PD$^{2}$GS: Part-Level Decoupling and Continuous Deformation of Articulated Objects via Gaussian Splatting
Authors: Haowen Wang
Xiaoping Yuan
Zhao Jin
Zhen Zhao
Zhengping Che
Yousong Xue
Jing Tian
Yakun Huang
Jian Tang
Venue: ICLR 2026 Poster (2026)
Keywords: articulated object; reconstruction; digital twin;
Primary area: applications to computer vision, audio, language, and other modalities

Abstract: Articulated objects are ubiquitous and important in robotics, AR/VR, and digital twins. Most self-supervised methods for articulated object modeling reconstruct discrete interaction states and relate them via cross-state geometric consistency, yielding representational fragmentation and drift that hinder smooth control of articulated configurations. We introduce PD$^{2}$GS, a novel framework that learns a shared canonical Gaussian field and models the arbitrary interaction state as its continuous deformation, jointly encoding geometry and kinematics. By associating each interaction state with a latent code and refining part boundaries using generic vision priors, PD$^{2}$GS enables accurate and reliable part-level decoupling while enforcing mutual exclusivity between parts and preserving scene-level coherence. This unified formulation supports part-aware reconstruction, fine-grained continuous control, and accurate kinematic modeling, all without manual supervision. To assess realism and generalization, we release RS-Art, a real-to-sim RGB-D dataset aligned with reverse-engineered 3D models, supporting real-world evaluation. Extensive experiments demonstrate that PD$^{2}$GS surpasses prior methods in geometric and kinematic accuracy, and in consistency under continuous control, both on synthetic and real data.

Published as a conference paper at ICLR 2026
PD²GS: PART-LEVEL DECOUPLING AND CONTINU- OUS DEFORMATION OF ARTICULATED OBJECTS VIA GAUSSIAN SPLATTING
Haowen Wang' Xiaoping Yuan
Zhao Jin
Zhen Zhao
Zhengping Che?
Yousong Xue* Jin Tian" Yakun Huang² 2- Jian Tang
'Anhui University "Bejjigg University Posts and Telecommunications
BBejjing Innovation Center Humanoid Roboties
*Beijing Institute of Architectural Design
wanghaowen@ahu.edu..
(mustafa jin, alex. zhao, 2. che, jian. (x-nggex-huuaaaaee com siaopingyuan, @chua. abb.t.eu..uu
edu. cn
ABSTRACT
Articulated objects are ubiquitous and important in robotics, AR/VR, and digital twins. Most self-supervised methods for articulated object modeling reconstruct discrete interaction states and relate them via cross-state geometric consistency, yielding representational fragmentation and drift that hinder smooth control of ar- ticulated configurations. We introduce PD*GS, novel framework that learns shared canonical Gaussian field and models the arbitrary interaction state as its continuous deformation, jointly encoding geometry and kinematics. By associ- ating each interaction state with a latent code and refining part boundaries using generic vision priors, PD*GS enables accurate and reliable part-level decoupling while enforcing mutual exclusivity between parts and preserving scene-level co- herence. This unified formulation supports part-aware reconstruction, fine- fineggrained continuous control, and accurate kinematic modeling, all without manual super- vision. To assess realism and generalization, we release RS-Art, real-to-sim RGB-D dataset aligned with reverse-engineered 3D models, supporting real-world evaluation. Extensive experiments demonstrate that PD2GS surpasses prior meth- ods in geometric and kinematic accuracy, and in consistency under continuous control, both on synthetic and real data.
Input
(a) Unitled 3DGS Representation
(b) Articulated Object Modeling
(c) Multi-Part Decoupled Deformation
State Code di
State
Cananical State
State
Figure 1: Given multi-view image sets at arbitrary interaction states, our framework (a) builds unified Gaussian representation for articulated objects, (b) achieves part-level articulated ob- ject reconstruction and joint motion analysis, and (c) enables continuous deformation of articulated objects with multi-part decoupling by interpolating latent codes.
INTRODUCTION
Articulated objects, from hinged doors and sliding drawers to foldable laptops, are ubiquitous in physical and virtual environments. Accurate 3D representations of articulated objects are critical
for robotics (Simeonov et al. 2022 Si et al. 2024 Zhao et al. 2024). AR/VR (Yang et al. 2024a
"Corresoonding author.

---

Published as a conference paper at ICLR 2026
Mangalam et al. 2024), , and digital twins (Li et al. 2025 Guo et al. 2024). Prior work articu- lated object modeling often builds on access to annotated 3D models with dense part and kinematic labels (Wang et al., 2019; Yan et al. 2 Mu al. [021 Jiang et al. 2022 Wei et al. 2022 Wang
et al. 2024). Such strong supervision, together with simplified appearance models and coarse geo-
metric priors, limits applicability to objects with simple kinematic structure and low part diversity.
Recent advances in neural rendering. including NeRF (Mildenhall et al. 2021) and 3DGS (Kerbl etal. al. 2023), enable multi-view learning of appearance and geometry, offering foundation for annotation-efficient articulated object modeling. PARIS (Liu et al. 2023) first employs a NeRF backbone (Mildenhall et al., (02I) for part-level modeling across two distinct interaction states. Subsequent studies (Guo et al., 2025; Wu et al. 2025), incorporating 3DGS (Kerbl et al. [203), im- prove rendering fidelity and convergence speed. However, these methods typically assume a single movable part across two states, limiting them to simple single-joint objects. In response, several ap- proaches infer multi-part partt decompositions by contrasting two state-specific 3D representations (Weng) et al. 2024 Liu et al. 2025b), typically via explicit Marching- -Cbbes meshes and per-state Gaussian fields with subsequent joint alignment. This discretization confines optimization to pairwise geomet- ric matching between the two states, typically augmented with physics basied--beeddd alignment constraints, which relies on exact correspondences and precludes modeling continuous part motion. Addition- ally, operating on exactly two interaction states provides only sparse observations of the articulation, which limits estimation accuracy and hampers the resolution of motion ambiguities. Recent dynamic variants of NeRF (Mildenhall al. (02I) and 3DGS (Kerbl et al. (023) typically learn continuous representations of dynamic scenes conditioned on time, enabling seh-fidelity novel-view synthesis from temporally ordered inputs (Pumarola al. 202T Wu al. 2022 Yang et al. 2024c Luiten
et al. 2024). However, articulated object modeling explicitly requires the decoupling of motions at the part level, whereas existing dynamic rendering methods inherently capture only holistic scene transformations. Moreover, without continuous temporal data, these dynamic approaches struggle to effectively disentangle individual part motions from a limited number of discrete interaction states, often resulting in severe geometric distortions and blurry rendering artifacts.
Our key insight is that each interaction state of an articulated object can be modeled as a continuous deformation of a shared canonical 3D Gaussian field, with per-primitive deformation trajectories coherent within parts and distinct across parts, thereby inducing part semantics and enabling unsu- pervised lert- grouping. Building on this idea, introduce PD2GS, which realizes Part-Level Decoupling and Continuous Deformation via Gaussian Splatting, enabling part-aware reconstruc- tion and smooth transitions to previously unseen configurations (Fig. []. We design Deformable Gaussian Splatting that represents each interaction state with a latent code used to parameterize per- primitive transformations of shared canonical Gaussian field. To enable part-level decoupling of segmentation procedure. We first obtain coarse
Gaussian primitives, we propose a coarse-to-fie grouping by clustering primitives according to deformation- trajeecoorrr similarity with guidance from languae model. We then refine part boundaries via a boundary- employs a tailored 3D-2D prompting scheme for SAM, yielding sharp interfaces and fine-grained per-primitive labels while preserving smooth part motion. Accordingly, our framework operates en- tirely within the 3DGS optimization paradigm, agnostic to the number of interaction states, and avoids imposing geometric or chysics-basee constraints that are not expressible within the Gaussian primitive parameterization.
splitting stage that
Moreover, most prior studies (Liu et al. 2023 Weng et al. 2024 Liu ct al. 2025b; Wu et al. 2025 evaluate at most one instance per category on MarbllttM (Xiang et al.) 2020), a synthetic corpus with limited intra-category diversity and weak evidence for real-world generalization. We enlarge per-category coverage on PartNet-Mobility and additionally release RS-Art, a real-to-sim evaluation dataset that pairs multi-view RGB captures of real objects with their reverse-engineered 3D models, enabling more rigorous assessment of sim-to-real performance.
Our contributions can be summarized as follows:
We introduce PD*GS, self-supervised framework that learns canonical Gaussian field and realizes interaction states as its continuous deformations, enabling part-level decoupling and the joint recovery of geometry, appearance, and kinematics.
We propose a coarse-to-fine segmentation of Gaussian primitives driven by deformation tra- jectories, with boundary refinement for sharp part interfaces and smooth part motion, yielding accurate part-aware segmentation.
2

---

Published as a conference paper at ICLR 2026
We evaluate multiple instances per category and release RS-Art, a real-to- evaluation dataset pairing real RGB captures with reverse-enginn -verrs--ngineeeee 3D models. Comprehensive experiments demonstrate that PD*GS outperforms prior methods.
2 RELATED WORK
Articulated object modeling. Early methods like PointNet require dense supervision and CAD-
quality inputs (Qi et al. 2017a b Yan al. 2019). Implicit SDFs relax input needs but demand watertight meshes, pre-alieee pre-aligned frames, and usually two interaction states (Mu et al. 2021; Wei et al.
2022 Diang et al. 2022). Label-free NeRF and 3DGS approaches (Liu al. 2023 Guo al. 2025
Wu et al. 2025) support only single-joint, two-state objects. Recent two-field registration methods
handle multiple parts but still assume known part counts and similar state configs (Weng et al. 2024
2025b). Distinct from these reconstruction tasks, conditional generative approaches (Lei ct al. 2023 Liu et al. 2025a) leverage diffusion models to synthesize articulated shapes from sparse inputs. However, these methods depend extensive labeled datasets and often hallucinate plausible geometries that deviate from the true instance structure. PD*GS overcomes these limitations with latent-conditioned deformation field that supports arbitrary states and infers part structure from motion, enabling fully self-supervised multi-part articulation modeling.
Liu et al.
Dynamic Gaussian splatting. Recent work extends static 3D Gaussians to dynamic scenes by parameterizing attributes as time-variant functions. Methods like Deformable 3DGS (Yang et al., 2024c Luiten al. 2024) employ time-conditioned MLPs predict deformations, often enforcing physical priors. For efficient spacetime representation, approaches (Wu et al., 2024, Yang et al,, 2024b) such as 4D-GS factorize the -igh-nimensional volume into compact feature planes to ac- celerate querying. Addressing the ambiguity of implicit deformations, recent works adopt explicit motion modeling via keyframes or neural flow fields for better tracking (Lee et al., 2024, Sun al,] 2025). In the context of articulated object modeling, these approaches inherently capture holistic scene dynamics, fundamentally lacking the ability to distinguish different motion semantics. More- over, when applied to non-continuous interaction states, their reliance on temporal continuity leads to trajectory ambiguity and geometric artifacts. In contrast, PD2GS employs a latent- conditiond deformation field to explicitly model deformations across discrete interaction states, establishing unified representation that facilitates subsequent -reeggraind part decoupling and control.
SAM-based 3D segmentation. Recent efforts lift SAM (Kirillov al., 2023) to neural field seg- mentation by projecting 2D masks or distilling them into Gaussian features. SA3D (Cen et al 2023)
and SANeRF HQ (Liu al. 2024) propagate and aggregate SAM masks in NeRF using multi-view and density cues. Within the Gaussian domain, SAGA (Cen et al. 2025) and SAGD (Hu et al. 2024
learn instance-aware embeddings or refine boundaries, while Gaussian Grouping (Ye et al.
2024
and SAM3D (Yang et al., 2023) directly lift 2D masks to 3D reconstructions. These approaches treat segmentation as static and depend on external 2D prompts or fer-frame masks, failing to lever- age motion cues across states. Our framework instead analyzes Gaussian motion trajectories to auto-generate state-aware prompts, then refines segments via SAM-guided splitting, enabling fully automatic part segmentation.
3 METHODOLOGY
This section explains the pipeline shown in Fig. 2 We first review the basics of 3D Gaussian Splat- ting [Sec.3.11 and then attach latent-conditioned deformation network that maps canonical Gaus- sian field to every interaction state (Sec. 3.2). On the resulting state-specific fields, we detect rigid parts from motion cues (Sec. 3.3) and refine their boundaries with visibility-guided SAM prompting followed by boundary-aware Gaussian splitting (Sec. 3.4). The refined part-aware Gaussian field then supports the multi-task modeling of each articulated object (Sec. 3.5).
3.1 PRELIMINARIES: 3D GAUSSIAN SPLATTING
3D Gaussian Splatting (3DGS) Kerbl et al. 2023 represents scene by finite set of oriented anisotropic Gaussian primitives
G {g: (ni Σ,, c, as))m=
3

---

Published as a conference paper at ICLR 2026
3.2 Deformable Gaussian Splatting
Motion-drivan separation
Input: Multi-riew RGB Images
(R
fiet
Sian
State
MLP
Prompt
Aa)
Structure
Latent Code a
Deformed
from Molion
Gaussian Splatling
Geussian Splatting
VVM
Visibiity- awall prompt generation
"purts
Proeege
Trajectory-basee clastering
Output: Refined, Part- aussian Field
Feneal
Boundary-aware Gaussian splitting
SAM
Local refinement
3.3 Coarse Part-Level Segmen tion Gaussian Primitives
g(o)
(parrs [9p
3.4 Refined Part-Level Segmentation of Gaussian Primitives
Figure 2: Overview of the PD'GS pipeline. Solid arrows indicate differentiable modules that participate in the joint optimization, whereas dashed arrows correspond to con-differentiable post- processing stages executed outside the optimization loop.
where ,,, RR3 denotes the center of the i-th Gaussian, Σ, RR33 its full covariance that encodes both scale and orientation, E [0, 1] the RGB color, and E [0, 1 the opacity.
perspective camera is modeled by a projection 3 R2. Linearization at μt maps the 3D covariance to a 2D screen-space covariance S; E 2x2 and the mean pixel coordinates IT()).. Each primitive therefore induces the density
(x(x) ag exp( - (x ,, 1 u:)
x E TR..2
With depth ordering that proceeds from front back, compositing yields the pixel radiance
C(x) Σ
(x) Ci. wx(xx) = px(x) II[ - [[[=-,(()]]
(3)
jai
All parameters {pt Eg, Ci: 1 are optimized by minimizing photometric loss between the rendered color C(x) and the corresponding ground-truth image.
3.2 DEFORMABLE GAUSSIAN SPLATTING
To capture the full continuum of interaction states we train an implicit network, conditioned on latent code, that warps canonical Gaussian field into state-specific configurations.
Each Gaussian primitive is g (14:: E,, C4 0z),, with the covariance factorised as
Σ, R(q:) Diag(s.) R(q.)".
where R(q:) converts the unit quaternion E SO(3) into its 3 x 3 rotation matrix, and Diag(s;) places the positive scale vector s; RR3, on the diagonal of a 3 matrix. This factorization sepa- rates orientation from per-axis stretch, keeping subsequent rotation and scale updates both intuitive and numerically stable.
Given latent code a E ERD that encodes one interaction state, multi-layer perceptron Sae predicts per-primitive offsets
(Api, Aq, As;) far 9; ()).
(5)
with Apt, E R3, As; E 33, and an unconstrained four-vector Ag, that is normalized to SO(3) by Aq. Aq./ Aq
Applying the learned offsets converts the canonical Gaussian field into the configuration of partic- ular interaction state k:
1 (k) i4 + Apt
(k)
Asi.
q (k)
Aq. q
(6)

---

Published as a conference paper at ICLR 2026
where denotes multiplication of quaternions. Normalizing Aq: produces unit quaternion, so (R) remains valid orientation. Eq. therefore converts the canonical Gaussians {1g, 8;, q:) into qi
the state-specific set {Mq (k) 8 9; (k) that describes the interaction state k.
For the K observed interaction states of the object, we joinly optimize the network parameters 0 face latents and the canonical Gaussian parameters by minimizing the following total loss:
Liotal
Σ
E
II (x) 1 (xx]l + D
K XEN
where C is the color rendered in pixel x, [(0) is the corresponding ground truth image, and Danus is the canonical 3DGS density similarity term that discourages overlapping Gaussians with dissimilar colors.
while sharing the appearance attributes {c,, a; ) A single model therefore yields a coherent Gaussian scene for each interaction state and jointly encodes geometry, appearance, and articulation.
After convergence, every latent α₁ produces state-specific geometry (n!² s
3.3 COARSE PART-LEVEL SEGMENTATION OF GAUSSIAN PRIMITIVES
Motion-driven separation of static and dynamic Gaussians. Without object masks or semantic priors, detect dynamic primitives by computing the maximum Euclidean displacement of each Gaussian center across the K interaction states. Let μl in state k. We define its maximal displacement as
IR.3 be the center of Gaussian primitives
d; max (.k.(I.....K)
(k) μ
1 = =ddmmaaax E [0, 1].
(8)
The Gaussians with d, 2 Tmot form the dynamic set Goyn, and the remainder Gstat static, where the threshold Tiet [0, 1] specifies the fraction of the maximum displacement of the entire scene that qualifies as motion.
Estimating the number of motion parts via VLM. To infer how many rigid parts appear in Goyn. we sample A/ image pairs (8p) 11
((e)) with different states hi * kg. visual language
model (VLM) (Dai et al. 2023) is queried with the fixed prompt:
"Compare the two images. How many components moved?"
"Answer: 'Number of moved components: [N]
The number of parts purss is set in the mode the VLM predictions M, i.e., the integer that occurs most frequently, making the estimate insensitive occasional miscounts.
Trajectory-based clustering of dynamic Gaussians. For each 9i E Gayn we assemble a motion descriptor
f: [A A| 12,, Âμ
(K-1)
Au
( (K-1) [1]] E 1)(
(9)
where
Ap
Ay4 (k) = pi
(k+1)
(R)
(10)
|| (k)
+
Unit directions encode orientation and lengths keep relative travel, so the descriptor transla- tion/rotation aware yet scale balanced. After normalization of fg, cluster the descriptors with K-means (Arthur & Vassilvitskii, (0066) using = Rparts On the unit sphere, Euclidean distance equals cosine distance, theretore Gaussians that share one rigid motion, even at different amplitudes, are grouped together.
Clusters containing fewer than 2% of dynamic Gaussians regarded noise and merged into the nearest larger cluster. Each dynamic primitive then receives part label c E {1..... marns ). while static ones labeled 0. These coarse labels initialize the fine-grained stage that follows.
5

---

Published as a conference paper at ICLR 2026
3.4 REFINED PART-LEVEL SEGMENTATION OF GAUSSIAN PRIMITIVES
Visibility-aware prompt generation for SAM. To sharpen the coarse part labels in Sec. 3.3 we
first render each part through visibility filter and then draw sparse point prompts for the Segment Anything Model (SAM) (Kirillov et al. 2023).
Per-Gaussian contribution at a pixel. For pixel x in view v, the contribution weight w (x)
(1)
from Gaussian 9i (1t; Σ,, C;, 0s) is obtained by first evaluating its screen-space density P3 (x)
(Eq. [ and then applying the front-to-back compositing rule (Fq. 3 which together map every
direeddmenssonal primitive to a continuous weight field whose value at x equals w!" (x).
Part specific visibility confidence. For each pixel we accumulate the weight of part as wp (e)
(x) Eg,gg, w."" (x) and compare it with the strongest competitor w ,x(x)
(1) maX Wi (x). The pixel is assigned to part p when
(x)/ max, px() + =}
Tvis
(11)
where Tvis visibility threshold, tuned on one or two representative instances, and & avoids division by zero. The winner margin test keeps only pixels in which part clearly dominates, thus reducing the ambiguity at overlaps.
Sampling prompts. We define the set of visible pixels corresponding to part p in view as 2 {x|
pixel assigned to part p} and the non-contributing set as 5.(²) = {x wp (x) = 0}. Furthest point sampling (FPS) on 2 and 2% selects ten positive prompts pf and twenty
negative prompts p(") which together with the RGB image are fed to SAM to obtain the mask p-
M
Boundary-awand Gaussian splitting. For each Gaussian gi we find its nearest view Upear by ray sampling and project the ellipsoid to two-dimensional ellipse. If the ellipse major axis extends beyond the mask of the part M (Nher) the Gaussian becomes a boundary candidate.
We follow SAGD (Hu al. 2024) split each candidate, as shown in the bottom part of Fig. 2 The fraction of the major axis that lies inside the mask is measured in image space and the same ratio is (hy) The part
applied to the center μt; and the scale vector s,, resulting in two children g, (part) and g,
child retains the in-mask portion and the background child captures the overflow. The background
child 5; (bg) is re-evaluated in its nearest view; if its ellipse still crosses another part mask the split is applied recursively until every descendant lies inside exactly one mask.
Part-aware Gaussian field via local refinement. Finally, parameters of unsplit Gaussians remain fixed, whereas all new children are locally fine-tuned for a few iterations on Lioaa (updating q and only) to restore the photo consistency. The recursive split-and-tune process produces sharply aligned, mask-consisten part boundaries while leaving the converged Gaussian field undisturbed.
The entire procedure yields refined, part-aware Gaussian field with interaction state
g( {gg Pipas p==
gfa)) {(1))) ,),),,,,
(12)
where E A indexes the interaction state ([A) = K)) and Gp denotes the set of Gaussian indices belonging to part p. Each state- sute-specific field ((a) encodes a coherent multi-pan configuration, while the union over all a compactly describes the full articulated motion range of the object.
3.5 MULTI-TASK MODELING FOR ARTICULATED OBJECTS
Given the part-aware Gaussian field g(o) (G)( Jomn. we extract three part-level outputs. First,
every subset g(()) is rendered in depth and color images in all calibrated views; marching cubes applied to the resulting volume produce the mesh MM E R/1/ Second, to classify the type of
joint part p. we align two interaction states with the Kabsch algorithm (Lawrence et al.) (019) and
inspect the residual displacement: low-rank residual indicates revolute joint, while full-rank

---

Published as a conference paper at ICLR 2026
residual indicates a prismatic joint. Third, the trajectories of the Gaussian centroids belonging to part p are fitted with a minimal motion model. revolute joint is parameterized by pivot point p R and unit quaternion q If with |/ql 1. A prismatic joint is parameterized by unit slide axis a E IR' with ||a|| = 1 and translation distance E IR. More details are provided in Sec. of the Appendix.
THE RS-ART DATASET
We establish RS-Art, high-quality, multi-modal benchmark that bridges the gap between syn- thetic and real-scene evaluation for articulated-object modeling. It comprises real-world captures of articulated objects alongside their reverse-engineered, part-level digital counterparts, providing a rare combination of dense sensory data and precise structural ground truth. Covering six rep- resentative object categories (drawers, desk lamps, eyeglasses, floppy-disk drives, woven baskets, and phone/laptop stands), the dataset includes three diverse instances per category. Each object is recorded in seven distinct articulation states, spanning both compound multi-joint configurations and single-joint extrema, resulting in over 400 wide-baseling RGB-D observations per instance. For every object, we reconstruct high-fidelity, textured, multi-part mesh annotated with joint axes and motion limits. All assets released in URDF format, enabling direct deployment in physics-based simulators for downstream tasks and rigorous, physically grounded evaluation. Further details of the dataset are provided in Sec. B of the Appendix.
EXPERIMENTS
5.1 EXPERIMENTAL SETTING
Datasets. Most studies evaluate only one object per category, which limits the statistical power. We extend PartNet-Mobility (Xiang al. 2020) by selecting eight categories and two three instances per category, each with two movable parts, so all methods face the same kinematic complexity. We also include four objects with three movable parts to the robustness under higher joint counts. Real-scene performance is measured on the RS-Art we proposed. Together, the enlarged PartNet- Mobility split and RS-Art form well-balanced platform for both synthetic and woald scenarios.
Baselines. We compare our method with recent SOTA methods. The single-joint baselines include PARIS (Liu et al. 2023) and ArticulatedGS (Guo et al. 2025). Each single-joint pipeline was run once for every joint: in each run, the input images show motion of a single joint while the other parts remain fixed, and the per-joint outputs were merged for evaluation. The multi-joint baselines include DTArt (Weng et al. 2024) and ArtGS (Liu et al. 2025b). Both baselines require prespecified part count, whereas our method infers the parts automatically. For the dataset setup, two-state basclines sample 100 views per state (200 RGB images: DTArt also requires depth). Matching this budget, sample 50 views across four states, totaling 200 RGB inputs. For more information on our method restricted two interaction states, refer Sec. of of the Appendix.
Metrics. We adopt exactly the evaluation metrics defined in DTArt (Weng et al. 2024 covering the geometry reconstruction and precision of the joint parameter. CD-w, CD-s, and CD-m are used to measure the Chamfer Distance for the whole object, static parts, and movable parts in mesh recon- struction. Axis Ang, Axis Pos, and Part Motion ground-truth joint axes parameters. The only extension is that our reported scores are aggregated over all movable parts of an object, rather than being limited a single target part.
used to evaluate the errors between predicted and
Additional implementation details are in Sec. Of of the Appendix.
5.2 COMPARISON ON OBJECTS WITH MULTIPLE MOVABLE PARTS
Tab. [ reports quantitative results on our expanded PartNet-Mobility split, which contains objects with two independently actuated parts. Previous studies usually average across several runs, yet we observe large run-to-run variance in several baselines, to reveal this sensitivity, we list the first run for every method. These numbers are not cherry-picked, and subsequent runs often produce lower scores. PD*GS needs no manual part specification and still outperforms the baselines in most metrics. Fig. which also shows object with three movable parts, qualitatively confirms that

---

Published as a conference paper at ICLR 2026
Table 1: Results on the PartNet-Mobility Dataset. superscript denotes that the method failed obtain a valid result for at least one object in the corresponding category. Note that DTArt requires additional depth input, while other methods rely on RGB inputs.
Synthctic Objects
Box
Door
Eyeglasses
Faucet
Oven
Fridge
Storage
Table
PARIS LLn ct 2024
$6.27
24,83
64.35'
13.75*
54.88
69.12
27.05
15.60
38.23
ArticalaiS8S
0.98
2.25
5.14
Axis Ang 0
DTTAn
Weng da 2024
20.65
0.38
18.18
1.06
3:37
40.99
0.46
0.40
10.69
AnGS
20 20236
0.01
0.35
0.06
8.05
2.33
0.13
6.05
1.98
2.37
PD
(Ouns)
0.06
PARIS
Liu pl. 2023
2,89
31.69
3.25*
2.65
17.29
49.39
18.00
48.0
21.72
ArticalaruUS C00 e1 2015
5.12
0.77
2.12
4.12
5.25
2.13
0.12
0.52
2.52
17TA Weng
42,60
0.75
1.62
1.44
14.21
0.22
18.12
10.14
Ang
AncsS Lau 00
20256
1.36
0.68
0.08
17.02
9.24"
1,41"
0.01
7.66
4.68
PDPCS
1D9GSS(Cing) (CKIS)
0.28
0.49
1.22
0.58
0.12
0.73
0.04
0.28
0.47
PARIS
2024
0.14
0.50
1,12"
0.99
0.10
01.45
ArticalatCUUS Lio 0
2025
0.97
0.26
2.11
0.24
3.46
0.26
0.74
0.79
1.10
Axis
DTAi Weng di 2034
7.09
0.01
4.96
0.02
14.89
11.35
0.07
0.03
4,80
O
AnG38
0.06
0.03
0.06
1:9
0.02"
1.28
39.
5.31
PDPGS (Ouns)
0.06
0.02
0.02
0.04
0.27
0.16
0.03
0.01
0.08
PARIS (Liu pl 2023
0.33
0.40
0.77
0.44
0.11
0.18
0.20
0.02
0.31
ArticlalEetS
2025
0.24
0.62
0.24
1.24
0.24
0.65
0.69
Axis
DTAn Weng di K11A4
3.96
0.21
11.75
0.02
32.87
0.15
0.01
0.01
6.12
Pos
AnGS
(L00 et al. 21256
0.51
0.03
0.04
0.05
6.24"
0.04
0.01
5.98
1.61
PD
0.00
0.02
0.09
0.04
0.00
0.01
0.03
PARIS
Liu el al. 2023
93.80
151.50
97.24'
65.79*
59.28
99.33
45.24
16.38
78.57
ArticalaretSS Cito ml 2025
4.24
2.65
34.24
2.46
6.35
3.35
2.33
0.36
7,00
17TA Wene
0.35
0.07
20.57
AnGS
2.78
0.05
0.07
6.80
1.67
0.03
6.69
3.38
PDPGS (Okmn)
2.09
0.05
0.02
0.95
0.74
0.10
0.43
0.32
0.59
PARIS (La gl. 2024
33.11
87.44"
19.35*
28.
57.09
63.11
ArticalaiCUSS 000 c1 2025
20.01
7,24
0.63
9.24
2.58
19.87
0.90
0.25
7.59
Part 1
DTAn Weng cl 2024
63.48
89.31
104.92
1.44
65.79
4.91
0.05
0.21
41..26
Mosion
AnGS
15.68
0.05
0.08
16.89
3.87
0.03
0.16
24.09
7.60
(Ous))
0.87
0.05
0.02
0.50
0.34
0.02
0.21
0.06
0.26
PARIS
Liu et pl. 2023
6.93
17.90
23.35*
9.36"
13.45
18.96
10.44
3.45
12.98
ArticulaGiiSS
18.17
34.
CDis
IYTAn
Wenp drar
2,45
20.00
49.28
0.49
1:27
11.17
AntS
L30 01 20236
3.48
0.35
0.13
1.05
5.4-1
9.69*
5.10
9.04
4.29
PD
1.97
0.80
0.64
2.78
4.27
2,05
PARIS
Liu et al. 2023
82.05
42.22
86.37'
34,79'
107.25
212.08
182.85
16.58
95.52
ArticalaneUUS 21 01
2015
9.65
0.84
26.88
35.63
1.91
11.24
7.32
7.24
12.59
CD-m
DTAm
Anti8
130
Weng e
21/61
363.75
2.47
0.22
0.44
47.24
0.16
0.58
0.22
157.26
8.89
0.86
0.23
3.46
143.78
46.30
20.06
76.98
PDPGS (OGin)
2.44
0.15
0.09
0.71
1.79
0.82
0.03
5.40
1.43
PARIS (La pl 2003
128.58
32.08
98.54
48.86*
301.18
76.82
125.06
76.18
110.91
ArticalatSiSS 0
2025
8.78
0.44
13.47
0.27
10.92
1.15
179.27
12.82
28.
CD-m
DTAi
AnGS
Weng d 2014
198,70
3.35
0.42
1.17
1133.05
0.17
0.46
0.22
140.52
8.47
0.86'
0.36
0.27
2.25
1145.91
0.22
184.31
145.23
(OUI)
0.11
PARIS Liu al. 2023
6.30
12.59
17.24
9.98
10.93
18.89
8.86
2.81
10.95
Articalaietts
2025
13.75
12.59
19.03
2.78
23.22
18.89
50.59
5.81
18.33
CDow
ArGSS LG0 el at. 20296
1УTAn Wene diar
5.91
1.08
1.40
1.56
0.15
0.17
0.50
0.58
7.35
1.73
16.82
10.17
8.66
12.73
1.39
6.72
2.18
PDRGS
4.07
1.24
0.13
0.47
1.48
10.16
5.48
3,02
GT
Ours
PARIS
ArticulatedGS
ArGSS
Table
Storage
Figure 3: Qualitative multi-task modeling results on multi-part articulated objects.
joint estimates align more closely with the ground truth. DTArt (Weng al. 2024) benefits from depth input and therefore renders smoother surfaces. but still lags behind in articulation accuracy. Overall, the of latent-conditioned deformation field spanning multiple interaction states yields
8

---

Published as a conference paper at ICLR 2026
markedly higher stability than single-state pairwise pipelines. Results objects with three movable parts are presented in Sec. D.2 of the Appendix, where the same trend persists.
GT State
Ours
PARIS
Movable part 0 (drawer)
Movable part (cabinet door)
Latent Code Interpolation
Figure 4: Generalization to unseen interaction states. We interpolate the latent code while deforming
only the Gaussians that belong to a chosen part.
5.3 GENERALIZATION TO UNSEEN INTERACTION STATES
Fig- and Fig. illustrate that method is the only one that is capable of disentangling and controlling the motion of several parts indepen-
Start state Interpolation state
End state
dently while maintaining plausible geometry in
DTArt
interaction states never shown during training. Fig. specifically demonstrates how we per- form interpolation between the start state and the end state. By interpolating the latent code and deforming only the Gaussians that belong to chosen part, generate smooth, collision- free trajectories for every drawer and for the door. In contrast, PARIS (Liu al.] (003)) cannot keep the parts separated, often leading part overlap blending due the inherent multi-solution nature of its method. The capac- ity to vary multiple joints independently and synthesize genuinely novel poses represents sub- stantial step toward
PARIS
Ours
Figure 5: Qualitative reconstruction results on in- termediate states.
digital twin modeling of articulated objects.
To further substantiate this capability, we ex- tend our analysis by comparing our method with recent dynamic scene modeling ap- proaches (Pumarola et al. [2021] Wu et al.) 2022; Yang et al.J 2024c) Luiten et al. 2024), including deformable NeRF- and 3DGS-band based method. Following the protocol in Tab. I evaluate the Storage category, supply- ing each method with four discrete interaction states input. We assess the capability of each method to synthesize intermediate interaction states by rendering novel views interpolated be- tween input configurations. Additionally, for the two-state-based ArtGS (Liu et al. (025b), we apply its learned joint parameters to rigidly transform the reconstructed Gaussian field to generate the cor- responding interpolated poses. As shown in Fig. 6 and Tab. 2 our method achieves significantly superior performance both visual fidelity and quantitative metrics. Notably, effectively elimi- nates geometric artifacts that commonly plague holistic deformation methods.
Table 2: Quantitative comparison with deformable NeRF- and 3DGS-based methods unseen-state rendering.
Method
PSNR
SSIM:
LPIPS!
D-NeKF Pumarola et al 2021
18.38
0.86
0.19
DNNeRF
Dynamic ApGS Catimmaaaaco
2023
25.96
0.89
0.17
4D-GS
(Wu et 2024
23.61
0.13
AnGS
POPGS (Ours)
28.02
0.93
0.09
5.4
RESULT ON THE RS-ART DATASET
Fig. shows qualitative results on a real object from our RS-Art dataset. Despite sensor noise and challenging lighting, the method reconstructs detailed part-level geometry and texture and reli- ably extrapolates to interaction states not seen during training. These observations indicate that our method remains stable real data. Further results provided in Sec. of the Appendix.

---

Published as a conference paper at ICLR 2026
D-NeRF
DRN
Dynamic 3DGS
4D-GGS
ArtGS
Ours
Figure 6: Qualitative comparison with deformable NeRF- and 3DGS-based methods on unseen-state rendering.
Real-World Object
Part-level Reconstruction
Latent Code Interpolation
drawers
eveglasses
Figure 7: Real object validation on RS-Art.
5.5 ABLATION STUDIES
To evaluate the effectiveness of our coarse-to- fine strategy (Sec. 3.3 and 3.4p. we conduct an ablation study by removing the refinement stage. Fig. [ compares the results without the refinement stage (top) to those with it (bottom) on an oven containing multiple movable panels. For the variant without refinement, we recon- struct multiple parts directly from the K-means clusters obtained in the coarse stage. Without refinement, the reconstructed parts bleed into another and exhibit artifacts; after refine- ment, the mesh shows clean separation, sharper boundaries, and no interpenetration. The im- provement stems from esibility-guidee SAM prompting and boundary-and nowadery-aware Gaussian splitting, which force the Gaussian field conform to the per-part masks. We provide additional visual and quantitative comparisons, along with further ablation analysis on movable-component count estimation via VLM, SAM-based segmentation, and each pipeline module, in Sec. D.7 of the Appendix.
w/o Refine
E
w/ Refine
Figure 8: Ablation on the coarse-to-fine refine- ment stage.
CONCLUSION
We introduce PD²GS, the fully self-supervised framework for articulated object modeling within unified 3D Gaussian Splatting paradigm. A latent-conditioned deformation network warps a canon- ical Gaussian field across interaction states, and visibility-guided coarse-to-fine scheme refines deformation trajectories into part-aware Gaussian clusters. The resulting field supports pert-level mesh extraction, joint typing, and motion parameter estimation. In expanded PartNet-Mobility split and the novel RS-Art dataset, PD"GS surpasses existing methods without requiring part count in advance, and its learned deformation space generalizes smoothly to unseen interaction states, property well suited to digital twin scenarios. The present implementation assumes accurate camera poses and cannot reconstruct regions that remain fully occluded all views, leaving robustness to pose noise and reasoning about unseen structures as directions for future work.
10

---

Published as a conference paper at ICLR 2026
ACKNOWLEDGEMENTS
This research was supported in part by the Natural Science Foundation of Anhui under Grant No. 2508085QF241, in part by the National Natural Science Foundation of China under Grant No. 62571055 and No. 62431015.
REFERENCES
David Arthur and Sergei Vassilvitskii. k-means++: The advantages of careful seeding. Technical report, Stanford, 2006.
Blender Foundation. Blender 4.2 lts release notes. https:://eevelopeet www..eer..edddde.r.rr setes//relaas__nteeeeee // 2024.
Jiazhong Cen, Zanwei Zhou, Jiemin Fang, Wei Shen, Lingxi Xie, Dongsheng Jiang, Xiaopeng Zhang, Qi Tian, et Segment anything in 3d with nerfs. Advances in Neural Information Processing Systems, (6:25971-22990 2023.
Jiazhong Cen, Jiemin Fang, Chen Yang, Lingxi Xie, Xiaopeng Zhang, Wei Shen, and Qi Tian. Segment any 3d gaussians. In Proceedings of the AAAI Conference on Artificial Intelligence, pp. 1971-1979, 2025.
Wenliang Dai, Junnan Li, Dongxu Li, Anthony Tiong, Junqi Zhao, Weisheng Wang, Boyang Li, Pascale Fung, and Steven Hoi. Instructblip: Towards general-purposs vision-language models with instruction tuning. Advances in neural information processing systems, 36:49250-49267, 2023.
Junfu Guo, Yu Xin, Gaoyi Liu, Kai Xu, Ligang Liu, and Ruizhen Hu. Articulatedgs: Self-supervised digital twin modeling of articulated objects using 3d gaussian splatting, In Proceedings of the Computer Vision and Pattern Recognition Conference, pp. 27144-27153, 2025.
Yuqing Guo, Lin Liu, Wei Huang, Min Shen, Xiaolie Yi, Jifa Zhang, and Shizhu Lu. Extending x- reality technologies to digital twin in cultural heritage risk management: comparative evaluation from the perspective of situation awareness. Heritage Science, 12(1):245, 2024.
Xu Hu, Yuxi Wang, Lue Fan, Junsong Fan, Junran Peng, Zhen Lei, Qing Li, and Zhaoxiang Zhang- Sagd: Boundary-enhanced segment anything in 3d gaussian via gaussian decomposition. arXiv preprint arXiv:2401. 17857, 2024.
Binbin Huang, Zehao Yu, Anpei Chen, Andreas Geiger, and Shenghua Gao. 2d gaussian splatting for geometrically accurate radiance fields. In ACM SIGGRAPH 2024 conference papers, pp- 1-11, 2024.
Zhenyu Jiang, Theng-Chure Hsu, and Yuke Zhu. Ditto: Building digital twins of articulated objects from interaction. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 5616-5626, 2022.
Kai Katsumata, Duc Minh Vo, and Hideki Nakayama. An efficient 3d gaussian representation for monocular/multi-vieer dynamic scenes. CoRR, 2023.
Bernhard Kerbl, Georgios Kopanas, Thomas Leimkühler, and George Drettakis. 3d gaussian splat- ting for real-time radiance field rendering. ACM Trans. Graph., 1,
Leonid Keselman, John Iselin Woodfill, Anders Grunnet-lepsen, and Achintya Bhowmik. Intel realsense stereoscopic depth cameras. Proceedings of the IEEE conference on computer vision and pattern recognition workshops, pp. 1-10, 2017.
Alexander Kirillov, Eric Mintun, Nikhila Ravi, Hanzi Mao, Chloe Rolland, Laura Gustafson, Tete Xiao, Spencer Whitehead, Alexander C Berg, Wan-Yen Lo, al. Segment anything. In Proceed- ings of the IEEE/CVF international conference computer vision, pp-
2023.
Nathan Koenig and Andrew Howard. Design and paradigms for gazebo, open-source multi- robot simulator. In 2004 IEEE/RSJ international conference on intelligent robots and systems (IROS)IEFF Cat. No. 04CH37566), volume 3, pp. 2149-115, leee, 2004.

---

Published as a conference paper at ICLR 2026
Jim Lawrence, Javier Bernal, and Christoph Witzgall. A purely algebraic justification of the kabsch- umeyama algorithm. Journal of research of the National Institute of Standards and Technology, 124:1, 2019.
Junoh Lee, Chang Yeon Won, Hyunjun Jung, Inhwan Bae, and Hae-Gon Jeon. Fully explicit dynamic gaussian splatting. Advances in Neural Information Processing Systems, 37:5384-5409, 2024.
Yeon
Jiahui Lei, Congyue Deng, William B Shen, Leonidas J Guibas, and Kostas Daniliddis. Nap: Neu- ral 3d articulated object prior. Advances in Neural Information Processing Systems, 1878- 31894, 2023.
Xin Li, Bin He, Zhipeng Wang, Yanmin Zhou, Gang Li, and Xiang Li. Toward cognitive digital twin system of human-robot collaboration manipulation. IEEE Transactions on Automation Science and Engineering, 22:6677-6690, 2025. doi: 10.1 100/TAAEE.224.44551211
Jiayi Liu, Ali Mahdavi-Amiri, and Manolis Savva. Paris: Part-level reconstruction and motion analysis for articulated objects. In Proceedings of the IEEE/CVF International Conference Computer Vision, pp. 352-363, 2023.
Jiayi Liu, Denys Iliash, Angel X Chang, Manolis Savva, and Ali Mahdavi Amiri. Singapo: Sin- gle image controlled generation of articulated parts in objects. In The Thirteenth International Conference on Learning Representations, 2025a.
Yichen Liu, Benran Hu, Chi-Keung Tang, and Yu-Wing Tai. Sanerf-hq: Segment anything for nerf in high quality. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 2216-3226, 2024.
Yu Liu, Baoxiong Jia, Ruijie Lu, Junfeng Ni, Song-Chun Zhu, and Siyuan Huang. Building inter- actable replicas of complex articulated objects via gaussian splatting, The Thirteenth Interna- tional Conference on Learning Representations, 2025b.
Jonathon Luiten, Georgios Kopanas, Bastian Leibe, and Deva Ramanan. Dynamic gaussians: Tracking by persistent dynamic view synthesis. In 2024 International Conference on 3D Vision (3DV), pp. 800-809, IEEE, 2024.
Madhur Mangalam, Sanjay Oruganti, Gavin Buckingham, and Christoph W Borst. Enhancing hand- object interactions in virtual reality for precision manual tasks. Virtual Reality, 28(4); 2024.
Ben Mildenhall, Pratul P Srinivasan, Matthew Tancik, Jonathan T Barron, Ravi Ramamoorthi, and Ren Ng. Nerf: Representing scenes as neural radiance fields for view synthesis. Communications of the ACM, 65(1):99-106, 2021.
Jiteng Mu, Weichao Qiu, Adam Kortylewski, Alan Yuille, Nuno Vasconcelos, and Xiaolong Wang. A-sdf: Learning disentangled signed distance functions for articulated shape representation. In Proceedings of the IEFE/CVF International Conference on Computer Vision, pp. 13001-13011, 2021.
NVIDIA. Release notes isaac sim 4.2.0 documentation. https://docs. isw.a//sss....a.iimmm.m.. _wweeseootes..eee html 2024a.
omn www.iieeeee..m awwidi..... wo..m....... 2.
NVIDIA. Isaac sim workflows isaac sim 4.2.0 documentation, htt https://ocs...sacc..
omn werse
http:///.......oooooooooo...aaa. intro Sarro_workfloom www..fow..ww.oooooo.oooo.o.....w html| 2024b.
Albert Pumarola, Enric Corona, Gerard Pons-Moll, and Francese Moreno-Noguer. D-nerf: Neural radiance fields for dynamic scenes. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pp. 10318-10327, 2021.
Charles R Qi. Hao Su, Kaichun Mo, and Leonidas J Guibas. Pointnet: Deep learning point sets for 3d classification and segmentation. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 652-660, 20.
12

---

Published as a conference paper at ICLR 2026
Charles Ruizhongtai Qi, Li Yi, Hao Su, and Leonidas J Guibas. Pointnet++: Deep hierarchical fea- ture learning on point sets in a metric space. Advances in neural information processing systems, 30, 2017b.
Zilin Si, Gu Zhang, Qingwei Ben, Branden Romero, Zhou Xian, Chao Liu, and Chuang Gan. Diff- tactile: A physics-based based differentiable tactile simulator for contact-rich robotic manipulation. In The Twelfth International Conference on Learning Representations, 2024.
Anthony Simeonov, Yilun Du, Andrea Tagliasacchi, Joshua Tenenbaum, Alberto Rodriguez, Pulkit Agrawal, and Vincent Sitzmann. Neural descriptor fields: Se (3)=equivariant object rep- resentations for manipulation. In 2022 International Conference on Robotics and Automation (ICRA), pp. 6394 6400. IEEE, 2022.
Su Sun, Cheng Zhao, Zhuoyang Sun, Yingjie Victor Chen, and Mei Chen. Splatflow: Self- supervised dynamic gaussian splatting in neural motion flow field for autonomous driving. In Pro- ceedings of the Computer Vision and Pattern Recognition Conference, pp. 27487-27496, 2025.
Haowen Wang, Zhen Zhao, Zhao Jin, Zhengping Che, Liang Qiao, Yakun Huang. Zhipeng Fan, Xiuquan Qiao, and Jian Tang. Sm 3: Self-supervised multi-task modeling with multi-view 2d im- ages for articulated objects. 2024 IEEE International Conference on Robotics and Automation (ICRA), pp. 22492-1249.. IEEE, 2024.
Xiaogang Wang. Bin Zhou, Yahao Shi, Xiaowu Chen, Qinping Zhao, and Kai Xu. Shape2motion: Joint analysis of motion parts and attributes from 3d shapes. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 8876-8884, 2019.
Fangyin Wei, Rohan Chabra, Lingni Ma, Christoph Lassner, Michael Zollhöfer, Szymon Rusinkiewicz, Chris Sweeney, Richard Newcombe, and Mira Slavcheva. Self-supervised neu- ral articulated shape and appearance models. In Proceedings of the IEEE/CVE Conference on Computer Vision and Puttern Recognition, pp. 15816-15826, 2022.
Yijia Weng, Bowen Wen, Jonathan Tremblay, Valts Blukis, Dieter Fox, Leonidas Guibas, and Stan Birchfield. Neural implicit representation for building digital twins of unknown articulated ob- jects. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 3141-3150, 2024.
Di Wu, Liu Liu, Zhou Linli, Anran Huang. Liangtu Song, Qiaojun Yu, Qi Wu, and Cewu Lu. Reartgs: Reconstructing and generating articulated objects via 3d gaussian splatting with geo- metric and motion constraints. arXiv preprint arXiv:2503. 06677, 2025.
Guanjun Wu, Taoran Yi, Jiemin Fang. Lingxi Xie, Xiaopeng Zhang, Wei Wei, Wenyu Liu, Qi Tian, and Xinggang Wang. 4d gaussian splatting for real-time dynamic scene rendering. In Proceedings of the IÉÉE/CVF conference on computer vision and pattern recognition, pp. 10310-20320, 2024.
Tianhao Wu, Fangeheng Zhong, Andrea Tagliasacchi, Forrester Cole, and Cengiz Oztireli. De Self-supervised decoupling of dynamic and static objects from a monocular video. Advances in neural information processing systems, 35:32653 32666, 2022.
Fanbo Xiang, Yuzhe Qin, Kaichun Mo, Yikuan Xia, Hao Zhu, Fangchen Liu, Minghua Liu, Hanxiao Jiang. Yifu Yuan, He Wang, et al. Sapien: A simulated part-based interactive environment. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pp. 11097- 11107, 2020.
Zihao Yan, Ruizhen Hu, Xingguang Yan, Luanmin Chen, Oliver Van Kaick, Hao Zhang, and Hui Huang. Rpm-net: recurrent prediction of motion and parts from point cloud. ACM Transactions on Graphics (TOG), 38(6):1-15, 2019.
Jifan Yang, Steven Bednarski, Alison Bullock, Robin Harrap, 7ack MacDonald, Andrew Moore, and TC Nicholas Graham. Fostering the ar illusion: a study of how people interact with shared artifact in collocated augmented reality. Frontiers in Virtual Reality, 5: 5:1486765, 2024a.
Yunhan Yang, Xiaoyang Wu, Tong He, Hengshuang Zhao, and Xihui Liu. Sam3d: Segment anything in 3d scenes. arXiv preprint arXiv:2306.033908 2023.
13

---

Published as a conference paper at ICLR 2026
Zeyu Yang, Hongye Yang, Zijie Pan, and Li Zhang. Real-time photorealistic dynamic scene repre- sentation and rendering with 4d gaussian splatting. In The Twelfth International Conference on Learning Representations, 2024b.
Ziyi Yang, Xinyu Gao, Wen Zhou, Shaohui Jiao, Yuqing Zhang, and Xiaogang Jin. Deformable 3d gaussians for high-fidelity monocular dynamic scene reconstruction. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp. 20331-20341, June 2024c.
Mingqiao Ye, Martin Danelljan, Fisher Yu, and Lei Ke. Gaussian grouping: Segment and edit anything in 3d scenes. In European Conference on Computer Vision, pp. 162-179. Springer, 2024.
Zihang Zhao, Yuyang Li, Wanlin Li, Zhenghao Qi, Lecheng Ruan, Yixin Zhu, and Kaspar Althoefer. Tac-man: Tactile-informed prior-free manipulation of articulated objects. IEEE Transactions on Robotics, 2024.
14

---

surface reconstruc- Published as a conference paper at ICLR 2026
Appendix
The supplementary material is organized as follows. Sec. A elaborates the technical details; Sec. [ details the acquisition and reverse modeling pipeline used to construct the RS-Art dataset; Sec. C lists the complete experimental settings; Sec. D presents additional quantitative and qualita- tive results; and Sec. [ discusses the current limitations of our approach and directions for future work. All code and datasets will be released upon publication.
A METHOD DETAILS
A.1 BOUNDARY-AWARR GAUSSIAN SPLITTING
Selecting boundary candidates. For each 3D Gaussian primitive 9i = (1u,, Di, Ci2 az), ) we first locate its ray-sampling nearest view Unear- Assuming local affine projection, the covariance Σ; is mapped to the image plane by
E JWE, W J
(13)
where W and J denote the camera projection matrix and its Jacobian, respectively (Kerbl et al. 2023). The resulting 2 x 2 matrix Σ defines an ellipse; its major axis is aligned with the eigenvector of Σ that has the largest eigenvalue. either end of this axis lies outside the part mask M, M(("er) the primitive is marked as boundary candidate.
(Maor)
Geometric split ratio. Let A and B be the two end points of the projected major axis and let O' be their intersection with the mask boundary (A* lies inside, B" outside). Following the split strategy of Hu er al. (Hu et al. 2024), the in- in-mask proportion in image space is
AạD = 110"A
(14)
Because the projection is affine locally, the same ratio applies in 3D. With denoting the unit eigenvector Σ; that corresponds to its largest eigenvalue and s; the length of the associated axis, the two children are
part = A2D Part child: pu part = pi + 1-220 s,e, St
Background child: pr = p4i
Anp 8,0,
be
AaD)
Both children inherit color, opacity, and spherical harmonic coefficients to maintain visual consis- tency.
Recursive splitting and mask consistency. The background child is re-evaluated in its own nearest view; if its projected ellipse still crosses another part mask, the split is applied recursively until every descendant ellipse is fully contained in a single mask. The recursion stops when the ellipse lies entirely inside its mask or the new scale falls below a minimum threshold. After each split, the children are queued in descending order of projected error, so the most inaccurate primitives are processed first. Finally, multiview voting scheme assigns consistent mask label every new Gaussian, ensuring cross-view agreement.
A.2 MESH EXTRACTION FROM THE PART-AWARK GAUSSIAN FIELD
Given the part-aware Gaussian field g(a) = g Pies for the interaction state a, we recover ex- Jp=1 plicit geometry by multiview depth rendering followed by implicit-to-expp
tion. For each subset of parts gfa) we render depth map in every calibrated view, treating each Gaussian primitive using the standard 3DGS rasterizer. The rendered depths are fused with a truncated signed-distancd function (TSDF): voxel size and the truncation threshold are chosen empirically balance detail and noise. The resulting TSDF volume provides an implicit surface for part p. from which we extract a triangle mesh M. E IR V/I33 using the Marching Cubes algorithm implemented in Open3D (Huang et al. (024)). This procedure yields high-resolution, watertight mesh for every rigid part, faithfully capturing its geometry while preserving the spatial correspondence with the underlying Gaussian field.
ellipsoid whose pose and covariance
projected onto the image plane
15

---

Published as a conference paper at ICLR 2026
A.3 JOINT TYPE IDENTIRICATION
For part p we gather Gaussian centroids in two states P= {pi} and Q - {qa). and align them with the Kabsch algorithm (Lawrence al., 2019), which yields rotation R and translation t. The residuals d, q: (Rp; + t) are stacked in the 3 x n matrix D = [d] ... d,]. where the is the number of Gaussian kernels.
A motion of revolute leaves points on common axis, so D is lank-1; a motion of prismatic rigidly translates the entire part, giving full rank. With singular values 01 2 02 dss we compute r (02 + 03)/01. We label the joint revolute if < 0.05 and prismatic otherwise, rule that proved to be reliable across reference objects.
A.4 JOINT PARAMETER ESTIMATION
Revolute joint. A revolute joint is parameterized by pivot point R and unit quaternion q R. with |||| = 1. From the Kabsch alignment (Lawrence et al. 2019) we obtain rotation matrix R E 33x3 Its rotation axis the normalized eigenvector that satisfies Ru u, and the rotation angle is A = arccos( ((rr(())rrr))t 1)/2). The pivot p is found by least-squares fitting the axis the static centroids Catatics
arg min
Σ (1(x-c) c) u/l2.
(15)
x
eECause
Finally, the quatermion becomes (cos 0 usin 9)
Prismatic joint. A prismatic joint is defined by unit slide axis a E IR& and translation distance d. Let P {p,} and Q } be the part centroids in the two states. Their means are p 1, E, and q = 1 >. 9s. so the rigid translation is t = q P. Hence a t/|[t|| and = ||t|| These n
1
parameters constitute the minimal motion model used in our evaluation.
B RS-ART DATASET
(a) Full green-screen booth
(b) Seamless pedestal platform
(c) Hand-held RGB-D capture
Figure 9: Capture platform.
Capture platform. Our data are acquired in purpose-built chroma-key booth (Fig. 9). Four aluminum beams support a seamless green curtain that encloses 2.5 m-high cubic volume and blocks stray reflections while maintaining uniform ambient illumination. In the center stands square pedestal 0.5 m x 0.5 m, fully wrapped in the same green fabric. The rear side of the cloth is glued to the floor so that the pedestal merges smoothly with the ground plane, eliminating visible seams in the depth and color images.
The operator mounts an Intel RealSense RGB-D camera (Keselman et al. 2017) rigidly on the lid of laptop, then walks circular trajectory whose radius is chosen in real time from the live video feed to keep the target object at the desired image scale. Each circuit produces a set of synchronized RGB and depth frames that share consistent chroma-key background, which simplifies subsequent background removal and calibration.
Real-scene acquisition pipeline. As illustrated in Fig. 10, to keep the real data fully compatible with the experimental settings used for the Mobilit-Mobilty dataset (Xiang et al.) 2222)). we record two complementary interaction groups for each object. (i) Multi-part sequences: all movable parts
16

---

Published as a conference paper at ICLR 2026
state 0 prismatic part: 0.55
state
state 2
state
prismatic part: 0,46
prismatic part: 0.38
prismatic part: 0.3
revolute part: 20"
revolute part: 36.6"
revolute part: 63.3"
revolute part: 70"
state 4
state prismatic parts 0
state 6
state 7 prismatic part: 0.3
prismatic part: 0
prismutic part: 0.55 revolute part: 0
revolute part: 20"
revolute part: 70"
revolute part: 0
Figure 10: Example of multi-state acquisition. Using a PartNet-Mobility object for illustration, we capture eight interaction states that span the full motion range every joint. States 0-3 (top row) depict multi-part motion in which all movable components change pose simultaneously, whereas States 4-7 (bottom row) show the single-part mode where one component moves while the others remain fixed.
actuated simultaneously, and the capture spans four evenly spaced configurations that bracket the mechanical limits, for example, fully closed, half-open, three-quarter open, and fully open. (ii) Single-pan sequences: each rotational translational part is moved while the others remain fixed; for every part, we acquire two extreme poses corresponding to its minimum and maximum joint limits.
For each interaction state, we sample RGB-D images along a circular path whose viewing elevation uniformly chosen in the range 30 60%. The operator walks once around the object with an Intel RealSense camera (Keselman et al. 2017) rigidly mounted on laptop lid, keeping the target centered in the live preview.
(a) Real object capture
(b) Object reverse model
(c) Part-level articulation model
Figure 11: Reverse modeling of a basket object.
Modeling and registration workflow. All digital assets are created Isaac Sim 4.2 (NVIDIA) 2024a), whose USD pipeline provides both photorealistic rendering and physically consistent simu- lation (see Fig. 11 for representative modeling scene). We first reverse-model each real object with calipers. producing watertight USD mesh; subparts are manually segmented according to func- tional affordances and joint boundaries. High-resolution textures and PBR materials are authored in Blender 4.2.0 (Blender Foundation, (024) and imported into Isaac Sim without loss of visual fidelity. The physical properties mass, inertia, and friction are assigned following the official Omniverse workflow (NVIDIA 2024b). The joint pivots and motion limits calibrated by sys- tem identification, ensuring that the articulation of the digital twin in Isaac Sim reproduces the joint behavior observed the physical object. The resulting USD files provide aixel-accurate appear-
17

---

Published as a conference paper at ICLR 2026
and dynamics-ready articulation, forming reliable ground truth for both vision and physics experiments.
RS-ART/
object_98C
meta.jsan
part list, joint limits, state groups multi-view RGB-D captures
real/
intrinsics.jsom
state_00/
rgb/000 png
depth/800.
noses.npy
state__/
usd/object__ee uss
full visual+physics asset
urdf crdj/objeet_Be0.
lightweight kinematic model
rendered/
optional re-renders, same layout as /real ground-truth part surfaces
meshes/
part_ p1.ply
identical structure
object_011
Figure 12: RS-Art Dataset directory layout.
Dataset structure. Fig. 12 outlines the RS-Art hierarchy. The dataset contains 18 articulated ob- jects drawn from six everyday categories:drawer, lamp, eyeglasses, floppy-disk drive, basket, and phone / laptop stand with three instances per class. For every object we supply the complete set of multi-view RGB-D captures for each recorded interaction state together with the shared camera intrinsics and the per-view extrinsics; a fully reverse-modeling digital twin comprising USD file that bundles part meshes, textures, physics properties, and joint definitions, a matching lightweight URDF, and watertight PLY meshes for geometry evaluation; and concise meta. json that merates all parts, joint types, axes, limits, and labels every state as either multi-part or single-part motion. This combination of real imagery and fully articulated digital twins enables training, quanti- tative evaluation, and sim-to-real studies for part-aware geometry reconstruction and joint parameter estimation.
C EXPERIMENTAL SETTINGS
To provide the most comprehensive comparison date, evaluated all publicly available meth- ods that match our task definition of multiview, multi-state articulated object reconstruction. Since competing pipelines differ in input assumptions and functional scope, group them into three categories and tailor the data acquisition protocol accordingly. aiming for maximum fairesss while respecting the design of each method.
Single-part assumptions (PARIS (Liu al. 2023) and ArticulatedGS (Guo et al. 2025)). These methods can reconstruct only one movable part at a time. For every movable part, we capture two interaction states in which that part moves while all other parts remain fixed, and we run the pipeline independently for each part. Each state is sampled with 100 random, calibrated RGB views, giving 200 images per part.
Multi-part, two-state methods (DTArt (Weng et al. 2024) and ArtGS(Liu et al., 2025b).. These pipelines accept two distinct object states and can handle several movable parts jointly, provided that the part count is known. We therefore collect two interaction states and sample 100 random views per state (total 200 RGB images). The ground-truth number of movable parts is passed to both methods. As DTArt requires depth input, depth maps for every view are rendered Gazebo (Koenig & Howard 2004).
Our method & PD handles an arbitrary number of parts and interaction states without knowing the part count. To match the total image budget of competing methods, we sample four
18

---

Published as a conference paper at ICLR 2026
interaction states in which multiple parts move simultaneously and capture 50 random views per state, producing the same 200-image input. No depth or manual parts information provided.
This protocol equalizes the per-run image budget to 200 views, making the inputs comparable across methods. Note, however, that single-part baselines must be executed once for the each movable part, so they ultimately consume 200 purts images per object.
D ADDITIONAL RESULTS
Table 3: Quantitative results with our method restricted to two interaction states as input.
Metric
Box
Door
Eyeglasses
Faucet
Oven
Fridge
Storage
Table
Mean
Axis Ang
1.08
8.70
0.35
2.40
1.59
2.64
2.46
3,70
2.87
Axis Pos
0.37
1.19
0.26
0.21
0.10
0.24
0.36
0.51
0.41
Part Motion +
6,86
3.25
7.73
2.96
8.06
9.54
1.74
3.55
5.46
CD-s 4
9.21
6.38
18,55
1.11
2.16
14.31
7,64
4,28
7.96
CD-m m
6.98
18.06
9.37
0.14
18.78
0.54
13.96
24.85
11.59
CD-w 8.90
1.73
11.83
0.54
9.15
10.43
4.67
3.75
6.38
D.1 RESULTS ON TWO INTERACTION STATES
Because the baselines can use only two states, we limit our method to total of 200 RGB images as input; our multi-state model therefore receives fewer views per state than the baselines, maintaining a comparable degree of fairness across methods. We add more state = 2 results for direct side-by- side comparison Tab. 3 further strengthening the fairness of the evaluation. All reported metrics are averaged across all parts and object categories. This experiment extends Tab. 1 setting of main paper directly assess performance under the two-state constraint. shown Tab. 3 our method still maintains strong performance under these settings.
Table 4: Joint-level metrics for PartNet-Mobility objects that contain three movable parts. A dash marks entries that are not applicable because the corresponding joint is prismatic and therefore has no pivot position.
Object
Axto 01
AL
11
Asis P.
PARIS
Crec A200
9:56
20.61
0.47
0.13
0.31
0.30
30.23
111.21
33.72
Amical
M055
0.12
6.11
3,00
0.6.
6.17
0.42
6.25
2.15
14:43
108993
7TAm
Worr
6.29
67.17
PARIS
M00
64.17
10.8
18.50
0.29
0.13
116.3
10094
0.33
Amiral Imores
4113
13.01
5.17
1.51
1.56
0.56
1.45
0
PARIS [i
57 00
76.5%
0.17
30
Amt38 Famerr
0.00
0.81
0000
7D (002))
0.80
0.34
0.36
8/0
0.00
0.00
0.58
PARUS Lis
152.14
Takle 33572
DTAm
Ween
0.31
0.14
0.68
Ant28 Ianerrsr 10001
0.00
10.0
14.44
0.17
1.75
1100
75.15
15.43
PD7C8 (00r))
8.01
0.12
0.29
0,03
0.12
0.00
0.12
0.45
D.2 RESULTS ON OBJECTS WITH MULTIPLE MOVABLE PARTS
Sec. 5.2
in the main paper reported our main evaluation on objects that contain two movable parts. Here, we extend the analysis to the more challenging subset, objects equipped with three indepen- dently actuated components, and provide both quantitative and qualitative evidence of performance.
Tab. and Tab. cob.pacc all baselines the three-part instances of PartNit-Mobility (Xiang al.) 2020). Our method achieves the lowest second-lowest error in nearly every joint metric (axis angle, axis position, axis motion) and remains highly competitive in the geometry metrics (Chamfer distances). The consistently smaller joint errors indicate that the latent- iient-conditioned deformation field captures the complex motion couplings that arise when three parts move independently. while the geometry scores confirm that the boundary regions between parts reconstructed sharply.
19

---

Published as a conference paper at ICLR 2026
Table Geometry-level metrics for PartNet-Mobility objects that contain three movable parts.
Object Instance
Method
CD-s
CD-m 0 4
CD-m
CD-m 2
CD-w
PARIS (Liu
2023
17.70
22.36
279.47
184.97
16.66
Articulateukss
(8o cl
2025
16.86
13.59
23.99
5.18
13.23
102373
(Weng ct
3.88
199.49
AnGS [10 et 2025b
9.70
14.18
5.38
2.63
7.78
PDPGS (Uurs)
6.70
0.88
0.39
2.21
5.75
PARIS (Liu ct 2025
28.16
8.77
193.38
656.10
ArticulateUGS (Cuo
2025
14.48
1.29
0.85
16.15
10.71
Storage 45194
DTAit (Weng el 2022
4.41
71.85
0.09
33.20
1.12
AntS
50.86
19.00
1.78
2041.00
6.77
PD'GSTOurS)
8.88
0.49
0.51
4.53
6,04
PARIS (Liu et al. 2023
5.09
668.39
703.55
19.35
5.50
Articulaten
1.28
0.85
Storage 45271
DTArt (Weng et A144
2.94
307.65
F
406.23
8.76
AnGS TTU0 ct 20256
1.40
0.38
0.46
0.14
PDPGS (Ours)
4.24
0.23
0.41
0.23
3.26
PARIS (Liu al. 2023
4.14
5.40
25.67
45.57
2.03
Articulateu (Cuo et
2025
5.72
25.34
0.72
15.96
Table 23372
DTArt Weng et
1.31
0.37
0.18
1.21
0.95
AnGS LTu et 20255
3.38
4,50
1.34
L.05
2.84
(Ours)
2.17
0.15
GT
Ours
PARIS
ArticulatedGS
DTA
ArtGS
Storage
Storage
Table
Figure 13: Qualitative multi- task modeling results on articulated objects with three movable parts.
Table Evaluation of our method on object instances with five movable parts. Each reported metric averaged across individual parts per instance.
OWjectt Instance
Method
Axis Ang
Axis Pos
Pur Motion
CD44
CD-m
CT>w
PARIS
36
Storage 45271
AnGS
40250
1.60
0.01
1,94
2.45
4.27
1.77
PD*GS
(Uus)
0.02
0.00
0,02
1.39
0.71
1.25
PARIS
1i
2025
61.37
0.14
46.16
5.89
577.17
5.07
Sturage
GS (Curs)
0.04
0.03
0.01
1.40
0.53
1.32
PARIS 1a a1
2023
36.58
0.30
7.73
361.76
6.52
Table 30666
AnGS
8.91
0.15
9.68
1159.33
5.70
(CRFS)
PARIS
at
2025
1.07
0.03
0.92
3.53
73.97
3.44
Table 33810
AnGS
20251
48.67
32.02
8.04
5.75
1346.58
3.18
PDRGS
compares our method with the baselines on the objects with three movable parts and vi- sualizes all recovered outputs: part-aware geometry (colored meshes), joint axes (red arrows) and part labels. The results demonstrate that our deformable- field formulation yields a coherent solution across all three modalities: the reconstructed geometry is complete and well aligned, the estimated
Fig. 13
20

---

Published as a conference paper at ICLR 2026
Reconstruction
Modeling
Real World
Interpolation
ArtGS
Ours
ArtGS
Ours
Figure 14: Qualitative comparison on real objects from RS-Art.
axes coincide with the true joint locations and orientations, and the segmentation cleanly separates the three movable parts. Together, these visual cues indicate that the latent-conditioned deformation field is able discover and model complex kinematic structures, even with three interacting joints, without manual specification of part identities.
To further validate scalability to higher articulation complexity, Tab. reports additional results on objects with five movable parts. These instances present substantially challenging kinematic couplings and occlusion patterns than the two- and three-part cases. Despite the increased difficulty, approach continues produce accurate joint estimates and detailed geometry.
D.3 RESULTS ON THE RS-ART DATASET
Fig. 14 and Tab. present qualitative and quantitative results on our RS-Art dataset. Although the capture setup avoids strong specular highlights and cast shadows, the real objects still exhibit com- plex materials, weak surface texture, and narrower viewing envelope than in simulation, making the task substantially harder than on PartNet- Mobility (Xiang al. 2020). Among the baselines. only AnGS can be made to run reliably the real data, so we compare against it on every instance that yields a converged model. Across all evaluated objects, our method achieves lower joint parameter and geometry eπrоrs and produces cleaner part segmentation, confirming that the deformation-fiee formulation transfers to real scenes. Meanwhile, the results highlight the open challenges discussed in Sec. E) fine surface details degrade under limited texture and grazing angles, and heavy occlusion can still disturb the 3DGS reconstruction. These observations underline the necessity of RS-Art as bridge between synthetic evaluation and real- weal-world deployment.
Fig. 15 shows qualitative results on RS-Art objects captured in real scenes, where cluttered back- grounds, natural illumination, and real-world materials make reconstruction noticeably more chal-
21

---

Published as a conference paper at ICLR 2026
Table Results on the RS-Art Dataset.
Real World Objects Fluppy- Disk
Metric
Desk Lamps
Eyeglasses
PhoneLLapiop Stand
Mean
1
cl
72.98
29:
Ang 0
PDPGS (CGrs)
0.84
0.32
4.45
1.71
0.58
0.54
1.46
Axis
AntiS
Liu et X0250
3.43
83.25
23.24
83.24
57.24
24.64
45.84
15.27
3,07
Pos
PDPGS (Cors)
0.36
2.07
0.89
1.17
1.12
Axis 1
AnGS
Lia al. 20256
20226
8.56
12.23
83.35
45.35
37.37
Pos
PDRCS (Ours)
0.32
0.36
0.40
9.31
2.60
AnGS
Liu
PDPGS (Cors)
0.38
0.87
1.79
2.49
Part Motion
AnG8 Liu et 32250
16.38
13.07
43.33
63.45
150.35
5.35
48.65
0.36
0.58
0.74
2.27
4.97
5.04
2.33
AnGS Liu al. 32.50
41.39
11.38
25.24
53.53
6.34
14.35
25.37
PDRcS (Chrr)
CDvm 0
AnG8 Liu cta. 20256 PD-GS
20226
121.69
39.09
33.24
104.35
58.24
26.19
63.85
3.09
4.83
7.19
10.37
5,63
10.08
6.86
CD
AnGS [iu et 20256 PDPGS
180.57
34.18
234.24
156.35
62.61
43.98
118.66
CD.w
ArGS [Luu 20256
16.55
7.96
6.09
3,05
14,80
96.
19.03
12.78
29.90
14.35
Object
PARIS
ArticulatedGS
ArtGS
Drawers
PARIS-Fridge
PARIS-Storage
Figure 15: Qualitative comparison on real-world scenes.
lenging. Even under these conditions, method recovers sharper geometry and more stable part motions, particularly when object boundaries remain reasonably clear. To ensure a fair evaluation, also conduct reconstruction comparisons the real-scene benchmark of the PARIS dataset. In these challenging scenarios where baselines often suffer from severe structural degradation or fail converge, PD consistently maintains structural integrity and cleaner part boundaries, pro- ducing practically usable reconstructions while suppressing artifacts such as surface blurring and deformation spillover.
Table Robustness evaluation under camera pose inaccuracies.
Method
Ang
Axis
Motion
CDis
J
CD
PARIS Liu et
2023
w/o Perturbation
29.98
0.38
70.84
12.98
103.22
10.95
AnGS
(Lm el
20256
w/o Perturhution
3,53
3.46
5.49
4.29
82.65
6.72
PDRGS
[1.0
0.02)
3.66
11.09
PDRGS (Ours) w/ (3.0%, 0.05)
10.00
0.24
1.55
13.60
24.71
9.19
PDRGS (Ouns) w/ colmap
1.93
3.85
7.39
6.82
7.63
PD'GS (Ours) w/o Perturbation
0.40
0.06
0.43
2.05
1.12
3,02
D.4 EFFECT OF CAMERA POSE ERRORS
To evaluate robustness camera pose inaccuracies. design three controlled perturbation set- tings. Starting from ground- truth poses, we inject Gaussian noise into the rotation and translation components form perturbation levels, denoted (u, v), where is the standard deviation
22

---

Published as a conference paper at ICLR 2026
of rotational noise measured in degrees and is that of translational noise measured in scene units. In addition, we test third setup that uses camera poses estimated by COLMAP. All methods are evaluated using the same protocol as Tab. Tin the main paper. Metrics averaged across all artic- ulated parts and objects. As shown in Tab. 8 although performance decreases slightly due to these perturbations, method consistently maintains superior results compared prior methods.
Table 9: Quantitative comparison with articulated generation baselines on the Storage category.
Object
Method
Axis Ang 4
Axis Pos
Part Motion +
CD-s
CD-m 4
CD-w
NAP (Lei 2023
3.88
2.45
7.29
5.56
5.19
8.54
Storage
SINGAPO Luu ala
2025a
2.72
0.86
9.03
PD (Ours)
0.13
0.02
0.32
2.78
0.07
5.48
D.5 COMPARISON WITH ARTICULATED GENERATION METHODS
We further extended our evaluation to include generative articulated object models, NAP Lei et al, 2023) and SINGAPO (Liu et al. 2025a)). NAP eL.. 2023) operates by generating target objects from Gaussian noise derived from specific instances, whereas SINGAPO (Liu et al.
2025a) infers them from single input view. To ensure robust evaluation for SINGAPO (Liu et al. 2025a)
given its single-view dependence, we randomly sampled 50 input views for each object and reported the metrics from the best-performing result. As shown in Tab. g both methods exhibit significant deviations in joint motion analysis compared to our approach, reflecting the inherent distinction between generative plausibility and the precise kinematic inference required for our task.
Table 10: Training and inference time for objects with varying numbers of articulated parts.
Number of parts
Method
PARIS (Liu al
2023
31.38
45.99
75.15
DTArtt
Weng
2024
26.31
31.42
43.76
Training (min)
ArGS
Li at.
2225
16.22
15.08
17.86
PD2GS (Ours)
35.59
38.20
44.82
PARIS Liu et al.
2023
24773.60
37180.59
61924.30
DTArt
Weng el 40Z4
568.67
525,70
613.30
Inference (ms)
AnGS
Liu ct al. 20256
3.42
3.71
4.16
PD*GS (Ours)
37.93
40.86
37.22
D.6 RESULTS ON TRAINING AND INFERENCE TIME
We provide statistics on training and inference overhead for reference, shown in Tab. 10 For fair comparison, all methods are trained on the same dataset of 200 views per object.
inference, since discrete-state baselines (DTArt (Weng al. 2024), ArGSS (Liu Regarding cannot natively infer arbitrary continuous states, we measured their timings by explicitly rigidly transforming their reconstructed models using inferred joint parameters. Specifically, for ArtGS (Liu et al.] (0255). we render by rigidly transforming the reconstructed Gaussian field; thus, the inference time is equivalent to standard static 3DGS (Kerbl et al. 2023). contrast, our method requires evaluation of a latent-conditioned deformation field. In the context of articulated object modeling, inference efficiency not the primary limiting factor. Thus, this difference is secondary to the substantial gains in modeling capability.
2025b
D.7 ABLATION STUDIES
Refinement stage. Sec. 5.5 in the main paper visualizes the qualitative benefit of coarse-to-fine refinement. Tab. complements that visual evidence with numerical results on four representative objects. Across all geometry metrics, the refined model (w/ Refined) consistently outperforms the same network trained without the refinement stage (w/o Refined). Averaged across the four objects, the refinement reduces CD-s by 35% and CD-m by 60%. The greatest gains occur at part bound- aries (CD-m columns), confirming that boundary-aware Gaussian splitting and local fine-tuning
23

---

Published as a conference paper at ICLR 2026
Table 11: Quantitative ablation study on the refinement stage.
Object Instance
Method
CD-s 4
CD-m 0 +
CD-m
CD-w 4
w/o Refined
11.66
2.12
2.14
10.16
Box 100676
w/ Refined
9.42
1.58
1.52
8.03
w/o Refined
21.56
5.44
2.16
17.58
Oven 7187
w/ Refined
16.58
0.32
0.54
13.91
w/o Refined
16.94
0.60
0.92
12.06
Refrigerator 12248
w/ Refined
13.63
0.21
0.23
9.53
w/o Refined
13.63
2.91
1.24
9,53
Storage 47254
w/ Refined
6.52
0.60
0.92
5.05
Table 12: Ablation on the number of interaction states K. Each column lists the performance metrics obtained with the corresponding K, evaluated on the PartNet-Mobility object Door 9168.
Metric
K=2
K=4
K=6
K=8
K=10 10
Axis Ang 0
31.45
0.30
0.14
0.07
0.36
Axis Ang +
47.83
0.33
0.22
0.17
0.15
Axis Pos 0 4
0.38
0.34
0.12
0.06
0.18
Axis Pos 1 +.
0.07
0.26
0.19
0.05
0.29
Part Motion 0 0.
57.60
1.44
1.35
1.24
1.03
Part Motion +
56.71
2.38
1.74
0.71
2.10
CD-s +
1.63
0.53
0.56
0.63
0.77
CD-m
85.87
0.63
0.49
1.38
1.24
CD-m
142.74
0.33
0.57
0.90
0.79
CD-w
0.81
0.60
0.64
0.84
0.87
markedly sharpen the reconstructed surfaces and prevent inter siterrpenetration. These numbers corrob- orate the qualitative observations in Sec, 5.5 highlight the refinement stage as a key component for accurate part-level geometry.
K 2
K 4
8
10
Figure 16: Qualitative effect of the number of interaction states.
The number of interaction states. Tab. 12 and Fig. 16 show how our method reacts to different numbers of input interaction states K. With just two interaction states (K 2). the network sees only start-to-end displacement for each Gaussian. This limited evidence allows multiple trajectory assignments fit the same images, so Gaussians can drift between neighboring parts, leading to inflated joint errors and indistinct part boundaries. As more states are provided, every primitive must follow longer and more distinctive trajectory. The stronger constraint eliminates ambiguity: Gaussian that does not truly belong to a part can no longer match the motion of that part in all states, and the optimizer moves to the correct rigid component, causing a rapid drop in error. However, after each joint has appeared in several diverse poses, additional states add little fresh kinematic information while still introducing measurement noise and extra training time, so the accuracy curve levels off and may fluctuate slightly.
Prompting strategies on component-count estimation. Tab. 1 compares our approach with two alternative prompting strategies, specifically single-view queries and generic cross-state queries, and shows that our method provides the most stable and accurate component-cour estimates. VLM- MI queries single views ("How many movable components does this object contain?"); VLM-M2
24

---

Published as a conference paper at ICLR 2026
Table 13: Movable-component count estimation accuracy (correct/total number) for three VLM prompting schemes across eight object categories (instance counts in parentheses).
Method
Box (2)
Dour (3)
Eyeglasses (2)
Faucet (2)
Oven (2)
Fridge (3)
Storage (3)
Table (3)
Overall Accuracy
VLM-MI
1/2
3/3
2/2
1/2
2/2
3/3
3/3
3/3
90 %
VLM-M2
0/2
0/3
1/2
2/2
0/2
0/3
0/3
0/3
15 %
VLM-Ours
2/2
3/3
2/2
2/2
2/2
3/3
3/3
100
Table 14: Comparison of SAM-based segmentation accuracy between our approach and the SAGD method.
Metric
Method
Box
Door
Eyeglasses
Faucet
Oven
Fridge
Storage
Table
Mean
SAGD Hu al
2024
45.37
42.79
28.49
34.71
38.32
45.02
44,70
58.04
42.18
loU
SAM-Ours
84.20
89.61
69.40
83.72
75.33
87.09
78.06
79.25
80.83
SAGD Hu ct al SAM-Ours
2024
94.63
97.1
97.96
97.46
91.64
95.23
94.54
97.79
95.80
Acc
98.06
98.75
99.57
99.47
98.70
99.37
97.92
98.76
98.82
SAGD et al. 2024
54.46
52.34
38.01
49.02
46.89
52.11
55.31
65.21
51.67
Fi-score
SAM-Ours
89.74
95.05
81.04
90.82
81.42
91.46
85.00
85.58
87.51
queries cross-state pairs ("How many movable parts are identifiable from these two states of the same object?"). Final counts are determined by the most frequent response. This design eliminates need for manual Plparts selection required in previous 3DGS pipelines.
SAM-based component segmentation. For SAM segmentation, as shown in Tab. 14 we compare SAM-based 3DGS segmentation method, SAGD (Hu et al. 2024). In all cases, these alternatives perform worse than the full pipeline, provid- ing quantitative evidence for the value of each component.
our approach to the current state-of-the-art
Table 15: Quantitative evaluation of each pipeline module all object categories. All metrics are averaged over parts. For Ace and IoU (reported as %), higher values are better; for CD-w (reported in mm), lower values are better.
Module Metric
Box
Door
Eyeglasses
Faucet
Oven
Fridge
Storage
Table
Mean
Deformable GS (CD-w)
8.32
0.64
0.27
0.57
13.78
9.43
3.94
3.05
5.00
Coarse Seg. (Ace, %)
72.63
86.93
86.45
66.82
59.45
67.57
67.64
82.45
73.74
SAM+Prompi (IoU, %)
84.20
89.61
69.40
83.72
75.33
87.09
78.06
79.25
80.83
Refined Seg. (Acc,%)
95.83
95.41
98.64
99.53
99.23
96.41
85.76
98.29
96.14
Each pipeline module. For each key module, we report a dedicated quantitative metric in the Tab. [5 For Deformable GS reconstruction(See.. (.2). Chamfer distance demonstrates stable and accurate geometric modeling across all categories. For VLMM-bssed part counting (Sec. (.3). Deliv- consistently high accuracy, validating the effectiveness of our task-specific prompt. For Coarse Gaussian Segmentation (Sec. (3.3), High accuracy confirms reliable part-level grouping, enabling ro- bust downstream point prompt for SAM. For SAM with prompt (Sec. Achieves precise seman- tic segmentation. For Refined Degmentation(Ser 3.4), Post-refinement clustering further increases accuracy, showing precise decoupling of part-level Gaussians. The consistency of these metrics across all objects and scenes confirms that each module is robust and that the pipeline as a whole is stable.
E LIMITATIONS
Incomplete part reconstruction under occlusion. Like other NeRF-based and 3D Gaussian Splatting-based approaches, PD*GS may struggle to reconstruct complete geometry and texture for every part of the object. This limitation arises in cases of severe occlusion, limited viewpoints, or coupled articulation, where certain surfaces are never observed. In addition, the representation not surface-an aware by design, with both the NeRF and 3DGS models radiance and density fields rather than explicit meshes, which can lead to surface artifacts and coarse or noisy geometry. Real-scene results also suggest that texture fidelity degrade under challenging lighting conditions. Future
25

---

Published as a conference paper at ICLR 2026
work may explore integrating surface priors, reflectance models, learned data- priors, such as diffusion models, to enhance reconstruction fidelity and plausibly complete unobserved geometry in under-constrained regions.
Limited articulation understanding from sparse states. PD'GS infers motion by comparing in- teraction states, but reasoning about joint types and motion limits remains difficult. In particular, screw-type joints are difficult to identify, as the motion between observed states may produce lit- lle or visible appearance change, making them indistinguishable from static or simpler joints under visual comparison alone. Similarly, estimating articulation limits (e.g., joint range or end stops) requires observing motions near those extremes, which sparse or biased sampling may not capture. Incorporating additional interaction sequences or learning from temporal transitions could help enrich articulation inference in future extensions.
Lack of physical properties for simulation. While PD²GS focuses on visual and kinematic model- ing, it does not capture physical properties such as mass, friction, or compliance, which are essential for high-fidelity digital twins. These properties are crucial for accurate simulation and downstream robotic tasks, but are currently absent from most NeRF/3DGS bbaeeed pipelines. Bridging this gap may require integrating material prediction models, learning from physical interactions, or coupling neural reconstruction with differentiable simulation frameworks.
26


Reviews:
[{"review_id": "EwLa3CR3jo", "reviewer": "Reviewer_8QYT", "summary": "This work presents PD$^2$GS, a framework for modeling articulated objects that overcomes the fragmentation and drift issues in existing self-supervised methods. It learns a shared canonical Gaussian field and represents arbitrary states as continuous deformations, jointly encoding geometry and kinematics. By associating each state with a latent code and using vision priors for part boundary refinement, PD$^2$GS enables accurate part-level decoupling while maintaining coherence. The method supports part-aware reconstruction, continuous control, and kinematic modeling without manual supervision.", "questions": "Please see the weaknesses. I am hesitant about the rating primarily due to the reconstruction quality. Since this is fundamentally a reconstruction task, the results appear too coarse and do not meet the expected level of fidelity for such work.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "1. The paper introduces a unified framework that models articulated objects through continuous deformations of a shared canonical Gaussian field, effectively addressing the fragmentation and drift issues inherent in previous discrete-state reconstruction methods. \n\n2. The method achieves part-level decoupling without manual supervision by leveraging generic vision priors and latent code associations, enabling fine-grained continuous control over articulated configurations. \n\n3. The paper contributes RS-Art, a valuable real-to-sim RGB-D dataset with reverse-engineered 3D models, facilitating rigorous evaluation on real-world data.", "weaknesses": "1. The reconstruction results exhibit excessive noise, particularly evident in the real-world examples shown in Figure 13, which raises concerns about the method's robustness in practical scenarios.\n\n2. In Section 3.2 on deformable Gaussian splatting, the methodology bears strong similarity to existing 4DGS works such as [a], yet these related approaches are not cited or discussed.\n\n3. The paper does not provide information about inference time per sample, which would be valuable for understanding the practical applicability of the method.\n\n4. There are some related works that are missing in the paper: [b][c][d][e]\n\n[a] 4D Gaussian Splatting for Real-Time Dynamic Scene Rendering;\n\n[b] SINGAPO: Single Image Controlled Generation of Articulated Parts in Objects;\n\n[c] Part2GS: Part-aware Modeling of Articulated Objects using 3D Gaussian Splatting;\n\n[d] REACTO: Reconstructing Articulated Objects from a Single Video;\n\n[e] NAP: Neural 3D Articulation Prior.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "ogYq5dwjXS", "reviewer": "Reviewer_VL5q", "summary": "The paper proposes PD²GS, a self-supervised framework for articulated object modeling using 3D Gaussian Splatting. It learns a shared canonical Gaussian field and represents each interaction state as a continuous deformation via latent codes. A coarse-to-fine segmentation clusters Gaussian primitives by deformation trajectories and refines part boundaries using SAM-guided splitting, enabling part-level reconstruction and motion estimation. The authors also introduce RS-Art, a real-to-sim RGB-D dataset for evaluating generalization. Experiments show strong improvements over prior work on both synthetic and real objects.", "questions": "see weakness", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- Technical contribution: the paper proposes a conceptually elegant unification of geometry and kinematics via continuous deformation of a canonical Gaussian field. Coarse-to-fine segmentation combining motion trajectories with SAM-driven boundary refinement is both novel and effective.\n    \n- RS-Art dataset is a meaningful contribution, bridging synthetic–real gaps with paired RGB-D data and 3D models.\n    \n- Comprehensive experiments on an expanded PartNet-Mobility split and the new dataset demonstrate strong performance and generalization.", "weaknesses": "- Pipeline is complex and involves many heuristic components, which limited the scalability of the method.\n- The method proposed in the paper seems to require  multiple states, which puts forward more requirements for the data curation.  Furthermore, ensuring that the camera coordinate systems of all states are aligned is a challenge.  Outside the laboratory environment, such as in simple home scenarios, it is difficult for us to obtain states with multiple coordinate systems aligned, and the errors caused by coordinate misalignment are very likely to lead to failure.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "BDVCXk5fgl", "reviewer": "Reviewer_5MT6", "summary": "The paper addresses the problem of reconstructing articulated objects from multi-view, multi-state observations. The approach first learns a smooth deformation of a shared canonical field for each interaction state, and then uses the resulting deformation trajectories to guide a progressive coarse-to-fine part segmentation. The segmentation is further refined using SAM-based cues and boundary-aware Gaussian splitting. The method then estimates per-part meshes as well as joint types and parameters. In addition, the paper introduces a new dataset, RS-Art, containing a large number of real-world captures of articulated objects.", "questions": "See above.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The newly proposed dataset RS-Art should be useful for further research work if made public, especially those real-world captures.\n2. The paper seems to achieve SOTA performance than baselines with multi-state multi-view images in most cases.\n3. The authors conducted extensive experiments on different datasets.", "weaknesses": "1. The whole systems seem to compose of numerous parts, which may be a little complicate and hard to extend.\n2. Some visualizations on the newly-proposed dataset, including the data itself and the reconstructed results in videos would help readers grasp the new dataset.\n3. The proposed method seem to be a little incremental though it achieves the best performance in most cases. It didn't deal with physical plausibility like 3D penetration. Its setting is also not unique as the main difference with previous method is changing from two-state to multi-state. The authors may elaborate on what's new that we are learning when building articulated objects.\n\nThough I still have the mentioned concerns, I currently vote for borderline accept due to the extensive experiments and the SOTA performance.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "hJzlPmebFR", "reviewer": "Reviewer_HeoQ", "summary": "This paper introduces PD²GS, a novel framework for reconstructing and modeling articulated objects from multi-view images without manual supervision. Its core idea is to represent an object's various interaction states as continuous deformations of a single, shared canonical 3D Gaussian field, enabling smooth control and interpolation. Key contributions include a coarse-to-fine segmentation that automatically discovers rigid parts by clustering motion trajectories and refining boundaries with SAM, and the release of the RS-Art dataset for real-world evaluation.", "questions": "1.Dynamic Scene Baselines: Why were foundational dynamic scene representations like D²NeRF or other deformable 3DGS methods not included as baselines? A comparison would help clarify whether the performance gains are specific to the articulated object modeling pipeline or also represent a general advance in deformation field modeling.\n\n2.Camera Pose Robustness: The paper states an assumption of accurate camera poses. Could you provide an ablation or sensitivity analysis on the robustness of PD²GS to noisy camera poses, which are common in real-world SfM pipelines? This would significantly strengthen the claim of real-world applicability.\n\n3.Handling Occlusion: The limitation of being unable to reconstruct unobserved geometry is acknowledged. Have the authors considered or experimented with incorporating learned or data-driven priors (e.g., diffusion models, symmetry) to plausibly complete the occluded parts of an object, especially around joints?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "The core idea of modeling all interaction states as continuous deformations of a single, shared canonical 3D Gaussian field is both simple and powerful. This elegantly sidesteps the \"representational fragmentation\" of prior two-state methods, enabling smooth, continuous control and interpolation of articulated poses, which is a major step towards high-fidelity digital twins. The framework automatically infers the number and boundaries of rigid parts without manual supervision. It achieves this through a clever coarse-to-fine process that first clusters Gaussians by their motion trajectories (using a VLM for part counting) and then refines boundaries using SAM, making it highly applicable to real-world objects with unknown kinematics.", "weaknesses": "The empirical evaluation lacks comparison to foundational dynamic scene representation works like D²NeRF (Dynamically Deformable NeRF) or Gao et al.'s deformable 3DGS, which also model scenes via a canonical field and latent-code-driven deformation. This omission makes it difficult to assess the true novelty and contribution of the deformation modeling component beyond the specific task of articulation.\nThe method is explicitly noted to assume \"accurate camera poses,\" and its robustness to pose estimation noise, a common issue in real-world applications, remains entirely unvalidated. This is a significant practical limitation that is not addressed through ablations or sensitivity analysis, casting doubt on the method's real-world readiness. While tested on objects with up to three parts, there is no evidence provided for the method's performance on objects with a higher number of articulated parts (e.g., >5). The clustering and segmentation pipeline may face challenges with increasing complexity, and its scalability remains an open and significant question.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)