proof relies upon should properly referenced.
4. Experimental result reproducibility
Does the paper fully disclose all the information needed to reproduce the main ex- perimental results of the paper to the extent that affects the main claims and/or conclusions of the paper (regardless of whether the code and data are provided or not)?
Question:
Answer: [Yes]
Justification: We provide sufficient methodological description to enable others reproduce our results.
Guidelines:
The answer NA means that the paper does not include experiments.
If the paper includes experiments, a No answer to this question will not perceived well by the reviewers: Making the paper reproducible is important, regardless of whether the code and data are provided or not.
If the contribution is dataset and/or model, the authors should describe the steps taken make their results reproducible or verifiable.
Depending on the contribution, reproducibility can be accomplished in various ways. For example, if the contribution is novel architecture, describing the architecture fully might suffice, or if the contribution a specific model and empirical evaluation, may be necessary either make it possible for others to replicate the model with the same dataset, or provide access to the model. In general. releasing code and data is often one good way accomplish this, but reproducibility instructions for how to replicate the results, access to a hosted model (e.g.. in the case of large language model), releasing of a model checkpoint, or other means that are appropriate to the research performed.
also be provided via detailed
While NeurlPS does not require releasing code, the conference does require all submis- sions to provide some reasonable avenue for reproducibility, which may depend on the nature of the contribution. For example
(a) If the contribution is primarily a new algorithm, the paper should make clear how to reproduce that algorithm.
(b) the contribution is primarily a new model architecture, the paper should describe the architecture clearly and fully.
(c) If the contribution is new model (e.g., a large language model), then there should either be way to access this model for reproducing the results or way to reproduce the model (e.g., with an open-source dataset instructions for how to construct the dataset).
(d) We recognize that reproducibility may tricky in some cases, in which case authors welcome describe the particular way they provide for reproducibility.
16

---

In the case of closed-source models, it may be that access to the model is limited in some way (e.g., registered users), but it should be possible for other researchers to have some path to reproducing or verifying the results.
5. Open access to data and code
Question: Does the paper provide open access to the data and code, with sufficient instruc- tions faithfully reproduce the main experimental results, as described in supplemental material?
Answer: [Yes]
Justification: We provide the source code in the supplementary materials, along with necessary instructions reproduce the main experimental results. Additionally, intend to publicly release the code upon official acceptance the paper.
Guidelines:
The answer NA means that paper does not include experiments requiring code.
Please see the NeurlPS code and data submission guidelines (https://nips. cc/
for more details.
While we encourage the release of code and data, we understand that this might not be possible, "No" is an acceptable answer. Papers cannot be rejected simply for not including code, unless this is central to the contribution (e.g., for new open-source benchmark).
The instructions should contain the exact command and environment needed to run reproduce the results. See the NeurIPS code and data submission guidelines (https
//nips.ccpputt wwtpcccccppccccceee haapllic/giiieee / seimiisssooPpii ssionPolicy for more details.
The authors should provide instructions on data access and preparation, including how to access the raw data, preprocessed data, intermediate data, and generated data, etc.
The authors should provide scripts to reproduce all experimental results for the new proposed method and baselines. If only subset of experiments are reproducible, they should state which ones are omitted from the script and why.
At submission time, to preserve anonymity, the authors should release anonymized versions (if applicable).
Providing as much information as possible in supplemental material (appended the paper) is recommended, but including URLs to data and code is permitted.
6. Experimental setting/details
Question: Does the paper specify all the training and test details (e.g., data splits, hyper- parameters, how they were chosen, type of optimizer, etc.) necessary understand the results?
Answer: [Yes]
Justification:
We provide implementation details in the supplementary materials.
Guidelines:
The answer NA means that the paper does include experiments.
The experimental setting should be presented in the core the paper to a level of detail that is necessary appreciate the results and make sense of them.
The full details can be provided either with the code, in appendix, as supplemental material.
7. Experiment statistical significance
Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?
Question:
Answer: [Yes]
Justification: We evaluate performance using established metrics (loU and AUC) and reports averaged results over all categories. Ablation studies (Tables 4-6) further validate component contributions with clear performance gaps.
Guidelines:
17

---

The answer NA means that the paper does not include experiments.
The authors should answer "Yes" if the results accompanied by emror bars, confi- dence intervals, or statistical significance tests, at least for the experiments that support the main claims of the paper.
The factors of variability that the error bars are capturing should be clearly stated (for example, train/test split, initialization, random drawing of some parameter, overall run with given experimental conditions).
The method for calculating the error bars should be explained (closed form formula, call a library function, bootstrap, etc.)
The assumptions made should be given (e.g.. Normally distributed errors).
It should be clear whether the error bar is the standard deviation or the standard error of the mean.
is OK to report 1-sigma error bars, but one should state it. The authors should preferably report a 2-sigma error bar than state that they have 96% CI, if the hypothesis of Normality of errоrs is not verified.
For asymmetric distributions, the authors should be careful not to show in tables figures symmetric error bars that would yield results that are out range (e.g. negative error rates).
If error bars are reported in tables or plots, The authors should explain in the text how they were calculated and reference the corresponding figures or tables in the text.
8. Experiments compute resources
For each experiment, does the paper provide sufficient information on the com- puter resources (type of compute workers, memory, time of execution) needed to reproduce the experiments?
Question:
Answer: [Yes]
Justification: We provide details of the computational resources used in the experiments in the supplementary materials.
Guidelines:
The answer NA means that the paper does not include experiments.
The paper should indicate the type of compute workers CPU GPU, internal cluster, or cloud provider, including relevant memory and storage.
The paper should provide the amount of compute required for each of the individual experimental runs as well as estimate the total compute.
The paper should disclose whether the full research project required more compute than the experiments reported in the paper (e.g., preliminary or failed experiments that didn't 't make it into the paper).
9. Code of ethics
Question: Does the research conducted in the paper conform, in every respect, with the NeurlPS Code of Ethics
Answer: [Yes]
Justification: This research focuses on algorithmic improvements for 6D object pose estima- tion without involving human subjects, sensitive data, ethically problematic applications. It adheres to NeurIPS guidelines by avoiding privacy violations, biased datasets, or high-risk deployment scenarios.
Guidelines:
The answer NA means that the authors have reviewed the NeurIPS Code of Ethics.
If the authors answer No, they should explain the special cireumstances that require a deviation from the Code of Ethics.
The authors should make sure to preserve anonymity (e.g., there special consid- eration due to laws or regulations in their jurisdiction).
10. Broader impacts
18

---

Question:
Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?
Answer: [Yes]
Justification:
We discuss the potential positive societal impacts on conclusion part.
Guidelines:
The answer NA means that there is no societal impact of the work performed.
If the authors answer NA or No, they should explain why their work has no societal impact or why the paper does not address societal impact.
Examples of negative societal impacts include potential malicious or unintended uses (e.g., disinformation, generating fake profiles, surveillance), fairness considerations (c.g., deployment of technologies that could make decisions that unfairly impact specific groups), privacy considerations, and security considerations.
The conference expects that many papers will be foundational research and not tied to particular applications, let alone deployments. However, if there is a direct path to any negative applications, the authors should point it out. For example, it is legitimate to point out that an improvement in the quality of generative models could be used to generate deepfakes for disinformation. On the other hand, it is not needed to point out that a generic algorithm for optimizing neural networks could enable people to train models that generate Deepfakes faster.
The authors should consider possible harms that could arise when the technology is being used as intended and functioning correctly, harms that could arise when the technology is being used intended but gives incorrect results, and harms following from (intentional or unintentional) misuse of the technology.
If there are negative societal impacts, the authors could also discuss possible mitigation strategies (e.g., gated release of models, providing defenses in addition attacks, mechanisms for monitoring misuse, mechanisms to monitor how system learns from feedback over time, improving the efficiency and accessibility of ML).
11. Safeguards
Does the paper describe safeguards that have been put in place for responsible release of data models that have high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?
Question:
Answer: [NA]
Justification: The paper focuses on category-level 6D object pose estimation using Rie- mannian flow matching framework. does not involve the release high-risk assets that would necessitate safeguards.
Guidelines:
The answer NA means that the paper poses such risks.
Released models that have high risk for misuse or dual-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring that users adhere usage guidelines or restrictions to access the model or implementing safety filters.
Datasets that have been scraped from the Internet could pose safety risks. The authors should describe how they avoided releasing unsafe images.
We recognize that providing effective safeguards challenging, and many papers do not require this, but we encourage authors to take this into account and make best faith effort.
12. Licenses for existing assets
Are the creators or original owners of assets (e.g.. code, data, models), used in the paper, properly credited and the license and terms of use explicitly mentioned and properly respected?
Question:
Answer: [Yes]
This paper references existing datasets (e.g., Omni6DPose, ScanNet++, IKEA, Matterport3D) and models (e.g., DINOv2, PointNet+++), with citations to the respective original works.
Justification:
19

---

Guidelines:
The answer NA means that the paper does not use existing assets.
The authors should cite the original paper that produced the code package or dataset.
The authors should state which version of the asset is used and, if possible, include URL.
The name of the license (e.g.. CC-BY 4.0) should be included for each asset. For scraped data from a particular source (e.g., website), the copyright and terms of service of that source should be provided.
If assets are released, the license, copyright information, and terms of use in the package should be provided. For popular datasets, paperswi thcode. com/ datasets has curated licenses for some datasets. Their licensing guide can help determine the license of dataset.
For existing datasets that re-packaged, both the original license and the license of the derived asset (if has changed) should be provided.
If this information is not available online, the authors are encouraged to reach out to the asset's 's creators.
13. New assets
Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets?
Answer: [Yes]
Justification: We provide the source code along with necessary instructions in the supple- mentary materials.
Guidelines:
The answer NA means that the paper does not release new assets.
Researchers should communicate the details of the dataset/code/model as part of their submissions via structured templates. This includes details about training, license, limitations, etc.
The paper should discuss whether and how consent was obtained from people whose asset is used.
At submission time, remember to anonymize your assets (if applicable). You can either create an anonymized URL or include an anonymized zip file.
Crowdsourcing and research with human subjects
Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and screenshots, if applicable, as well details about compensation (if any)?
Answer: [NA]
Justification:
This paper does not involve crowdsourcing nor research with human subjects.
Guidelines:
The answer NA means that the paper does not involve crowdsoureing nor research with human subjects.
Including this information in the supplemental material is fine, but if the main contribu- tion of the paper involves human subjects, then as much detail as possible should be included in the main paper.
According the NeurIPS Code of Bthies, workers involved in data collection, curation, or other labor should be paid at least the minimum wage in the country of the data collector.
15. Institutional review board (IRB) approvals equivalent for research with human subjects
Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or an equivalent approval/review based on the requirements of your country or institution) were obtained?
20

---

Answer:
[NA]
Justification:
This paper does not involve crowdsourcing nor research with human subjects.
Guidelines:
The answer NA means that the paper does involve crowdsourcing nor research with
human subjects.
Depending on the country in which research is conducted, IRB approval (or equivalent)
may be required for any human subjects research. If you obtained IRB approval, you should clearly state this in the paper.
We recognize that the procedures for this may vary significantly between institutions and locations, and we expect authors to adhere to the NeurlPS Code of Ethics and the guidelines for their institution.
For initial submissions, do not include any information that would break anonymity (if applicable), such the institution conducting the review.
16. Declaration of LLM usage
Question: Does the paper describe the usage of LLMs if it is an important, original, or non-standard component of the core methods in this research? Note that if the LLM is used only for writing, editing, or formatting purposes and does not impact the core methodology, scientific rigorousness, originality of the research, declaration is not required.
Answer: [NA]
Justification:
Guidelines:The core method development in this research does not involve LLMs as any important, original, or non-standard components.
The answer NA means that the core method development in this research does not involve LLMM as any important, original, ntanstad components.
Please refer to our LLM policy
for what should or should not be described.
21


Reviews:
[{"review_id": "dBnKcHCssh", "reviewer": "Reviewer_wpVz", "summary": "This paper introduces a framework for category-level object pose estimation by adapting the flow matching paradigm to the non-Euclidean geometry of pose space. The core contribution is the development of a Riemannian Flow Matching process, which correctly operates on the manifold of rotations (SO(3)). To address key challenges within this framework, the authors make two specific technical contributions: (1) They propose a Riemannian Optimal Transport loss designed to effectively learn the multi-modal distributions associated with symmetric objects, a long-standing problem in pose estimation. (2) They incorporate a Likelihood Estimation method to intelligently fuse multiple pose candidates generated by the flow matching process, enhancing the robustness of the final prediction. The effectiveness of this comprehensive framework is validated through experiments on the challenging Omni6DPose dataset, where the proposed method is shown to achieve superior performance for category-level object pose estimation.", "questions": "1. In the context of category-level object pose estimation, how to estimate object size under the proposed Riemannian flow matching framework?\n\n2. How about the performance under different levels of occlusions?\n\n3. Under what circumstances that the proposed Riemannian flow matching would exhibit obvious advantages?", "limitations": "Yes.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Pros:\n\n+ The proposed method is well-motivated, and the proposed Riemannian flow matching framework is well-designed and self-contained.\n\n+ Experiments on the Omni6DPose dataset that covers over 140 categories demonstrate the state-of-the-art performance for category-level object pose estimation.\n\n+ Comparison with conventional Euclidean flow matching demonstrates the effectiveness of  Riemannian flow matching for the task of object pose estimation.\n\n+ The effectiveness of Riemannian Optimal Transfer is also validated via an ablation study.\n\nCons:\n\n- It is unclear how to compute the object size, given the proposed Riemannian flow matching framework. It is expected to have a description for this part. What does \"we used the same scale estimation results as GenPose++\" mean? How about the accuracy for the object size estimation?\n\n- Apart from the object symmetry, occlusion is another important concern for an object pose estimation model. I am wondering about the performance of the proposed flow matching method under different levels of occlusions. In addition, I am also wondering about the accuracy of the likelihood estimation method under occlusions.\n\n- A qualitative comparison between the Euclidean flow matching and the proposed Riemannian flow matching would be appreciated. Under what circumstances that the proposed Riemannian flow matching would exhibit obvious advantages?", "was_revised": true, "final_justification": "The rebuttal has resolved my concerns about the object size calculation, robustness to occlusion, and the advantageous application scenarios for the proposed Riemannian flow matching algorithm. Therefore, I am willing to keep my original score of 'Accept'. Meanwhile, I highly recommend that the authors integrate these clarifications into the final manuscript to improve its completeness and impact.", "rebuttal": "Dear Reviewer:\n\nWe sincerely appreciate your acknowledgement of our work, particularly your recognition that the proposed method is **\"well-motivated”** **\"well-designed\"** and **\"self-contained\"**. We hope address all your concerns with following responses:\n\n_________________\n**Q1. It is unclear how to compute the object size, given the proposed Riemannian flow matching framework. It is expected to have a description for this part. What does \"we used the same scale estimation results as GenPose++\" mean? How about the accuracy for the object size estimation?**\n\n**A1:** Thanks for bringing it up. We would like to clarify that the object size estimation in our method builds on the implementation in GenPose++, which employs an extra Scale Network to predict the object's scale using concatenated features from the RGB image and point cloud. This Scale Network features a very simple architecture with three linear layers and, notably, is trained independently of the main pose estimation networks. To ensure a fair comparison, we employ the same standalone Scale Network and weights as GenPose++ for scale estimation, thereby isolating our model's performance from potential variations in scale prediction.\n\nTo evaluate the accuracy of object size estimation, we performed an evaluation with the object's center point and rotation fixed. This evaluation yielded a mean 3D Intersection over Union (3D IoU) of **67.61%** for 3D bounding boxes.\n\n_________________\n**Q2. Apart from the object symmetry, occlusion is another important concern for an object pose estimation model. I am wondering about the performance of the proposed flow matching method under different levels of occlusions. In addition, I am also wondering about the accuracy of the likelihood estimation method under occlusions.**\n\n**A2:**  Thank you for your insightful feedback.  The Omni6DPose[1] dataset does not include occlusions in training and testing. Our work and previous works like GenPose++ and GenPose do not consider the occlusion issue. As during training, the networks do not see objects under occlusions, these works may not work robustly under occlusions. \n\nDespite that,  we agree that studying the performance under occlusion is important, and we designed an experiment to evaluate robustness. We introduced random square occluders covering 10% of the object’s RGB image area and correspondingly removed the depth information from the occluded regions in the point cloud.\n\nUnder this 10% random occlusion setting, our model achieves a performance of **40.9 (-7.1)** on $IoU_{25}$ and **26.0 (-5.6)** on $10^{∘}5cm$. For comparison, GenPose++[1] achieves **36.8 (-7.1)** on $IoU_{25}$ and **23.8 (-4.7)** on $10^{∘}5cm$. These results indicate that occlusion exerts a notable performance degradation on the 6D pose estimation performance for both our model and GenPose++. We primarily attribute this to the complete absence of occluded instances in the training set. \n\nTo further assess the impact of occlusion on our likelihood estimation, we performed an ablation study. Disabling the likelihood module resulted in a performance of 39.8 on $\\mathbf{IoU}_{25}$, 8.1 on $5^{∘}2cm$, and 12.2 on $5^{∘}5cm$. In comparison, with likelihood estimation enabled, the performance improves to 40.9, 9.3, and 12.8, yielding performance gains of **+1.1**, **+1.2**, and **+0.6** on the respective metrics. These findings demonstrate that the proposed likelihood estimation remains effective even in the presence of occlusion.\n\nThank you for your constructive suggestion, and we will incorporate these experimental results into our revised supplementary material.\n\n[1]  Omni6DPose: A Benchmark and Model for Universal 6D Object Pose Estimation and Tracking, ECCV 2024.\n\n_________________\n**Q3. A qualitative comparison between the Euclidean flow matching and the proposed Riemannian flow matching would be appreciated. Under what circumstances that the proposed Riemannian flow matching would exhibit obvious advantages?**\n\n**A3:** Thank you for your valuable feedback. Due to the NeurIPS 2025 rebuttal policy, which prohibits the inclusion of images or external links, we regret that we are unable to provide additional visualization analysis for the ablation studies on Riemannian Flow Matching. However, we can still address the question of when our Riemannian Flow Matching exhibits clear advantages. We conducted a statistical analysis of the performance changes across 145 object categories and found that this method enhances performance in the vast majority of cases, yielding improvements in 82% of categories. These statistical results suggest that our Riemannian Flow Matching is broadly effective in learning object pose distributions, particularly in asymmetric classes (yielding improvements in 90% of categories)."}, {"review_id": "favXqXF3jW", "reviewer": "Reviewer_gw9Y", "summary": "The paper introduces a new method for category-level object pose estimation using Riemannian Flow Matching. A conditional probability distribution of object pose is learned, which is conditioned on sensory input. Flow matching in SE(3) space is leveraged to learn this distribution. The method also considers symmetry of objects using multiple feasible ground truth poses. Experiments are conducted on the Omni6DPose dataset to verify the effectiveness of the proposed method.", "questions": "Please see weaknesses above regarding questions.", "limitations": "Yes", "rating": 4, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Positives:\n\n-\tThe idea of using Riemannian Flow Matching for category-level object pose estimation is new and novel.\n\n-\tThe proposed method demonstrates improvements over existing methods on the Omni6DPose dataset.\n\nNegatives:\n\n-\tThe paper writing needs to be improved by incorporating more details towards how to do object pose estimation using the Riemannian Flow Matching. Most of the description in the paper is about the theory side of the method. Details about the specific problem of object pose estimation are missing. For example, how to process images, how to prepare the dataset for learning, how to define symmetry of objects in the dataset, how to perform inference in details to obtain the final object poses.\n\n-\tIn another word, an algorithm-level description of how to use the method for object pose estimation is missing in the paper. Most description is about flow matching in the SE(3) space, which can be independent of the pose estimation problem.\n\n-\tThe paper does not consider shape variation in category-level object pose estimation. Some previous works jointly estimate the object poses and shapes.\n\n-\tWhy NOCS got all zeros in table 2?\n\n-\tNo qualitative visualization of the method provided in the paper.", "was_revised": true, "final_justification": "The authors claim to improve the paper according to their rebuttal.", "rebuttal": "Dear Reviewer:\n\nWe sincerely appreciate your acknowledgement of our work, particularly your recognition that our idea is **\"new and novel\"**. We hope to address all your concerns with the following responses:\n_________________\n**Q1. The paper writing needs to be improved by incorporating more details towards how to do object pose estimation using the Riemannian Flow Matching. Most of the description in the paper is about the theory side of the method. Details about the specific problem of object pose estimation are missing. For example, how to process images, how to prepare the dataset for learning, how to define symmetry of objects in the dataset, how to perform inference in details to obtain the final object poses.**\n\n**Q2. In another word, an algorithm-level description of how to use the method for object pose estimation is missing in the paper. Most description is about flow matching in the SE(3) space, which can be independent of the pose estimation problem.**\n\n**A1&A2:** We sincerely appreciate your constructive feedback. Given that the two aforementioned questions are closely related, we therefore respond to them together.\n\n Due to the strict page limits of the NeurIPS submission, we had to move **Implementation Details** that are not directly germane to the core innovations of our methodology to the supplementary material. We kindly refer you to “Section A. More Implementation Details” in the supplementary material for these details, where we have already elaborated on: 1) How we process images; 2) How we design the network architectures; 3) How we define the symmetry of objects; 4) How we perform training and inference to obtain the final object poses.\n\nFurthermore, we completely agree  the importance of clarifying the overall workflow and algorithm-level descriptions in the main manuscript. To enhance readability, we will revise our manuscript to include:\n\n**1)Overall Pipeline Introduction:** We will add a concise introductory paragraph at the beginning of the “**Section 3 Methodology”** in the revised manuscript that provides an overarching introduction to our entire pose estimation pipeline.\n\n**2) Algorithm-Level Description:** Crucially, to directly address your suggestion, we will incorporate some content from the supplementary material, such as implementation details and visualizations, into the main manuscript, while refining the theoretical introduction in the Preliminaries section.\n\n**3) Enhanced Cross-Referencing:** We will enrich the main manuscript with cross-references to the **Implementation Details** in the supplementary material, ensuring readers can easily access detailed algorithm-level descriptions in the supplementary material.\n\nWe believe these revisions will ensure readers can readily grasp the methodological framework, stay focused on the core contributions and novelties, and easily access detailed descriptions when they wish to delve deeper. Thank you again for helping us strengthen our manuscript.\n_________________\n**Q3. The paper does not consider shape variation in category-level object pose estimation. Some previous works jointly estimate the object poses and shapes.**\n\n**A3:** Thank you for this valuable suggestion. Our work focuses on the category-level pose estimation task without joint shape modeling, which aligns with the current mainstream research in this field.   As listed in a recent survey[1], the vast majority of works also concentrate exclusively on the pose estimation task and it is still a distinct challenge. \n\nMeanwhile, we agree that jointly estimating pose and shape is a promising research direction with broad application potential. Given that single-image 3D shape reconstruction has evolved into a well-established field that is now dominated by generative models, this presents an opportune moment to integrate these two domains.\n\nWe greatly appreciate your insightful suggestion and concur that joint modeling is a compelling research topic for future exploration, which we will take into serious consideration in our future research.\n\n[1] Deep Learning-Based Object Pose Estimation: A Comprehensive Survey, arXiv:2405.07801.\n_________________\n**Q4. Why NOCS got all zeros in table 2?**\n\n**A4:** Thank you for highlighting this point.  The NOCS methodology operates by first predefining a canonical coordinate space for each object category. It then estimates the pose by predicting a NOCS map from an input image and aligning this map with the corresponding canonical template. While this approach is effective for a small number of categories, such as the six classes in the original NOCS dataset, it faces significant challenges on large-scale and more complex datasets like Omni6DPose. This performance collapse is consistent with the findings in the GenPose++[2], which also reported NOCS's failure on this benchmark but did not provide a detailed analysis of the underlying causes. Here, we would like to elaborate on the two primary reasons for NOCS's failure:\n\n**First**, the scalability of NOCS is limited. When applied to the 140+ classes in our manuscript, the high inter-class visual similarity and large intra-class shape variation become particularly pronounced. Consequently, the NOCS struggles to reliably infer the correct canonical shape from RGB information alone, leading to severe mismatches between the predicted NOCS map and the actual object geometry.\n\n**Second**, the NOCS method is inherently sensitive to visual domain shifts, such as variations in texture and lighting. Our evaluation protocol, where all baseline models are trained on the simulated SOPE dataset and tested on the real-world ROPE dataset, exposes this vulnerability. This significant sim-to-real gap exacerbates the fragility of the NOCS approach, amplifying prediction errors when the model confronts the diverse and challenging conditions of real-world scenarios.\n\n[2] Omni6DPose: A Benchmark and Model for Universal 6D Object Pose Estimation and Tracking, ECCV 2024.\n_________________\n**Q5. No qualitative visualization of the method provided in the paper.**\n\n**A5:** Thanks for your question. Due to the NeurIPS page limit, we have to include the visualizations for qualitative analysis in the supplementary material. We kindly ask you to review  our supplementary material for the qualitative visualization results. Accordingly, we will revise our manuscript by carefully condensing certain sections to incorporate representative visualizations from the supplementary material into the main manuscript."}, {"review_id": "GYcvcKAEeg", "reviewer": "Reviewer_pCdW", "summary": "This paper aims at solving category-level object pose estimation task, and proposes RFMPose that utilizes Riemannian Flow Matching for pose trajectory alignment. The method is designed upon GenPosee++ framework and proposes a novel matching strategy for precise pose learning. Experiments show the superior performance of this paper.", "questions": "please refer to weaknesses.", "limitations": "yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n1. This paper is well organized and written.\n2. The novelty is convincing.\n3. Experiments are sufficient.\n\nWeaknesses:\n1. Basicaly, this is an incremental work that builds RFM into GenPose++ framework and obtain an improvement performance. Although it proposes a new principle and many theorical derivations, personally, I am concerned about its value and novelty. In fact, category-level rigid object pose estimation is a well studied topic, espicially when foundation models, e.g. FoundationPose, are proposed, new types of objects such as garments and transparent objects or new visual tasks such as grasp and manipulation policy are more worthy investigating. Thus, I do not believe that an old visual task with incremental improvement should be accepted. Even though, I give a boardline accept score since this is a technically sound work.\n2. Experiments show some object tracking results. But most of baselines are not designed for tracking task, the authors should compare more methods in this table.\n3. There are few figures and qualitative results in the main text, making it hard to understand how RFM works and how good results RFMPose obtains.", "was_revised": true, "final_justification": "After rebuttal, I tend to accept this paper.", "rebuttal": "Dear Reviewer:\n\nWe sincerely appreciate your acknowledgement of our work, particularly your recognition that our idea is **\"well organized and written\"** and **\"the novelty is convincing\"**. We hope to address all your concerns with the following responses:\n_________________\n**Q1. Basicaly, this is an incremental work that builds RFM into GenPose++ framework and obtain an improvement performance. Although it proposes a new principle and many theorical derivations, personally, I am concerned about its value and novelty. In fact, category-level rigid object pose estimation is a well studied topic, espicially when foundation models, e.g. FoundationPose, are proposed, new types of objects such as garments and transparent objects or new visual tasks such as grasp and manipulation policy are more worthy investigating. Thus, I do not believe that an old visual task with incremental improvement should be accepted. Even though, I give a boardline accept score since this is a technically sound work.**\n\n**A1:** We sincerely appreciate your recognition of our work again, specifically your comment that “this is a technically sound work.” We appreciate this opportunity to clarify the value and novelty of our contribution, especially in the context of the important points you have raised.\n\n**First**, we respectfully argue that category-level 6D pose estimation remains a vital research area with significant unsolved challenges for the following two reasons: **1) Limited Generalization in Existing Models**: While category-level rigid object pose estimation has been well-studied,  most of existing methods are validated on benchmarks with a limited number of categories (e.g., 6 classes in NOCS[1] or 10 classes in Housecat6D[2]). These small-scale settings do not fully expose the challenges of high inter-class similarity and large intra-class variation. As demonstrated in our paper, the proposed method obtains superior performance on datasets of great diversity and scale. **2) Impractical Task Setting**: We thank you for mentioning FoundationPose[3], which is indeed a landmark work. However, it is crucial to distinguish its instance-level task from our category-level one. FoundationPose[3] requires a specific 3D CAD model or a set of reference 2D images for each object instance before inference. This prerequisite is often impractical for real-world applications where systems must handle novel, unseen objects within a known category.\n\n**Second**, we completely agree with your insightful comment that \"garments and transparent objects or new visual tasks such as grasp and manipulation policy are more worth investigating\". In fact, these are research avenues we are actively exploring. Nevertheless, we maintain that 6D object pose estimation remains a fundamental perception module, critical for enabling many of those downstream manipulation tasks, such as [4][5]. Notably, the generative architecture of our approach enables  seamless integration into contemporary diffusion-based Vision-Language-Action (VLA) frameworks, offering superior flexibility for downstream manipulation tasks.\n\nWe hope our response clarifies the value of our contribution and its relevance to the broader goals of the computer vision and robotics community. Thank you again for your constructive feedback.\n\n[1] Normalized Object Coordinate Space for Category-Level 6D Object Pose and Size Estimation, CVPR 2019.\n\n[2] HouseCat6D - A Large-Scale Multi-Modal Category Level 6D Object Perception Dataset with Household Objects in Realistic Scenarios, CVPR 2024.\n\n[3] FoundationPose: Unified 6D Pose Estimation and Tracking of Novel Objects, CVPR 2024.\n\n[4] VTAO-BiManip: Masked Visual-Tactile-Action Pre-training with Object Understanding for Bimanual Dexterous Manipulation, IROS 2025.\n\n[5] 6D Object Pose Tracking in Internet Videos for Robotic Manipulation, ICLR 2025.\n_________________\n**Q2. Experiments show some object tracking results. But most of baselines are not designed for tracking task, the authors should compare more methods in this table.**\n\n**A2:** Thank you for your kind suggestions. \n\n**First**, we would like to clarify that our baseline selection was the result of a thorough literature review. To ensure a comprehensive comparison, we referred to the latest survey paper [6] and recent tracking works [8][10] to identify four prominent category-level 6D pose tracking methods published after 2021: BundleTrack[7], CATRE[8], CAPTRA[9], and GenPose++[10].  The only method from this list not included in our table is CAPTRA[9], as its performance is reported to be on par with CATRE[8] (see Table 4 in [8]), which is already one of our key baselines. Therefore, we believe that our selected baselines encompass the most significant and impactful algorithms from top-tier conferences in recent years.\n\n**Second**, we would like to emphasize that our method achieves competitive tracking performance without any dedicated modules or losses designed for tracking, rather than focusing on tracking performance itself. This inherent versatility is a core strength of our approach, showcasing its ability to adapt to downstream tasks like pose tracking with minimal modification. When compared to GenPose++[10], a model that also possesses the aforementioned advantages, our method demonstrates clear superiority in both performance and efficiency.\n\n[6] Deep Learning-Based Object Pose Estimation: A Comprehensive Survey, arXiv:2405.07801\n\n[7] BundleTrack: 6D Pose **Tracking** for Novel Objects without Instance or Category-Level 3D Models, IROS 2021.\n\n[8] CATRE: Iterative Point Clouds Alignment for Category-level Object Pose Refinement, ECCV 2022.\n\n[9] CAPTRA: CAtegory-level Pose **Tracking** for Rigid and Articulated Objects from Point Clouds, ICCV 2021.\n\n[10] Omni6DPose: A Benchmark and Model for Universal 6D Object Pose Estimation and **Tracking**, ECCV 2024.\n_________________\n**Q3. There are few figures and qualitative results in the main text, making it hard to understand how RFM works and how good results RFMPose obtains.**\n\n**A3:** Given the page limits of NeurIPS submission, we have to include visualizations for qualitative analysis and implementation details in the supplementary material. Please refer to the supplementary material for the qualitative visualization results.\n\nAs for few figures to illustrate how RFM works, we would like to highlight Figure 2 and Figure 1(b). Specifically, Figure 2 illustrates the overall process of Riemannian Flow Matching for pose estimation, showing the transformation from a random Gaussian pose to the target pose. In contrast, Figure 1(b) details the step-by-step process within the RFM framework, including velocity field matching, likelihood estimation, and supervision. Due to the non-linear nature of SE(3), RFM learns a velocity vector field  in Riemannian space that governs the evolution of poses, endowed with explicit physical interpretability. This enables the enforcement of geodesic constraints on the Riemannian manifold, thereby ensuring geometric consistency throughout the pose generation process. We hope that the explanation above, along with the discussion in Section 3.5, addresses your concern regarding how RFM works.\n\nThank you for your valuable comment. We will update our schematic diagram and add a paragraph at the beginning of Section 3 in revised manuscript to further clarify the overall pipeline and how our method works.  Additionally, we will revise our manuscript by carefully condensing certain sections to incorporate representative visualizations from the supplementary material into the main manuscript."}, {"review_id": "ocLa88Ebqf", "reviewer": "Reviewer_iY4w", "summary": "This work applies conditional flow matching (CFM) to the category-level pose estimation task. Specifically, it first formulate category-level pose estimation as a conditional probability distribution fitting problem and derive the corresponding CFM loss. Second, pose distance is measured in Riemannian space (as opposed to traditional Euler space) to construct the conditional vector field, while incorporating symmetry-aware pose distance metrics for optimal transport (OT) computation on Riemannian manifolds. Finally, the category-level pose is obtained by weighting multiple generated pose candidates based on their likelihood values.", "questions": "See Weaknesses.", "limitations": "Yes.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n\n1. Theoretical Contribution: The work leverages the advantages of flow matching to address limitations of score matching (e.g., in GenPose), with rigorous derivations. The integration of Riemannian geometry for pose distance/interpolation with flow matching is innovative and well-motivated.\n2. Experimental Validation: Comprehensive comparative experiments substantiate the effectiveness of the proposed contributions.\n\nWeaknesses:\n\n1. Marginal Gains: Although the utilization of the flow model and the analysis of Riemannian geometry are impressive, the improvements on the real-world dataset (ROPE) are relatively modest. I'd like to know more about insights on it.\n2. More Ablations: There's no discussion or ablation study on the impact of the number of pose candidates on performance, which should be very important to assess a generative model.\n3. Efficiency: What's the inference time of the proposed method? It's important for industrial applications.\n3. Writing Issues: The framework lacks a clear schematic diagram, which would aid in understanding the overall pipeline.\nLine 158: Incorrect explanation of log and exp operations (should specify SO(3)).\nLine 221: Redundant phrase \"the this\".", "was_revised": true, "final_justification": "The authors provided reasonable explainations of my concerns, and supplemented necessary ablations. I'm glad to hold my borderline accept for this paper.", "rebuttal": "Dear Reviewer:\n\nWe sincerely appreciate your acknowledgement of our work, particularly your recognition that our idea is **\"rigorous derivations\"** and **\"innovative and well-motivated\"**. We hope to address all your concerns with the following responses:\n_________________\n**Q1. Marginal Gains: Although the utilization of the flow model and the analysis of Riemannian geometry are impressive, the improvements on the real-world dataset (ROPE) are relatively modest. I'd like to know more about insights on it.**\n\n**A1:** Thank you for your insightful comment. We agree that the performance gains on the real-world ROPE dataset are more modest compared to those on the synthetic dataset, and we appreciate the opportunity to elaborate on the reasons.\n\n**First**, we would like to emphasize a crucial aspect of our experimental setup: all models are trained exclusively on the synthetic (SOPE/ScanNet++) dataset and evaluated on both simulation and real-world datasets. This poses a highly challenging zero-shot Sim2Real transfer task. The well-known domain gap between synthetic and real-world data, stemming from differences in visual appearance (e.g., textures, lighting), sensor noise, and scene complexity, creates a significant performance bottleneck.\n\n**Second**, a closer analysis of the metrics in Table 1 and Table 2 reveals a telling pattern. Compared to GenPose++[1], our method achieves more substantial improvements on the ROPE dataset on metrics with higher tolerance, such as $\\mathbf{IoU}_{25}$(**+3.1**), $10^∘2$cm(**+1.5**), and $10^∘5$cm (**+1.4**). However, the gains are indeed more modest on the most stringent high-precision metrics, namely $5^∘2$cm(**+0.4**) and $5^∘5$cm (**+0.6**).\n\nWe posit that this pattern directly reflects the impact of the Sim2Real gap. The noise and appearance shifts from the real world likely introduce a \"performance floor\" on the final achievable precision. Our method, by leveraging flow models and Riemannian geometry, learns a more accurate pose distribution than GenPose++. This advantage is fully realized on clean, in-domain synthetic data. When confronted with real-world data, while this precision advantage is partially masked by the noise induced by the domain gap, the superior geometric priors learned by our model still lead to a more accurate and robust pose estimate overall.  This is clearly demonstrated by the more significant gains on the less strict metrics (such as $\\mathbf{IoU}_{25}$).\n\nIn summary, we believe the more modest, yet still consistent and comprehensive, gains on the ROPE dataset should not be seen as a limitation of our model's theoretical foundation, but rather as a testament to its successful generalization in a demanding zero-shot Sim2Real setting. The results demonstrate that our approach consistently outperforms the strong baseline even when challenged by a significant domain gap. We believe these findings are very promising and represent a solid step towards solving category-level pose estimation in the real-world.\n\n[1] Omni6DPose: A Benchmark and Model for Universal 6D Object Pose Estimation and Tracking, ECCV 2024.\n_________________\n**Q2. More Ablations: There's no discussion or ablation study on the impact of the number of pose candidates on performance, which should be very important to assess a generative model.**\n\n**A2:** Thanks for your insightful comment. Below is the ablation study on the impact of the number of pose candidates on performance. As shown in the table, when the number of pose candidates increases from 10 to 50, the performance improvement is significant, but when it increases from 50 to 100, the performance improvement is already very marginal, while the computational resources required for inference still increase.\n\n| Number of pose candidates | $\\mathbf{IoU}_{25}$ | $\\mathbf{IoU}_{50}$ | $\\mathbf{IoU}_{75}$ | $5^{∘}2cm$ | $5^{∘}5cm$ | $10^{∘}2cm$ | $10^{∘}5cm$ |\n| :---: | --- | --- | --- | --- | --- | --- | --- |\n| 10 | 44.6 | 21.1 | 3.9 | 11.4 | 15.1 | 21.7 | 29.3 |\n| 30 | 46.8 | 27.9 | 4.6 | 12.2 | 15.7 | 24.6 | 30.1 |\n| 50 | 48.0 | 28.9 | 5.0 | 12.8 | 16.2 | 25.2 | 31.6 |\n| 100 | 48.2 | 29.1 | 6.0 | 12.8 | 16.4 | 25.8 | 31.9 |\n_________________\n**Q3. Efficiency: What's the inference time of the proposed method? It's important for industrial applications.**\n\n**A3:** Thank you for your valuable comment regarding the inference time of our proposed method. We completely agree that inference efficiency is a crucial aspect for industrial applications.\n\nWe have reported the inference speed of our proposed method in Table 3 of the manuscript, measured in **Frames Per Second (FPS)**. As shown in the Table 3, our model achieves 11.3 FPS on a single A100 GPU (under equivalent computing power). We appreciate your attention to this key performance metric. We hope the results in Table 3 adequately addresses your question about the model's efficiency.\n_________________\n**Q4. Writing Issues: The framework lacks a clear schematic diagram, which would aid in understanding the overall pipeline. Line 158: Incorrect explanation of log and exp operations (should specify SO(3)). Line 221: Redundant phrase \"the this\".**\n\n**A4:** Thanks for your kind suggestion. Figure 2 illustrates the overall process of Riemannian Flow Matching for pose estimation, showing the learning process from a random Gaussian pose to the target pose.  Figure 1(b) details the step-by-step process within the RFM framework, including velocity field matching, likelihood estimation, and supervision. We will update our figure and add a paragraph at the beginning of Section 3 in revised manuscript to further clarify the overall pipeline of the proposed method.\n\nWe thank the reviewer for pointing out these typos, and we have corrected them in the revised manuscript."}]

Author rebuttal:

Meta-review: The authors propose a Riemannian Flow Matching procedure for pose estimation. It includes a novel optimal transport loss and a method to fuse multiple pose candidates. The reviewers welcomed the well-motivated and novel approach and acknowledged that the approach was well evaluated in experiments and ablation studies.

Before the discussion phase, there were some reservations regarding clarity and the reviewers were asking for qualitative results to validate the approach. Clarity concerns could be resolved while qualitative results could not be shown in the discussion phase. All in all, the reviewers remained with their positive stance on the paper. I follow and recommend to accept this work.
Decision: Accept (poster)