Grasp2Grasp: Vision-Based Dexterous Grasp Translation via Schrödinger Bridges
Authors: Tao Zhong
Jonah Buchanan
Christine Allen-Blanchette
Venue: NeurIPS 2025 poster ()
Keywords: dexterous grasping
generative modeling
robotic manipulation
robot learning
Primary area: applications
TL;DR: We translate grasps between different robot hands using vision and Schrödinger Bridges, enabling generalizable, stable grasp synthesis without paired data or hand-specific retraining.

Abstract: We propose a new approach to vision-based dexterous grasp translation, which aims to transfer grasp intent across robotic hands with differing morphologies. Given a visual observation of a source hand grasping an object, our goal is to synthesize a functionally equivalent grasp for a target hand without requiring paired demonstrations or hand-specific simulations. We frame this problem as a stochastic transport between grasp distributions using the Schrödinger Bridge formalism. Our method learns to map between source and target latent grasp spaces via score and flow matching, conditioned on visual observations. To guide this translation, we introduce physics-informed cost functions that encode alignment in base pose, contact maps, wrench space, and manipulability. Experiments across diverse hand-object pairs demonstrate that our approach generates stable, physically grounded grasps with strong generalization. This work enables semantic grasp transfer for heterogeneous manipulators and bridges vision-based grasping with probabilistic generative modeling. Additional details at https://grasp2grasp.github.io/.

Grasp2Grasp: Vision-Based Dexterous Grasp Translation via Schrödinger Bridges
Tao Zhong', Jonah Buchanan 12.3, Christine ' Princeton University, San Jose State University, *Lockheed Martin Corporation {tzhong, carineeon. edu jonah. buchanan8088gmail. com
Abstract
We propose a new approach to vision-based dexterous grasp translation, which aims transfer grasp intent across robotic hands with differing morphologies. Given a visual observation of source hand grasping an object, our goal is to synthesize functionally equivalent grasp for target hand without requiring paired demonstrations or sand-specific simulations. We frame this problem as a stochastic transport between grasp distributions using the Schrödinger Bridge formalism. Our method learns to map between source and target latent grasp spaces via score and flow matching, conditioned on visual observations. To guide this translation, we introduce chysics-informe contact maps, wrench space, and manipulability. Experiments across diverse hand- object pairs demonstrate that approach generates stable, physically grounded grasps with strong generalization. This work enables semantic grasp transfer for heterogeneous manipulators and bridges vision-based grasping with probabilistic generative modeling. Additional details at grraspgrrap.githie github.
cost functions that encode alignment in base pose,
Introduction
Robotic grasping remains a central challenge in autonomous manipulation, especially in the context of dexterous, multi-fingen fingeree hands. Unlike parallel-jaw grippers or simple suction devices, dexterous hands offer significantly more control and flexibility but also bring high-dimensional configuration spaces B [8
and non-trivial contact dynamics [65]. These properties pose difficulties [5$] in data
collection, modeling, and learning robust grasp strategies. While recent data-driven works (9] 46
52
91
100
101 have shown success in generating feasible grasps from large-scale datasets 32
46
94 key limitation persists: models typically operate in a hand-specific setting. This lack of generalization requires retraining significant fine-tuning to adapt to new robotic hands [4]]
which poses a practical bottleneck in the rapidly evolving landscape robotic hardware and limits the applicability of learned policies in real-world systems (97].
Therefore, it desirable to reuse the grasp knowledge acquired from one hand infer meaningful grasp strategies for another. However, the morphological differences between hands mean that naive transfer, such as copying joint angles or end-effector poses, might lead to physically invalid or unstable grasps 2 58 68 A more fundamental challenge is the acquisition of paired demonstration data, where a grasp for source hand mapped Manually creating algorithmically discovering such pairings at scale is extremely difficult. This motivates the need for a framework that can learn to translate the intent of a grasp from a source hand to target hand using only unpaired, hand-specific grasp datasets, leveraging the underlying object geometry and physics to bridge the morphological gap.
functionally equivalent grasp for a target.
Buchanan contributed to this work in the capacity an independent researcher. The views expressed (or the conclusions reached) are their own and do not necessarily represent the views of Lockheed Martin Corporation.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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This paper aims to address the problem of usioo-bbsed dexterous grasp translation. As shown in Fig. [ given visual observation of source robotic hand grasping an object. we aim to gen- erate plausible grasp for target hand with different morphology. This setting arises natu- rally in scenarios such as human-to-robot imitation [71 96]. hardware substitution
manipu- lation pipelines [30], and learning from heterogeneous demonstrations [38]. Although reminis- cent of telcoperation [24] 37 or behavior cloning [16 197, our formulation diverges critical way: the goal is not to replicate the precise joint configuration or trajectory of the source hand. Instead, we seek to preserve the functional intent of the grasp, expressed through physical quantities such contact locations, grasp wrenches, or stability measures, while accounting for the morphological differences be- tween the source and target manipulators.
To this end, we cast the grasp translation task as probabilistic transport problem between the distribu- tion of grasps executed by the source hand and those executable by the target hand. We leverage the formal- ism of the Schrödinger Bridge (SB) models the most likely stochastic process interpolating between two distributions under reference dynam- ics. This perspective allows us to frame grasp trans- lation as learning distributional flow from observed source grasps to compatible target grasps, guided by meaningful notion of grasp similarity and grounded in physics.
45 777, which
Curs
Figure I: (top) Comparison of morphology and scale across hands. (bottom) Object-agnostic methods often miss fine-grained contacts, lead- ing to invalid grasps. Our method produces contact-consistent, stable grasps diverse hand morphologies.
Our approach builds on growing body of work [15 27
79 90, 93 that frames generative modeling as Schrödinger Bridge problem, which enables prob- abilistic transport between arbitrary data distributions under stochastic dynamics. In particular, recent devel- opments have demonstrated how score-based [21] 93]
be leveraged to learn such bridges without the need for simulating full stochastic processes, offering scalable and flexible tools for distribution alignment.
and flow-based [22
84 85
objectives
We adapt and extend these ideas to the domain of dexterous grasp translation, where the source and target distributions represent physically meaningful grasps from different robotic hands. To this end, develop latent-space learning pipeline for distribution-level grasp translation conditioned vision-based observations of the source hand. Within this framework, we design custom ground cost functions that capture task-reles melevrelevant physical properties, such as contact patterns and grasp stability, rather than relying on generic Euclidean or geodesic distances. This allows us to generate grasps that are not only kinematically feasible for the target hand but also functionally aligned with the intent of the source grasp.
We summarize contributions follows:
We formulate vision- based dexterous grasp translation as Schrödinger Bridge problem between source and target grasp distributions, capturing the stochastic nature of plausible grasps.
We introduce novel ground cost functions tailored the grasping domain, enabling semantic and physically-infomee translation across different hand morphologies.
We develop a latent-space learning pipeline based on score and flow matching, enabling simulation- free, distribution-level training on unpaired visual grasp observations.
We evaluate method across diverse hand-object combinations, demonstrating that ap- proach generates functionally equivalent and physically robust grasps with strong generalization capabilities.
Related Work
Dexterous Grasp Generation has been long-standing topic in robotics, aimed at enabling robotic hands with multiple degrees of freedom (DoFs) to securely and effectively manipulate diverse objects.
Early approaches 6
23
29
62 67 relied on analytical models of hand kinematies and contact

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mechanics [7,60] to compute force-closuse 49 62
64, 67 87 / or form- worm-closure [59
86 grasps, which
are often constrained by assumptions of perfect information and simple object geometries 60). The advent of vision-based data-driven techniques has led to significant advances 666 99 particularly
through direct regression [8 [6] or generative modeling techniques 33
such as VAFs [41
46 [1]. GANs [19] 54 55, 61] and diffusion models [66 52
95]. These generative approaches enable the synthesis of diverse grasp configurations conditioned on visual inputs such as RGB-D images [39 40) segmented point clouds [36] [2 (95), allowing for more flexible and scalable grasp generation. For example, GenDex [46] introduces a hand-agnostic grasping algorithm trained on the MultiDex dataset [46], which leverages contact maps as intermediate representations to efficiently generate diverse and plausible grasping poses transferable among various multi multti-ingeeed robotic hands. Similarly, UGG [52] presents unified diffusion- -based dexterous grasp generation model that operates within object point cloud and hand parameter spaces. While these generative approaches have advanced the field, they often remain tailored to specific robotic hands and lack mechanisms for transferring grasp knowledge across different hand morphologies. Our work addresses these limitations by developing grasp translation framework that operates at the distributional level, enabling the reuse of grasp knowledge across different robotic platforms through a physically meaningful transport mechanism.
88
Grasp Transfer is closely related to teleoperation 72] and imitation learning 4. where the objective is to map motions actions from source agent (e.g., human or robot) to a target robot. Teleop- eration methods [24 37 77 78 80 [04] often aim for one-to-one replication of joint trajectories or end-effector poses, which is generally effective when the source and target share similar kinematics. However, such approaches struggle when transferring grasps between manipulators with significantly different morphologies, as direct replication can lead to infeasible or suboptimal grasps 2 58 68
To address this morphological gap, retargeting methods have been explored. For instance, works
like [4 35 72] explore positional optimization for key points, while CrossDex (98] uses neural network trained with data generated from (72) for retargeting. These approaches, however, often rely on pre-defined link-to-link correspondences or human-annotated templates, which can limit their generalizability. More recent work, such as RobotFingerPrint [1]. addresses this challenge by mapping grippers into shared Unified Gripper Coordinate Space (UGCS) based on spherical coordinates to facilitate grasp transfer. While promising, this approach requires simulation-bais preprocessing and detailed gripper models, which impose a strong prior that limits flexibility. More- over, the UGCS approach focuses on point correspondences and is thus object-agnostic, rather than explicitly preserving functional grasp intent. In contrast, our formulation aims to translate grasps in distributional sense grounded in physical properties. It requires no hand-specific simulation preprocessing, which enables broader applicability and more semantically meaningful grasp transfer.
Optimal Transport (OT) and Schrödinger Bridges (SB) have recently emerged as powerful frameworks in the machine learning community for modeling distributional transformations. OT [69 75, 92] provides a principled way to compute mappings between probability distributions that minimize a cost function, typically grounded in geometric distances. Aligning distributions is central challenge in tasks like domain adaptation [17 [102], and classical OT has been successfully applied for this purpose 20 as well as for other applications like shape matching 25
X3
However, Schrödinger
it often requires solving computationally intensive optimization problems 63
81
Bridges [45] 77 extend OT by introducing a stochastic reference process, which enables more flexible and entropically regularized transport. This has proven particularly useful in generative modeling [1
90, 93,, where SBs offer a probabilistic interpolation between data distributions. Recent advances in simulation-free training methods [50)
84 85] have made these techniques more scalable by bypassing the need to simulate stochastic processes during training. In robotics, these frameworks have been explored for motion planning [43]. distribution alignment [82), and dynamical system modeling [0). However, their application to grasp synthesis and translation remains underexplored. Our work leverages SBs not just for smooth transport between distributions, but for preserving task-specific physical properties of grasps across different hand morphologies, pushing the boundaries of OT/SB utility in robotic manipulation.
3 Preliminaries
3.1 Schrödinger Bridge Formulation
The Schrödinger Bridge (SB) problem 45
77 provides a principled framework for defining the most likely stochastic evolution between two probability distributions, source g0(x)) and target
3

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X
xi
Vlog pi(x, Xxo x1)
go(x)
(1(x)
Figure 2: Illustration of the Schrödinger Bridge Models. The Schrödinger Bridge process transports samples from source distribution (go) to target (q)). At an intermediate point xy on a Brownian bridge trajectory between coupled samples (zo, our model learns the conditional flow drift og that drives transport and the conditional
Vlog Pe that corrects the path.
(z), under a reference process, The optimal process can be found by weighting paths according to an entropically regularized optimal transport (OT) plan, x² This plan seeks coupling between the distributions that minimizes ground cost d(..-) plus regularization term:
/ d(zo. d x1) + =KL(T T/ Igo @ 89)),
T
arg min
(I)
EEU (go.a))
where U(qo- @1) is the set of all couplings between go and 91 This connection allows the complex dynamic optimization to be grounded more tractable static transport plan. We refer readers to Appendix A for detailed formulation.
3.2 Score-based and Flow-Matching Methods
We model the stochastic dynamics of the SB with an Itô SDE the form:
dx, ue (x, (2)) dt + g())
where (ar)) is a drift vector field and Wy is standard Brownian motion. This process induces time marginals Pe (z) that can also be described by an equivalent deterministic probability flow ODE:
g(t) 2
dr. (x(x))
V log Pa (x+))
dt,
5 (a)
Following the MSF] framework (84, we learn the stochastic dynamics by training neural networks (t, x) and 8o (f, .)) to approximate the ODE drift (u;) and the score term (V log Pt (æ)), respectively. The training targets derived from conditional Brownian bridge paths between pairs of samples (zo, 21) drawn from the entropic OT plan गद (Eq. 1]. A visualization of these conditional targets is provided in Fig.
The resulting conditional loss function combines flow and score matching terms:
x
[loo(t,x) uz zo. x1)1 + X())² [[se(t, V Vlog 2x)o
1-1110,1) props (ar (1) (sto.r) 1
where up and V loggp(()) are the conditional ODE drift and score targets, and X(t) is a weighting schedule. The full derivation the training targets and weighting schedule is provided in Appendix
3.3 Problem Definition
We formalize the vision-based dexterous grasp translation problem as a stochastic transport task between grasp distributions associated with different robotic hands. Let Gsource C R. and Guarget. C I denote the source and target hand configuration spaces with and degrees of freedom, including the pose of the hand base in SE(3), and O represent the space of grasp observations. Given segmented visual observation (oobj, Ohand) e O depicting the source hand with configuration

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Syource
Dec
Tokenize
U-VIT
U-VIT
Dec
Bsource
Layer
Contact
Tokanine
Mtarge
Anchor
Figure 3: Architecture overview. Blue modules correspond to stage I: the source hand observation is encoded via VAE. Orange modules correspond to stage 2: the latent is translated using U-ViT Schrödinger Bridge model conditioned object shape and contact anchors. The translated latent is decoded produce the target hand grasp.
Isource E Gsuuree grasping an object, our goal is to generate corresponding grasp configuration Starget E Itarget for the target hand such that certain physical grasp properties are preserved.
We assume that grasps from the source hand follow distribution go [ while feasible grasps for the target hand follow Q1 (9targes Oobj). both conditioned on the same object observation. These distributions capture the variability and physical plausibility of grasps within each hand's morphology. The problem to learn a mapping between go and yi that respects both the structure of the source grasp and the constraints of the target hand.
To achieve this, we define a stochastic process (giargetDeeep, interpolating between qo and @ı governed by Schrödinger Bridge with suitable reference dynamics. The transport should min- imize the deviation from reference process (e.g., Brownian motion) while aligning the marginal distributions at 0 and / 1. Crucially, common choice [84] (5) in related works is to define the transport cost d(-,)) :) in terms Euclidean or geodesic distances, which primarily capture geometric dissimilarities. However, such measures are insufficient in our context, as they do not reflect the functional equivalence of grasps. Therefore, we also require a physically grounded notion of cost that considers the grasp's effect the object, motivating the design of more expressive transport mechanisms aligned with the task's 's semantics.
The translation task thus reduces to learning generative model for (Starget lobj) that aligns with go [o under the formulation, leveraging both vision-based cues and physical constraints.
4 Methodology
4.1 Latent Score and Flow Matching
We now apply the general Schrödinger Bridge framework from Sec. to our specific problem of grasp translation. The abstract distributions go and 9I become the latent distributions of source and target grasps, respectively. The transport process between them is learned by optimizing the [ objective from Eq. 4 in latent space. We approach grasp translation stochastic transport in learned latent space, where the high-dimensional grasp configurations source and target hands are first embedded into shared latent representation. This is achieved through two-stage pipeline, as illustrated in Fig. In the first stage, we train a variational autoencoder (VAE) 42 that encodes segmented visual observations of the source hand grasping object into latent variable + and a decoder mapping - G. The decoded Dec(2) is passed through differentiable kinematic layer FK G R3N
Z.
The VAE consists of an encoder mapping grasp configuration yielding the 3D mesh vertices of the hand à FK(Ø). The VAE is optimized with a combined loss with small KL term:
LV = Eo-o 1l9 gl| a FK( 3KL (2)m(
(5)
where I denotes the ground truth grasp configuration and a, weighting coefficients. This training encourages the latent space Z to encode semantically meaningful and physically grounded grasp features that generalize across hands.
'err, Ssource implicitly defined by Ohand.
5

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Algorithm VAE Training
Algorithm 3 Inference
Algorithm 2 Latent SB
Require: a dataset of (o, g). ini- tial network Enc, Dec, FK
Require: Trained Enc, source target
Require: Trained Enc, Dec, va.
dataset, OlPlaa, initial
so, test observation O,
layer
1:
while Training do
1: 20 + Enc(o,)
2: Sample o.. ot from dataset
for all (o, g) in dataset do
3:
&a + Enc(o.)
2: 21 (z(00) using 00, $0
2:
~ Enc(o)
2. Enc(or)
3: 3r < Dec(21)
3:
9 f- Doc(z)
5:
- OTPian(=a;
4: return ÿt.
(sp. ~ stz
4:
+- FK(O)
24(00, 1)
5:
Update LVAR with Eq. 5
8: a" (e
6: Update Enc, Dec
Update & with Eq
Algorithm 1: Training and infereace pro-
10: Update my,
cedures. Left: VAE training. Center: Simulation free Schrodinger Bridge training latent space. Right: Inference by latent evo- lution.
7: end for
11:
end while
8: return Enc, Dec
12:
return 2g.96
In the second stage, model Schrödinger Bridge between the latent source and target distributions, qu &source (ab;)) and Q1 (ttageet (0bb)). with a simulation free framework. The stochastic path 2' E 2, E [0, is governed by the SDE in Eq. 2 with marginals (2) and corresponding deterministie flow ODE as in 3
As introduced in Sec. 3.2 we train neural networks v0(4, 2) and so((, to approximate the condi- tional flow ug [= 21 and score V [z] zg. 21), respectively. The training is performed using conditional Brownian bridge samples 2" ~ [=(2] [2] 20, 21) where (20, 21) ) ~ m.. which is the entropic OT plan defined in Eq. between Yo and qı. The training objective then defined as Eq.
During inference, given a visual observation of a grasp with the source hand (Oobj. Ohand), ) we sample a latent trajectory starting from source encoding 2u Enn((oand) ~ go (ssourcee (obj) and evolve forward using the learned SDE dynamics to obtain a translated grasp latent code 21 ~ (Ztarget (obb)). This code is decoded to produce the target hand configuration Itarget Dec(z)), which is then used to actuate the target hand. The training and inference processes are detailed in Alg. 1, 2, and 3.
A central challenge in learning this SB is the absence of paired samples between source and target hand configure configurations. Without principled coupling, arbitrary samples from and @i may lead to latent translations that are uninformative misaligned. This motivates the next section, where we introduce physically grounded ground costs for entropic OT to induce meaningful correspondences between source and target grasps.
4.2 Grasp-specific OT Cost Design
To guide the Schrödinger Bridge, we must first compute an entropic OT plan म (Eq.[), which is defined by a ground cost .. We design several physics-ine physics-informed informeed costs for this purpose. For a given cost, we compute the OT plan between minibatches of source and target latent samples. We then draw pairs (Zo, 21) ) ~ x and use these pairs construct the conditional training targets for the SB model as described in Sec. Sec.3.2 and used in the loss function of Eq. 4 This allows us to enable meaningful grasp translation between different hand morphologies by guiding the process with a ground cost that reflects task-relevant physical properties rather than naive geometric alignment. Conventional entropic OT approaches 84 (85] typically define the ground cost .(:..) using Fuclidean geodesic distances in either configuration or latent space. However, such metries fail to capture the functional equivalence of grasps, particularly when source and target hands differ significantly in kinematics and contact modalities. We propose set of phisics-informed cost functions that better encode grasp quality and intent.
Base Pose Cost. We define a cost dpose on the global wrist pose in SE(() between the source and target hands. The pose is represented
concatenation of the 3D base position and 6D continuous representation for the rotation [103] to ensure smoothness. The 6D vector is first converted to a 3 x 3 rotation matrix E 50(3). The cost then combines the squared 1.2 norm for translation and the squared Frobenius norm for rotation:
dpose Iloure Marrger + Raouree Rtarget
where h E 3 is the translation vector and R E SO(3) is the rotation matrix of the base pose, extracted from Isouren and Itarget, respectively. This cost encourages coarse alignment the grasps in workspace coordinates.

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Contact Map Similarity. Each grasp is associated with contact map indicating the location of contacts on the object surface. We represent these contact maps as 3D point clouds and compute the bidirectional Chamfer distance between the source and target maps Csources Otarget:
dcontact Chanfer(Csource Ctarget)
min WeCrgeee
||2
y/l2+
min
l1y
2ECruuree
#EC CACUTTE
(7)
This encourages preservation of local interaction geometry across morphologically distinct hands.
Grasp Wrench Space Overlap. The grasp wrench space (GWS) [29] characterizes the set of wrenches (forces and torques) that can be exerted on an object by a grasp. For each grasp, we compute set of wrench vectors from contact locations and normals, then take the convex hull to approximate the GWS in I to form the grasp wrench hull (GWH). We define the cost based on the interseetionn-vve--niion (IoU) of GWH volumes between source and target hulls:
Vol (GW
Hull GWS S Starget))
dwrench
(8)
Vol H S soarce) U Hull (GW ttarget))
This term promotes similarity in the mechanical capabilities of the two grasps.
Jacobian- Manipulability. To capture the grasp's ' potential for object actuation, we execute the grasp in a differentiable simulator (56) and compute the Jacobian E ( of the object's translational and rotational motion with respect to the hand's joint angles, excluding the translation and rotation of the hand base. Taking a max over the joint dimension yields a 6D vector summarizing the maximal motion in each direction m max, |Jy| E 12.. The cost then defined the squared L2 distance between these maximal effect vectors:
diue=
M - Mearget
(9)
This metric encourages the translated grasp to retain similar object-level controllability.
Minibatch Approximation. For each of the four cost functions above, we compute separate entropic OT plan गद using Sinkhorn's algorithm (81). Following Tong et al. [84). we adopt
simulation-free approach train the SB dynamics using these plans as static couplings. Since exact
OT scales quadratically with sample size, we employ minibatch entropic OT 226 28 to efficiently estimate the plans during training. Specifically, for each minibatch of source- tarcet samples, we compute a local OT plan using the corresponding cost matrix and regularization parameter E. These minibatch couplings serve as conditioning for generating Brownian bridge paths and estimating regression targets for score and flow matching. This strategy preserves the SB formulation's 's structure while enabling scalable learning in nigh-dimensional latent spaces.
4.3 Implementation Details
Our VAE is implemented using a PVCNN- backbone [5]]. For object shape representation, we encode the object point cloud using a LION VAE 89 pretrained on ShapeNet [3]. which yields one global shape token and 512 local tokens. The hand observation latent is encoded into a single token. We further incorporate five contact anchor tokens, following the strategy introduced in [52], to guide translation via physical grounding. The latent Schrödinger Bridge is modeled using V-V model (5), which serves as the backbone for 89 and Ug.
For the Grasp Wrench Space Overlap cost, we reduce the 6D convex hull to its first three spatial dimensions, approximating the set of achievable center-of-mass forces. Monte Carlo estimation is used to evaluate the IoU of these 3D hulls efficiently on GPUs. For the Jacobian- based maximal effect descriptor, we leverage the Warp differentiable simulator (56) to simulate the grasp and compute the Jacobian of object pose with respect to joint angles. At inference time, latent samples are evolved using Euler-Maruy Maruyama integration of the learned SDE with discretized steps. No test-time finetuning is performed. Additional architectural and hyperparameter details are provided in the supplementary materials.
5 Experiments
5.1 Experimental Setup
Dataset. We evaluate our method on the MultiGripperGrasp dataset 12 large-scale benchmark containing 30.4 million grasps across 11 robotic manipulators and 345 objects. For experiments,
7

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Table 1: Comparison of grasp translation methods success rate, diversity, and 6D GWH IoU. Tasks include Human Juman-+Alleroo AAllgro, Human Sluman->Shadoee +haadow Shadow Shadow->Allegro, and the mean across them.
Success
Rate (%)
Diversity (rad)f
6D GWH
IoU (%)f
Method
H-A
H-S
S-A
Mean
H-+A
H-SS
S-A
Mean
H-+A
H-SS
S-AA
Meun
REP 41
66.80
33.89
70.31
57.00
0.225
0.186
0.199
0.203
7,51
6.62
8.99
7.77
72
56.93
16.21
56.44
43.19
0.221
0.186
0.196
0.201
5.67
4.41
6.97
5.68
Cex 98
36.51
8.97
35.12
26.87
0.195
0.201
0.223
0.206
5.69
4.24
5,86
5.26
Diftusion
72.57
38.74
71.19
60.83
0.301
0.206
0.307
0.271
9.54
9.12
10.07
9.58
Ourspose
74.68
42.16
76.11
64.32
0.269
0.194
0.288
0.250
9.83
11.04
11.16
10.68
vurs
74.78
37.10
76.37
62.75
0.294
0.211
0.311
0.272
15.89
15.18
12.54
14.54
Oursown
77.73
42.59
78.74
66 34
0.293
0.197
0.309
0.266
15.09
14.14
14,67
14,63
OurSpcotia
77.23
45.15
79.98
67.45
0.278
0.205
0.292
0.258
11.16
9.77
11.73
10.88
we select 138 objects for training and 34 unseen objects for testing. Our primary evaluation scenarios focus on translating grasps between articulated human hand (5 fingers, 20 DoFs), the Allegro hand (4 fingers, 16 DoFs), and the Shadow hand (5 fingers, 22 DoFs).
Metrics, We assess performance using several quantitative metrics. First, we report the grasp success rate using IsaacGym (57), following the GenDexGrasp [46] evaluation protocol. A grasp is considered successful if it maintains a stable hold on the object under six perturbation trials, where external forces are applied along t.,, tty, and iz axes. We apply each force as a uniform acceleration of 0.5m/s² s² for 60 simulation steps and measure whether the object translates more than 2 cm. A grasp passes if it withstands all six trials. Simulation parameters include a friction coefficient of 10 and an object density of 10,000. We use IsaacGym's 's built-in positional controller to achieve the desired joint configurations. In addition to the success rate, we report the diversity of the generated grasps, computed as the average standard deviation across all revolute joints, as well as the functional similarity between source and translated grasps. The latter is measured using the full 6D IoU of GWH defined in Eq. [8]
Baselines. We evaluate all four variants of our model, each trained using a distinct physics-based OT
cost introduced in Sec. 4.2 As baselines, we compare against several methods. We include three recent grasp transfer approaches: RobotFingerPrint [41], which uses unified gripper coordinate space; Dex-Retargeting (72), an optimization-basel method that retargets key points on finger links; and the neural retargeting module from CrossDex [98]. Notably, both nex-Rettrgeting and CrossDex require pre-defined, manually annotated link-to-link correspondences, which limit their generality for arbitrary hand morphologies. Finally, we compare against a generative baseline: a diffusion based model trained with samples from Contact Map Similarity OT and conditioned on the source contact map.
5.2 Quality of Translated Grasps
We evaluate the overall quality of the translated grasps using two key metrics: success rate under physical perturbations and configuration diversity across generated samples. Table D (left and middle blocks) reports these metrics across three grasp translation tasks: Human->Allegn (H-+)), Human->Shaan (H (H+S), and Shadow AAllego (S AA,, as well as their mean.
Our method significantly outperforms all baselines in terms of grasp success rate. Our approach using the Jacobian-based OT cost and GWH-based variants achieves the highest mean success rates (67.45% % and 66.34%, respectively). which suggests that both wrench- and control-aligned transport costs are particularly effective for grasp transfer. The IK-style optimization baselines, Dex- Rex-Reetggg [72 and CrossDex Retargeting Module 198. perform poorly. Their focus on select links often ignores collisions with other parts of the hand (c.g., the palm), leading to high rate of physically invalid grasps. In contrast, our generative approach learns produce configurations that respect the full-hand morphology. Qualitative results in Fig. 4 (left) further illustrate that our method generates stable grasps even from sub-optimal source poses where baselines fail.
On the diversity metric, our contact-based variant achieves the highest mean diversity, producing a wide range of plausible grasps. This highlights that our methods can generate diverse grasp configurations while maintaining physical feasibility. Interestingly, other OT costs show lower diversity despite achieving high success rates, indicating that geometric alignment alone may lead to more conservative grasps. While the diffusion baseline is also highly diverse, our method achieves this while demonstrating superior performance on stability and functional alignment.
8

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Source
RFP
Pose
Contact
GWH
Jacobian
Failure Mode
Source
Generated
Figure 4: (left) Qualitative results. The 'Pose". 'Contact', 'GWH', and 'Jacobian' columns show results from our method when trained using the respective OT cost functions from Sec. Se2. Our method generates stable and consistent grasps across different OT variants, even when the source grasp is sub-optimal, where RFP [4]] fails. (right) Failure Modes where our method struggles with thin-shell objects due to challenging geometry.
In addition performance, our approach offers significant computational advantages over optimization-basse baselines. Methods like RobotFingerPrint [41 require costly per-grasp iter- ative optimization, leading to an average inference time of over 5 seconds. contrast, our generative method amortizes this cost through batch processing. With 100 integration steps. our model achieves an average inference time of approximately 0.8 seconds per grasp, comparable to the diffusion base- line and substantially faster than RobotFingerPrint. While lightweight methods like CrossDex [98] are faster due to their single-pass architecture, our approach provides a strong balance between computational efficiency and the generation of high-quality, physically robust grasps. A more detailed efficiency report included Appendix D.2
5.3 Physical Alignment between Translated Grasps
To evaluate whether our translated grasps preserve the functional intent of the source grasp, we compute the 6D GWH IoU between the source and the translated target grasps. As shown in Table (right block), our methods trained with the GWH-based and Contact-based based OT costs achieve the highest mean IoU by substantial margin (14.63% and 14.54%, respectively), significantly outperforming all baselines. This indicates that our approach more effectively preserves the object- level physical capabilities of the grasp, rather than simply mimicking coarse finger geometry. We provide a complementary analysis on the geometric alignment of contact points in Appendix D.3] which further supports these findings.
Taken together, our results reveal key trade-off between the different physics-informnn objectives. The Jacobian-based cost yields the highest success rate, suggesting it is most effective at capturing the kinematic relationships required for stability. However, the GWH and Contact costs achieve superior functional alignment, measured by GWH IoU. This indicates that directly optimizing for force-excrtion capabilities (GWH) or contact patterns (Contact) is more effective for transferring the grasp's underlying mechanical intent, even if this sometimes results in a slightly lower stability score compared to a pure manipulability-bast objective.
5.4 Ablation Study
We conduct an ablation study to assess the sensitivity of our method to two key hyperparameters in the Schrödinger Bridge formulation: the magnitude of the diffusion rate and the number of discretization steps used during Fuler-Maruyama integration at test time. Both ablations are performed the H task using the Contact Map OT model, and results are reported in Tables 2 ]
Effect of Diffusion Rate. We vary the diffusion rate E {0.01, 0.1, L.0} and observe that smaller diffusion magnitudes lead to better grasp success and GWH loU. Larger diffusion (o = 1.0) produces noisier paths and degrades both physical precision and grasp quality, despite yielding higher diversity, This supports the intuition that overly noisy reference processes can disrupt fine nee-grained transport and hinder alignment with physical intent.
Effect of Discretization Steps. evaluate our method under varying numbers time steps during test-time integration: (10, 100, 200). As shown in Table using 100 steps offers strong tradeoff between accuracy and efficiency, while more steps lead to better physical alignment. Interestingly, method remains robust even with as few as 10 steps, outperforming the diffusion bascline across

---

Table 3: Effect of number of discretization steps performance (H- from our method and the diffu- sion baseline.
Table 2: Effect of diffusion rate on perfor- mance (H-+A).
Success %1
Div. (rad)?
IoUt
Success %6 Diff.
Div. (rad)
IoUf
# Steps
0.01
77.16
0.284
16.72
Ours
Ours
Diff.
Ours
Diff.
0.1
74.78
0.294
15.89
10
71.45
60.00
0.278
0.344
13.80
6.19
1.0
64.39
0.378
13.83
100
75.12
72.57
0.283
0.301
14.00
9.54
200
74.78
73.17
0.294
0.297
15.89
9.66
all metrics and steps. In contrast, the diffusion model's performance degrades substantially under low discretization, highlighting the benefit of our SB-based formulation, which yields more stable and sample-efficient generation dynamics.
6 Discussion
In this work, present novel formulation of vision-based dexterous grasp translation as Schrödinger Bridge problem between grasp distributions. By leveraging a latent score and flow matching framework and designing physics-informed ground costs, our method enables simulation- free, distribution-level grasp transfer across robotic hands with distinct morphologies. Empirical evaluations across several hand-object settings demonstrate that our approach not only produces stable and diverse grasps but also preserves functional grasp properties more effectively than object- agnostic or geometry- based baselines. These results highlight the promise of distributional transport techniques for advancing semantic grasp understanding and generalization in robotic manipulation.
Limitations. Despite its strengths, our approach has some limitations. Most notably, shown in Fig. 4 (right), the performance drops in scenarios involving thin-shell objects with ambiguous or minimal contact regions, where the valid grasp configuration space is largely confined. Additionally, we observe that the results for the Shadow hand are consistently lower than for the Allegro hand across multiple metrics, which aligns with prior findings in the MultiGripperGrasp dataset [22 due to its more complex kinematics and larger workspace. Furthermore, our current framework does not generalize to unseen hand morphologies at inference time. The VAE decoder implicitly learns the kinematic structure of the target hand, and would thus require retraining fine-tuming on data from a new hand to generate valid grasps. Finally, these discrepancies suggest that improving dataset quality and coverage for specific hands may further enhance generalization and translation fidelity.
Societal Impact. Finally, while framework is designed for general-purposs manipulation, it introduces broader implications for deployment in real-world systems. Effective grasp translation could accelerate learning from heterogeneous demonstrations or expand manipulation capabilities in assistive robotics. However, it also raises considerations around safe deployment, failure detection, and responsible generalization across users and hardware. We encourage future work to examine how distributional grasp priors can be integrated into transparent and human- human-aligned manipulation pipelines.
References
[1] Panos Achlioptas, Olga Diamanti, Joannis Mitliagkas, and Lconidas Guibas. Learning representations and generative models for 3d point clouds. In International conference on machine learning, pages 40-49, PMLR, 2018.
[2] Ananye Agarwal, Shagun Uppal. Kenneth Shaw, and Deepak Pathak. Dexterous functional grasping. arXiv preprint arXiv:2312.02977 2023.
[3] Heni Ben Amor, Oliver Kroemer, Ulrich Hillenbrand, Gerhard Neumann, and Jan Peters. Generalization of human grasping for multi-fingered robot hands. In 20/2 IEEE/RSI International Conference on Intelligent Robots and Systems, pages 2043-2050. IEEE, 2012.
[4] Shan An, Ziyu Meng, Chao Tang, Yuning Zhou, Tengyu Liu, Fangqiang Ding, Shufang Zhang, Yao Mu, Ran Song, Wei Zhang, et al. Dexterous manipulation through imitation learning: A survey. arXiv preprint mrXiv:2504.035.4 2025.
[5] Fan Bao, Shen Nie, Kaiwen Xue. Yue Cao. Chongxuan Li, Hang Su, and Jun Zhu. All are worth words: A vit backbone for diffusion models. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 22669-22677 2023.
10

---

[6]
Dmitry Berenson and Siddhartha S Srinivasa. Grasp synthesis in cluttered environments for dexterous hands. In Humamoids 2008-8th IEEE-RAS International Conference on Humanoid Robots, pages 189-196. IEEE, 2008
[7] Antonio Bicchi and Vijay Kumar. Robotic grasping and contact: A review. In Proceedings 2000 ICRA. Millennium conference. IEEF international conference on robotics and automation. Symposia proceedings (Cat. No. 00CH37065), volume 1, pages 348-353. IEEF, 2000.
[8] Ch Borst, Max Fischer, and Gerd Hirzinger. Grasp planning: How to choose suitable task wrench space. In IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004, volume 1, pages 319-325. IEEE, 2004.
[9] Samarth Brahmbhatt, Ankur Handa, James Hays, and Dieter Fox. Contactgrasp: Functional multi multi-finger grasp synthesis from contact. In 2019 JEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pages 2386-2393. TEFF, 2019.
[10] Charlotte Bunne. Optimal transport in learning, control, and dynamical systems. ICML. Tutorial, 2023.
[11] Charlotte Bunne, Ya-Ping Hsieh, Marco Cuturi, and Andreas Krause. The schrödinger bridge between gaussian measures has closed form. In International Conference on Artificial Intelligence and Statistics, pages 5802 5833. PMLR, 2023.
[12] Luis Felipe Casas. Ninad Khargonkar, Balakrishnan Prabhakaran, and Yu Xiang, Multigrippergrasp: A dataset for robotic grasping from parallel jaw grippers to dexterous hands. In 2024 IEFE/RS/ International Conference on Intelligent Robots and Systems (IROS), pages 2978-2984 2984. IEEE, 2024.
[13] Angel X Chang, Thomas Funkhouser, Leonidas Guibas, Pat Hanrahan, Qixing Huang, Zimo Li, Silvio Savarese, Manolis Savva, Shuran Song, Hao Su, et al. Shapenet: An information-rich 3d model repository. arXiv preprint 15
2015.
[14] Jiayi Chen, Yubin Ke, Lin Peng. and He Wang. Dexonomy: Synthesizing all dexterous grasp types in a grasp taxonomy. Robotics: Science and Systems, 2025.
[15] Tianrong Chen, Guan Guan-Horn Liu, and Evangelos Theodorou. Likelihood training of schrödinger bridge using forward- bawkardd sdes theory. arXiv preprint arXiv:21 /1211, 2021.
[16] Cheng Chi, Zhenjia Xu, Siyuan Feng, Fric Cousineau, Yilun Du, Benjamin Burchfiel, Russ Tedrake, and Shuran Song. Diffusion policy: Visuomotor policy learning via action diffusion. The International Journal of Robotics Research, page 02783649241277666 2023.
[17] Zhixiang Chi, Li Gu, Tao Zhong, Huan Liu, YUANHAO YU, Konstantinos N Plataniotis, and Yang Wang. Adapting distribution shift by visual domain prompt generation. In The Twelfth International Conference on Learning Representations, 2024.
[18] Matei T Ciocarlie and Peter K Allen. Hand posture subspaces for dexterous robotic grasping. The International Journal of Robotics Research, 28(7):851-867, 2009.
[19] Enric Corona, Albert Pumarola, Guillem Alenya, Francesc Moreno-Noguer. and Grégory Rogez. Ganhand: Predicting human grasp affordances in multi-object scenes. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 5031-5041, 2020.
[20] Nicolas Courty, Rémi Flamary, Devis Tuia, and Alain Rakotomamonjy. Optimal transport for domain adaptation. JEEE transactions on pattern analysis and machine intelligence, 193)) 2016.
[21] Valentin De Bortoli, James Thornton, Jeremy Heng, and Arnaud Doucet. Diffusion schrödinger bridge with applications to score-based generative modeling. Advances in Neural Information Processing Systems, 14915-91777799 2021.
[22] Valentin De Bortoli, Iryna Korshunova, Andriy Mnih, and Arnaud Doucet. Schrodinger bridge flow for unpaired data translation. Advances in Neural Information Processing Systems, 17:103384-103441, 2024.
[23] Rosen Diankov and James Kuffner. Openrave: A planning architecture for autonomous rohotics. Robotics Institute, Pittsburgh, PA, Tech. Rep. CMU-RI-7R-00-34 34, 79, 2008
[24] Runyu Ding, Yuzhe Qin, Jiyue Zhu, Chengzhe Jia. Shiqi Yang. Ruihan Yang, Xiaojuan Qi, and Xiaolong Wang. Bunny-visionpro: Real-time bimanual dexterous teleoperation for imitation learning. arXiv preprint arXiv:2407.00 001622 2024.
[25] Marvin Eisenberger, Aysim Toker, Laura Leal- and Daniel Cremers. Deep shells: Unsupervised shape correspondence with optimal transport. Advances in Neural information processing systems, 33: 10491- 2020.
[26] Kilian Fatras, Younes Zine, Rémi Flamary, Rémi Gribonval, and Nicolas Courty. Learning with minibatch wasserstein: asymptotic and gradient properties. arXiv preprint arXiv: 1910.0490, 2019.
[27] Kilian Fatras, Thibault Séjourné, Rémi Flamary, and Nicolas Courty. Unbalanced minibatch optimal transport: applications to domain adaptation. In International Conference on Machine Learning, pages 3186-3197 PMLR, 2021.
11

---

[28]
Kilian Fatras, Younes Zine, Szymon Majewski, Rémi Flamary, Rémi Gribonval, and Nicolas Courty. Minibatch optimal transport distances; analysis and applications. arXiv preprint arXiv:2101.01992 2021.
[29]
Carlo Ferrari, John Canny, et al. Planning optimal grasps. In Proceedings.. 1992 IEEE International Conference on Robotics and Automation, 1992., volume 3, pages 2290-2295. IEFE, 1992.
[30] Brian Flynn, Kostas Bekris, Berk Calli, Aaron Dollar, Adam Norton, Yu Sun, and Holly Yanco. Develop- ing modular grasping and manipulation pipeline infrastructure to streamline performance benchmarking. arXiv preprint arXiv:2504.066 2025.
[31] Hans Föllmer. Random fields and diffusion processes. Lect. Notes Math,
1988.
[32] Corey Goldfeder, Matei Ciocarlie, Hao Dang, and Peter Allen. The columbia grasp database. In 2009
IEEE international conference on robotics and automation, pages 1710-1716. IEEE, 2009.
[33] Ian Goodfellow, Jean Pouget-Abadic, Mchdi Mirza, Bing Xu, David Farley Sherjil Ozair, Aaron Courville, and Yoshua Bengio. Generative adversarial networks. Communications of the ACM, 63(11);
139-144, 2020.
[34] Jonathan Ho, Ajay Jain, and Pieter Abbeel. Denoising diffusion probabilistic models. Advances in neural information processing systems, 33:6840-6851, 2020.
[35] Linyi Huang, Hui Zhang, Zijian Wu, Sammy Christen, and Jie Song. Fungrasp: Functional grasping for diverse dexterous hands. IEEE Robotics and Automation Letters, 2025.
[36] Siyuan Huang. Zan Wang. Puhao Li, Baoxiong Jia, Tengyu Liu, Yixin Zhu, Wei Liang, and Song-Chun
7hu. Diffusion-hased generation, optimization, and planning in 3d scenes. In Proceedings of the IEEF/CVF Conference on Computer Vision and Pattern Recognition, pages 16750-16761, 2023.
[37] Aadhithya Iyer. Zhuoran Peng, Yinlong Dai, Irmak Guzey, Siddhant Haldar, Soumith Chintala, and Lerrel Pinto. Open teach: A versatile telcoperation system for robotic manipulation. In CoRL 2024 Workshop on Mastering Robot Manipulation in World of Abundant Data, 2024.
[38] Sravan Jayanthi, Letian Chen, Nadya Balahanska, Van Duong, Erik Scarlatescu, Ezra Ameperosa, Zulfiqur Haider 7aidi, Daniel Martin, Taylor Keith Del Matto, Masahiro Ono, et al. Droid: Learning from offline heterogeneous demonstrations via reward- -ooley distillation. In Conference on Robot Learning. pages 1547-1571. PMLR, 2023.
[39] Korrawe Karunratanakul, Jinlong Yang, Yan Zhang, Michael J Black, Krikamol Muandet, and Siyu Tang. Grasping field: Learning implicit representations for human grasps. In 2020 International Conference on 3D Vision (3DV), pages 333-344. IEEE, 2020.
[40] Ninad Khargonkar. Neil Song. Zesheng Xu, Balakrishnan Prabhakaran, and Yu Xiang. Neuralgrasps: Learning implicit representations for grasps of multiple robotic hands. In Conference on Robot Learning, pages 516-526. PMLR, 2023.
[41] Ninad Khargonkar, Luis Felipe Casas, Balakrishnan Prabhakaran, and Yu Xiang- Robotfingerprint: Unified gripper coordinate space for multi-gripper grasp synthesis. arXiv preprint 14X15:2409.14519 2024.
[42] Diederik P Kingma, Max Welling, et al. Auto-encoding variational bayes, 2013.
[43] An T Le, Georgia Chalvatzaki, Armin Biess, and Jan R Peters. Accelerating motion planning via optimal transport. Advances in Neural Information Processing Systems, 36:78433-78482, 2023.
[44] Tung L.e, Khai Nguyen, Shanlin Sun, Nhat Ho, and Xiaohui Xie. Integrating efficient optimal transport and functional maps for unsupervised shape correspondence learning. Proceedings of the IEEF/CVF Conference on Computer Vision and Pattern Recognition, pages 231 23188-23198, 2024.
[45] Christian Léonard. A survey of the schrödinger problem and some of its connections with optimal transport. arXiv preprint arXiv:13088 0215, 2013.
[46] Puhao Li, Tengyu Liu, Yuyang Li, Yiran Geng, Yixin Zhu, Yandong Yang, and Siyuan Huang. Gen- dexgrasp: Generalizable dexterous grasping. In 2023 IEEE International Conference on Robotics and Automation (ICRA), pages 8068-8074. IEEE, 2023.
[47] Guan-Homg Liu, Yaron Lipman, Maximilian Nickel, Brian Karrer, Evangelos A Theodorou, and Ricky TQ Chen. Generalized schrödinger bridge matching. arXiv preprint arXiv:2310.02233 2023.
[48] Min Liu, Zherong Pan, Kai Xu, Kanishka Ganguly, and Dinesh Manocha. Deep differentiable grasp planner for high-dof grippers. arXiv preprint vrXiv:2002.01522 2020.
[49] Tengyu Liu, Zeyu Liu, Ziyuan Jiao, Yixin Zhu, and Song-Chun Zhu. Synthesizing diverse and physically stable grasps with arbitrary hand structures using differentiable force closure estimator. IEEE Robotics and Automation Letters, 71):470-477, 2021.
[50] Xingchao Liu, Chengyue Gong. and Qiang Liu. Flow straight and fast: Learning to generate and transfer data with rectified flow. In The Eleventh International Conference on Learning Representations (ICLR), 2023.
12

---

[51] Zhijian Liu. Haotian Tang, Yujun Lin, and Song Han. Point-voxel cnn for efficient 3d deep learning. Advances in neural information procesxing systems, 32, 2019.
[52] Jiaxin Lu, Hao Kang, Haoxiang Li, Bo Liu, Yiding Yang, Qixing Huang, and Gang Hua. Ugg: Unified generative grasping. In European Conference Computer Vision, pages 414-433. Springer, 2024.
[53] Qingkai Lu, Mark Van der Merwe, and Tucker Hermans. Multi-fingered active grasp learning. In 2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pages 8415 8422. IEEE, 2020.
[54] Jens Lundell, Enric Corona, Tran Nguyen Le, Francesco Verdoja, Philippe Weinzaepfel, Grégory Rogez, Francesc Moreno-Nogues and Ville Kyrki. Multi-fingan: Generative coarse-to-fine sampling of multi- finger grasps. In 2021 IEEE International Conference on Robotics and Automation (ICRA), pages 4495 4501. IEEE, 2021.
[55] Jens Lundell, Francesco Verdoja, and Ville Kyrki. Ddge: Generative deep dexterous grasping in clutter. IEEE Robotics and Automation Letters, 6(4):6899-6906, 2021.
[56] Miles Macklin. [WARP: A High-performance Python Framework for GPU Simulation and Graphics March 2022. NVIDIA GPU Technology Conference (GTC).
[57] Viktor Makoviychuk, Lukasz Wawrzyniak, Yunrong Guo, Michelle Lu, Kier Storey, Miles Macklin, David Hoeller, Nikita Rudin, Arthur Allshire, Ankur Handa, et al. Isaac gym: High performance gpu-based physics simulation for robot leamning arXiv preprint arXiv:2108 10470, 2021.
[58] Priyanka Mandikal and Kristen Grauman. Dexvip: Learning dexterous grasping with human hand pose priors from video. In Conference on Robot Learning, pages 651-661. PMLR, 2022.
[59]
Xanthippi Markenscoff, Luqun Ni, and Christos Papadimitriou. The geometry of grasping. The International Journal of Robotics Research, (1):61174, 1990.
[60] Matthew T Mason and Kenneth Salisbury Robot hands and the mechanics of manipulation. 1985.
[61] Vincent Mayer, Qian Feng, Jun Deng. Yunlei Shi, Zhaopeng Chen, and Alois Knoll. Ffhnet: Generating multi-ingered robotic grasps for unknown objects in real-time. In 2022 International Conference on Robotics and Automation (ICRA), pages 762-769. IEEE, 2022.
[62] Andrew T Miller and Peter K Allen. Graspit! versatile simulator for robotic grasping. IEEE Robotics & Automation Magazine, I 10)2110- 2004.
[63] Sina Moradi. A survey algorithmic developments in optimal transport problem with applications. arXiv preprint wwxiv:2500100244 2025.
[64] Richard M Murray, Zexiang Li, and S Shankar Sastry. A mathematical introduction to robotic manipula-
tion. CRC press, 2017.
[65] Anusha Nagabandi, Kurt Konolige, Sergey Levine, and Vikash Kumar. Deep dynamics models for learning dexterous manipulation. In Conference on robot learning, pages 1101-1112. PMLR, 2020.
[66] Rhys Newbury, Morris Gu. Lachlan Chumbley, Arsalan Mousavian, Clemens Eppner, Jürgen Leitner. Jeannette Bohg, Antonio Morales, Tamim Asfour, Danica Kragic, et al. Deep learning approaches to grasp synthesis: A review. IEEE Trunsactions on Robotics, 99(5):399440015 2023.
[67] Van-Due Nguyen. Constructing force-closure grasps. The International Journal of Robotics Research, 7
(3)3-16, 1988.
[68] Sungjae Park, Seungho Lee, Mingi Choi, Jiye Lee, Jeonghwan Kim, Jisoo Kim, and Hanbyul Joo. Learning to transfer human hand skills for robot manipulations. arXiv preprint arXiv:2501 04060,, 2025.
[69] Gabriel Peyré, Marco Cuturi, al. Computational optimal transport: With applications to data science. Foundations and Trends@ in Machine Learning, 1 11(-6))355-607. 2019.
[70] Yuzhe Qin, Hao Su, and Xiaolong Wang. From one hand multiple hands: Imitation learning for dexterous manipulation from single-camera teleoperation. IEEE Robotics and Automation Letters, 7(4): 10873-10881, 2022.
[71] Yuzhe Qin. Yueh-Hua Wu, Shaowei Liu, Hanwen Jiang. Ruihan Yang. Yang Fu, and Xiaolong Wang. Dexmv: Imitation learning for dexterous manipulation from human videos. European Conference on Computer Vision, pages 570-587. Springer, 2022.
[72] Yuzhe Qin, Wei Yang, Binghao Huang, Karl Van Wyk, Hao Su, Xiaolong Wang. Yu-Wei Chao, and Dieter Fox. Anyteleop: A general vision-based dexterous robot arm-hand teleoperation system. Robotics: Science and Systems, 2023.
[73] Hannes Risken and Hannes Risken. Fokker-planck equation. Springer, 1996.
[74] Javier Romero, Dimitrios Tzionas, and Michael Black. Embodied hands: Modeling and capturing hands and bodies together. arXiv preprint arXiv:2201.026100 2022.
13

---

[75] Yossi Rubner. Carlo Tomasi, and Leonidas J Guibas. The earth mover's distance as metric for image retrieval. International journal of computer vision, 40:99-121, 2000.
[76] Philipp Schmidt, Nikolaus Vahrenkamp, Mirko Wächter, and Tamim Asfour. Grasping of unknown objects using deep convolutional neural networks based on depth images. In 2018 IEEE international conference on robotics and automation (ICRA), pages 1831-6838 IEEE, 2018.
[77] Erwin Schrödinger. Sur la théorie relativiste de I' l'électron et ''interréttation de mécanique quantique. Annales de l'institut Henri Poincaré, volume 2. pages 269- 310, 1932.
[78] Kenneth Shaw, Ananye Agarwal, and Deepak Pathak. Leap hand: Low-cost, efficient, and anthropomor- phie hand for robot learning. arXiv preprint 0ttp::22.09.044444 2023.
[791 Yuyang Shi, Valentin De Bortoli, Andrew Campbell, and Amaud Doucet. Diffusion schrödinger bridge matching. Advances in Neural Information Processing Systems, 36:62183-62221 2023.
[80] Zilin Si, Kevin Lee Zhang, Zeynep Temel, and Oliver Kroemer. Tilde: Telcoperation for dexterous in-hand manipulation learning with deltahand. arXiv preprint arXiv:2405. /8000 2024.
[81] Richard Sinkhorn. A relationship between arbitrary positive matrices and doubly stochastic matrices. The annals of mathematical statistics, 35(2):876-879, 1964.
[82] Vignesh Ram Somnath, Matteo Pariset, Ya-Ping Hsieh, Maria Rodriguez Martinez, Andreas Krause, and Charlotte Bunne. Aligned diffusion schrödinger bridges. In Uncertainty in Artificial Intelligence, pages 1985-1995, PMLR, 2023.
[83] Zhengyu Su, Yalin Wang, Rui Shi, Wei Zeng, Jian Sun, Feng Luo, and Xianfeng Gu. Optimal mass transport for shape matching and comparison. IEEE Irunsactions on pattern analysis and machine intelligence, 37(11):2246-22
2015.
[84] Alexander Tong, Nikolay Malkin, Kilian Fatras, Lazar Atanackovie, Yanlei Zhang, Guillaume Huguet, Guy Wolf, and Yoshua Bengio. Simulation free schrödinger bridges via score and flow matching. arXiv preprint arXiv:2307. 03672, 2023.
[85] Alexander Tong. Kilian FATRAS, Nikolay Malkin, Guillaume Huguet, Yanlei Zhang, Jarrid Rector- Brooks, Guy Wolf, and Yoshua Bengio. Improving and generalizing flow-based generative models with minibatch optimal transport. Transactions on Machine Learning Research, 2024. ISSN 2835-8856.
[86] Jeffrey C Trinkle. On the stability and instantancous velocity of grasped frictionless objects. IEEE Transactions on Robotics and Automation, 8(5):560-577 572, 2002.
[87] Dylan Turpin, Tao Zhong, Shutong Zhang, Guanglei Zhu, Eric Heiden, Miles Macklin, Stavros Tsogkas, Sven Dickinson, and Animesh Garg. Fast-grasp d: Dexterous multi-finger grasp generation through differentiable simulation. In 2023 IEEE International Conference on Robotics and Automation (ICRA). pages 8082-8089. IEEE, 2023.
[88] Julen Urain, Niklas Funk, Jan Peters, and Georgia Chalvatzaki. Se (3)-diffusionfiilds: Learning smooth cost functions for joint grasp and motion optimization through diffusion. In 2023 IEEE International Conference on Robotics and Automation (ICRA), pages 0930. JEEE, 2023.
[89] Arash Vahdat, Francis Williams, Zan Gojeic, Or Litany. Sanja Fidler. Karsten Kreis, et al. Lion: Latent point diffusion models for shape generation. Advances Neural Information Processing Systems, 35: 10021-10039, 2022.
[90] Francisco Vargas, Pierre Thodoroff, Austen Lamacraft, and Neil Lawrence. Solving schrödinger bridges via maximum likelihood. Entropy, 23(9):1134, 2021.
[91] Jacob Varley, Jonathan Wcisz, Jared Weiss, and Peter Allen. Generating multi-fing fingered robotic grasps via deep learning. In 2015 IEEE/RSJ international conference on intelligent robots and systems (IROS), pages 4415-4420. IEEF, 2015.
[92] Cédric Villani et al. Optimal transport: old and new, volume 338. Springer, 2008
[93] Gefei Wang, Yuling Jiao, Qian Xu, Yang Wang, and Can Yang. Deep generative learning via schrödinger bridge. In International conference on machine learning, pages 10794-10804, PMLR, 2021.
[94] Ruicheng Wang, Jialiang Zhang, Jiyy Chen, Yinzhen Xu, Puhao Li. Tengyu Liu, and He Wang. Dex- graspnet: A large-scale robotic dexterous grasp dataset for general objects based on simulation. In 2023 IEEE International Conference on Robotics and Automation (ICRA), pages 11359-1 1366. IEEE, 2023.
[95] Zehang Weng, Haofei Lu, Danica Kragic, and Jens Lundell. Dexdiffuser: Generating dexterous grasps with difffusinn models. JEEE Robotics and Automation Letters, 2024.
[96] Haoyu Xiong, Quanzhou Li, Yun- Chun Chen, Homanga Bharadhwaj. Samarth Sinha, and Animesh Garg. Learning by watching: Physical imitation of manipulation skills from human videos. In 2021 IEEE/RS/ International Conference Intelligent Robots and Systems (IROS), pages 7827-7834, IEEE, 2021.
14

---

[97] Zhao-Heng Yin, Changhao Wang, Luis Pineda, Francois Hogan, Krishna Bodduluri, Akash Sharma. Patrick Lancaster, Ishita Prasad, Mrinal Kalakrishnan, Jitendra Malik, et al. Dexteritygen: Foundation controller for unprecedented dexterity, arXiv preprint arXiv:2502.04300 2025.
[98] Haoqi Yuan, Bohan Zhou, Yuhui Fu, and Zongqing Lu. coos-embbdiimntt dexterous grasping with reinforcement learning. arXiv preprint arXiv:2410.02479 2024.
[99] Hanbo Zhang. Jian Tang, Shiguang Sun, and Xuguang Lan. Robotic grasping from classical to modern:
A survey. arXiv preprint arXiv:2202.03663 2022.
[100] Hui Zhang, Sammy Christen, Zicong Fan, Otmar Hilliges, and Jie Song. GraspXL:
Generating grasping motions for diverse objects at scale. In European Conference on Computer Vision (ECCV), 2024.
[101] Tao Zhong and Christine Allen- Blanchette. Gagrasp: Geometric algebra diffusion for dexterous grasping. 2025 I.F.F. International Conference Robotics and Automation (ICRA). IERE, 2025.
[102] Tao Zhong, Zhixiang Chi, Li Gu, Yang Wang, Yuanhao Yu, and Jin Tang. Mcta-dmoe: Adapting to domain shift by meta-distillation from mixture-of-experts Advances in Neural Information Processing Systems, 35:22243-22255 2022.
[103] Yi Zhou, Connelly Barnes, Jingwan Lu, Jimei Yang, and Hao Li. On the continuity of rotation representa- tions in neural networks. In Proceedings of the IEEE/CVF conference computer vision and pattern recognition, pages 5-533, 2019.
[104] Anya Zorin, Irmak Guzey, Billy Yan, Aadhithya Iyer. Lisa Kondrich, Nikhil X Bhattasali, and Lerrel Pinto. Ruka: Rethinking the design of humanoid hands with learning. arXiv preprint arXiv:2504.3366. 2025.
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A Background on Schrödinger Bridges and Simulation-Free Training
A.1 The Schrödinger Bridge Problem
The Schrödinger Bridge (SB) problem seeks stochastic process P that evolves from a source distribution (2( to a target distribution q (3) while being as "close" as possible to a reference process (typically Brownian motion). This is formally expressed minimizing the Kullback- Leibler (KL) divergence between the path measures:
I
arg min QL
(10)
The optimal process PP" can be characterized as a mixture of Brownian bridges weighted by an entropically regularized optimal transport (OT) plan [11 As shown in Eq. i the main text, this plan प. finds a low-cost coupling between go and q1. The work of Föllmer [31 shows that if Q is Brownian motion, the SB is uniquely described by mixture of Brownian bridges drawn according to næ. This insight crucial, as it reduces a complex dynamic optimization problem to a more tractable computation over static distributions.
A.2 Learning Stochastic Dynamics with [SF]
The dynamics of the SB are modeled by the Itō SDE in Eq. by this SDE evolve according to the Fokker-Plance equation 773
2 The marginal densities pe (x) induced
Op. - (prw:) + 9()² 2
Apr.
(11)
Øt
where Apt V (Vpt) is the Laplacian. 'he probability flow ODE in Eq. shares the same marginals (xr). To learn these dynamics from data without direct access to the marginals Pt. the [SF] framework (84) leverages the connection to entropic OT. By sampling source-target pair (zo, x1) from the entropic OT plan n., one can construct conditional Brownian bridge path between them. For constant diffusion rate g(t) a, the conditional distribution pr (r 2o, 21) ) is Gaussian
N(:; (1 - -)may + tæ o²t(1 t) From this, we obtain closed-fone expressions for the conditional
score and probability flow drift, which serve regression targets for the neural networks:
(x) x1) = t(1 - t)
(x ((1 t)zo + (xx)) + (01 xo);
(12)
V (log 21) (1 f).0 + t.n
0²t(1- -
These targets are used in the loss function shown in Eq.
A.3 Weighting Schedule X(t)
Following Tong et al. 84 we apply time-dependent weighting schedule A(4) to stabilize the score regression loss across time. This is essential because the conditional score V, Po (x: | x1) grows unbounded as + 0 or t + 1, leading to an imbalance in the loss. To address this, we adopt the formulation that standardizes the regression target to have unit variance. This is done by predicting the noise added in sampling z; from the linear interpolation μ4 = (1 - t)z0 + tx under Brownian bridge with variance of ==²t(1 t). This leads to:
X(t) o. = =
This setting ensures that the target score V, a p: To, .1) corresponds to c/0,, with ~N I). making the scaled target distributed as standard Gaussian.
In practice, we use an alternative numerically stable formulation derived by rescaling the target by o V.Pt. which yields the weighting schedule:
2 gz 01 2V((1-1)
x(t)
(13)
Under this form, the squared score loss term simplifies to:
X(t) [t)
(A(t)sa(t,x) + eell.
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This avoids any division by small values resulting from boundary conditions and improves numerical stability. All models in our experiments were trained using this second formulation and the simplified regression objective:
( =
E 1- znope m1)
[lvo(t, 2) - (2/ x1) =1) [[A(t)so(tt,) tell?]
(14)
B
Architecture and Training Details
B.1
VAE Training
Our VAE consists of two main components: a point cloud encoder for the segmented hand point cloud, and an MLP-based latent autoencoder that encodes and decodes grasp configurations.
Hand Encoder.
We use a PVCNN-based architecture [51] to process the input hand point cloud. The input to the encoder is point cloud of size N The PVCNN follows hierarchical structure with point and voxel convolution blocks as described below:
Table 4: PVCNN Point Feature Blocks
Output Channels
Num Layers
Kernel Size
Voxel Resolution Multiplier
64
1
32
2
128
1
16
1024
1
N/A
X
The final 1024-dimensional global features are passed through an MLP consisting of [256. 128] hidden units, followed by max pooling to produce single global feature vector for each input.
Grasp Configuration VAE. The latent grasp representation is modeled using fully connected variational autoencoder. The encoder receives the hand representation and maps it into a latent space of size 768. The decoder reconstructs the full hand joint configuration. Layer sizes are follows:
Table 5: Latent VAE Layer Sizes
Network
Input
Hidden Layers
Latent Dim
Output Dim
Encoder
1472
[2048, 1024] [2048, 1024, 256]
768
Decoder
768
9 # DoFs
Training Configuration. We train the VAE for 18 epochs using a batch size of 256, Adam optimizer with learning rate of 10 and 16 dataloader workers. The loss function includes a weighted combination of reconstruction losses with a = 0.6 and a KL divergence term with a very small weight (3 = 10-5). The training time is approximately one GPU day on a single NVIDIA A6000 GPU.
B.2
Score and Flow Model Architecture
Both the score network se and the flow network vp in our pipeline share the same U- U-ViT-based backbone architecture [5]. The input to each model consists of concatenation of latent hand representations, object shape encodings. and contact anchor tokens, following the conditioning design described in Sec. 4.3 of the main paper.
U-VIT Backbone. We use a vision transformer architecture adapted for point-based data. The network is composed of 12 transformer blocks, each with multi-head self-attention and MLP layers. Time conditioning injected via learned embeddings scaled by a temperature factor. The configuration detailed in Table 6

---

Table U-ViT Backbone Configuration
Parameter
Value
Number of Transformer Layers (Depth)
12
Embedding Dimension
512
Number of Attention Heads
MLP Expansion Ratio
Time Embedding Scale
1000.0
Dropout Rate
0.0
Attention Dropout Rate
0.1
Input Dimensions. The model conditioned on several input tokens:
Latent Hand Token: 768-dimensional vector produced by the VAE encoder.
Global Object Token: 128-dimensional latent from the pretrained LION object encoder.
Local Object Tokens: 2048 points, each with 4 dimensions (XYZ latent code).
Contact Anchor Tokens: 5 tokens computed by applying farthest point sampling object points identified via thresholding (within 0.005 m) to the nearest point to the hand point cloud.
Training Configuration. We train both the score and flow networks using the loss in Eq. 14 with the weighting schedule described in Appendix [A.3] The training setup is summarized in Table The training time is approximately 650 GPU hours on NVIDIA L40 GPUs.
Table 7: Training Hyperparameters for Score and Flow Models
Hyperparameter
Value
Total Steps
20000
Batch Size (on each GPU)
512
Learning Rate
2 10
Linear Warmup Steps
256
Gradient Clipping
1.0
EMA Decay
0.999
EMA Start Step
10000
a (used in Table.
0.1
C OT Cost Formulation and Computation
We implement four distinct ground costs for the optimal transport (OT) coupling in our framework. Two of these (Euclidean base pose and contact map Chamfer distance) are computed closed form using standard metrics in R. The remaining two involve more complex geometry- and physics-informed reasoning.
Grasp Wrench Space Overlap. The grasp wrench space (GWS) 29 of a grasp represents the set of all wrenches (forces and torques in RR.) that the grasp apply to object through contact. For grasp with l contact points {c; 1k and associated contact normals (n,), we construct a set of unit wrench vectors }w;} follows:
ft C x fi
E R
fi == a.74, 0.
We form the convex hull of these wrenches approximate the GWS, denoted as the grasp wrench hull (GWH). The distance between two grasps is then defined as minus the intersection-over (IoU) of their GWH volumes:
Vol(Hull GW Soource) Hull(GW Starget)) Vol(Hull(GW soorree) U HullGGW Starget))
dwrench
25

---

Since computing the exact intersection and union volumes of 6D convex hulls is intractable in closed form, we approximate the GWH IoU using GPU-accelerated Monte Carlo sampling. We sample large number of points (typically )(10)) in the 6D bounding box enclosing both hulls, and compute membership in each hull using their supporting hyperplane inequalities. Intersection and union volumes are then estimated as:
#pts both #samples
Volinersect
Volyax.
A 3D implementation of this approximation is used to compute batch-wise GWH IoU efficiently during training, and the full 6D implementation reported for the experiments.
Jacobian- based Manipulability. To capture the potential of grasp to actuate the object, we compute the Jacobian matrix J E ( relating hand joint velocities to object motion. The Jacobian is computed using the Warp differentiable simulator (56) following the setup from Turpin et [87 with fixed object and grasp configurations. We exclude the 6-DoF base pose of the hand, focusing only on internal joints.
Each column Jj of the Jacobian represents the effect of joint j on the object's linear and angular velocity. We summarize the object-level actuation capability of grasp by computing 6D vector of maximal manipulability across joints:
max رزز R
The OT cost is then defined as the squared lg distance between source and target maximal actuation vectors:
djac- M - Mearget ||2
This cost encourages the translated grasp to maintain similar controllability over object motion.
D Additional Results
D.1 Qualitative Examples Across Tasks
Figure 5 presents additional qualitative examples across all three grasp translation tasks: Human Allegro, Human--Shdow,, and Shadow- Our method remains robust and pro- duces stable, contact-consistent grasps even when the source grasp is suboptimal or incomplete. In contrast, the object-agnostic baseline RFP often fails to recover valid contact configurations, particularly for complex hand-object interactions or gcometrically mismatched hands.
D.2 Inference Time Comparison
We compare the amortized inference time of our method against all baselines in Table While our framework designed primarily as an offline planner, inference speed competitive.
As shown in the table, our method takes approximately 0.8 seconds to generate a grasp using 100 Euler-Maruyama steps. This comparable to the diffusion baseline (0.5s). The iterative sampling process, where each of the 100 steps requires a full forward pass through our U-ViT model, is the primary factor for this timing. In contrast, lightweight methods like CrossDex are significantly faster, as they only require single forward pass through a small MLP. Nevertheless, our approach is substantially faster than the optimization based RobotFingerPrint, which requires over 5 seconds per grasp due to its costly per-instance optimization procedure.
Table 8: Average inference time per grasp (amortized, in seconds). Our method is comparable to the diffusion baseline and significantly faster than optimization-bant based approaches.
Time (sec/grasp)
Method
H-
H-S
S-A
Mean
CrossDex Retargeting 998
1.le-5
1.le-5
1.le-5
1.le-5
Rex-Reetgggting [72]
0.13
0.16
0.08
0.12
Diffusion (100 steps)
0.5
0.5
0.5
0.5
Ours (100 steps)
0.8
0.8
0.8
0.8
RobotFingenPrint
41
5,2
5,8
5.1
5.37
26

---

D.3 Contact Alignment
In addition to the GWH IoU metric presented in the main text, we evaluate the geometric alignment of contact patterns using Contact Alignment metric. This metric is defined the squared Chamfer distance between the source and target contact maps on the object surface, where a lower value indicates better alignment. This serves as useful proxy for how well the local interaction geometry of the grasp is preserved during translation.
Tableppreeent the results. Our model trained with the Contact OT cost (OurScommezr) achieves a mean distance of just 4.99 cm², significantly outperforming all other methods. This quantitatively confirms that this variant is highly effective preserving the precise locations of contact, which is critical precondition for achieving a functionally similar and physically stable grasp. The other baselines struggle to align contact points, resulting in much larger distances and, as shown in the main paper, lower success rates.
Table 9: Comparison on Contact Aligmment (cm²) N. Lower values indicate better alignment between the source and target grasp's contact points on the object surface.
Contact Alignment (cm (
Method
H-A
H-*
S-A
Mean
RobotFingerPrint [1
19.21
16.66
11.27
15.71
Dex-Rettin mex-Rettrgeting [72]
9.53
12.92
6.68
9,71
CrossDex Retargeting
998
9.85
14.52
7.06
10.48
Ours (Contact OT)
5.05
3.37
6.54
4.99
Ours (GWH OT)
10.71
7.26
10.19
9.39
D.4 VAE Ablation Study
To validate the design choices for our Variational Autoencoder (VAE), we conduct an ablation study comparing our full model against three alternatives:
PointNet VAE: A baseline inspired by [1] that reconstructs the hand point cloud via Chamfer distance and decodes hand parameters in a separate branch.
Ours w/o Mesh Loss: Our VAE trained only on the hand parameter reconstruction loss
(Cv = Blll@ - D. without the differentiable FK layer and mesh vertex loss.
Ours w/o Param Loss: Our VAE trained only the mesh vertex loss (Cv
FK()) without the direct parameter reconstruction loss.
We evaluate reconstruction quality using the L2 error the decoded hand parameters, tested on a held- out set of objects. As shown in Table TO our proposed VAE architecture significantly outperforms all alternatives.
Table 10: Evaluation of VAE architectures using Hand Parameters L2 Error..
Method
Allegro
Shadow
Human
PointNet VAE
0.1965
0.2001
0.2468
Ours w/o Mesh Loss
0.0967
0.0933
0.1270
Ours w/o Param Loss
0.0439
0.0441
0.0534
Ours (Full)
0.0335
0.0286
0.0523
Our analysis indicates that the PointNet VAE struggles because the Chamfer distance loss can be indiscriminative; it may achieve a low value even if the reconstructed pose is incorrect but has large overlapping regions with the ground truth. Ablating the mesh loss harms the learning of fine-grained geometric details, while ablating the parameter loss can lead to memorization issues, as the high- capacity latent space (dim=768) can overfit to the relatively low-dimensional hand configuration space (typically ~0 DoFs).
27

---

D.5 Results on Additional Transfer Settings
To provide a more comprchensive evaluation, we run experiments on the three remaining transfer settings: Allegro-+Huanl (A (A-+H), Shadow->Huma (S HH), and Allegro-+Shann
(A-+S).
We note a technical limitation in reporting the IsaacGym success rate for tasks where the human hand is the target. Our human hand is an articulated model based MANO [74] with non-watertigh link meshes, which causes instabilities in the IsaacGym simulator. We are therefore unable to report success rates for the A- and S-+H settings.
The results for success rate (A-S only), diversity, and 6D GWH IoU are presented in Tables and [3] respectively. Our method consistently outperforms the baselines in preserving functional intent, achieving significantly higher GWH IoU, particularly when transferring the complex human hand. We also generate more diverse set of plausible grasps, highlighting the flexibility of our learned transport plan. Finally, in the A-S setting where direct stability comparison was possible, our method achieved the highest success rate, demonstrating superior physical plausibility. These findings show that the advantages of our approach are robust across these challenging transfer settings.
Table 11: Comparison on Success Rate (%) for A-S.
Method
A-S
RobotFingerPrint
30.27
Diffusion
33.96
Ours (Contact OT)
38.00
Ours (GWH OT)
41.49
Table 12: Comparison on Diversity (rad)f-
Diversity (rad) S-+H
Method
A-HH
A-$
Mean
RobotFingerPrint
0.196
0.180
0.182
0.186
Diffusion
0.283
0.298
0.207
0.263
Ours (Contact OT)
0.317
0.332
0.212
0.287
Ours (GWH OT)
0.310
0.327
0.178
0.272
Table 13: Comparison on 6D GWH IoU (%)t.
6D
GWH IOU (%)
Method
A
S-HH
A-S
Mean
RobotFingerPrint
3.46
4.11
3.51
3.69
Diffusion
10.41
11.82
8.78
10.34
Ours (Contact OT)
13.59
15.37
8.87
12.61
Ours (GWH OT)
11.76
13.30
9.16
11,41
E
Compute Resources
Our experiments were conducted on combination of local servers and high-performange computing cluster. The local server consists of a 24-core CPU and NVIDIA A6000 GPUs, which were used for model development, ablation studies, and VAE training. For large-scale training, utilized compute cluster, where each cluster node is equipped with two 26-core CPUs and 8 NVIDIA L40
GPUs.
28

---

H
H
S-A
Source
RFP
Pose
Contact
GWH
Jacobian
Figure 5: More qualitative examples. Each column shows a source grasp and its translated output for different methods. Our method consistently recovers physically plausible grasps across tasks, while RFP frequently fails, especially with noisy source grasps.
29


Reviews:
[{"review_id": "HyGjPQD82T", "reviewer": "Reviewer_AEMy", "summary": "This paper presents an approach to grasp translation across robot hands. It formulates the problem as a stochastic transport between grasp distributions of different hands and learns to map between two latent distributions via score and flow matching. The translation is guided using alignment cost functions, such as pose, contact maps, wrench space, and manipulability alignment. Experiments include comparisons with previous methods and a diffusion baseline in terms of quality, diversity, and alignment, as well as ablation studies for diffusion rate and discretization steps.", "questions": "See weaknesses.", "limitations": "Yes.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "**Strengths:**\n\n1. The formulation of stochastic transport for grasp translation and learning the mapping via score and flow matching is novel and interesting.  \n2. Compared to previous works, the four types of alignment (pose, contact maps, wrench space, and manipulability alignment) are comprehensive.  \n3. The proposed method outperforms the previous method RFP in all metrics in Table 1.  \n4. The presentation quality is high, and the figures are clear.  \n\n**Weaknesses:**\n\n1. It is unclear which alignment metric is most suitable for the task. The paper adopts 6D GWH IoU as the alignment metric, and the contact map alignment cost achieves better alignment. However, this metric may not be useful for teleoperation tasks, which are likely the main application of grasp translation. It would be better to incorporate pose alignment metrics for evaluation.  \n2. Since grasp translation is often used for real-time teleoperation, a detailed efficiency report is expected, especially for the diffusion-based methods.  \n3. While the main contribution is latent score and flow matching for grasp translation, it would be better to include more baselines such as Dex-Retargeting, which is widely used in teleoperation papers, or neural retargeting method like CrossDex. The reviewer would like to see comparisons in terms of success rate, pose alignment, and efficiency.  \n4. Real-world experiments would make the paper more convincing.\n\nDex-Retargeting: https://github.com/dexsuite/dex-retargeting  \nCrossDex: https://github.com/PKU-RL/CrossDex/", "was_revised": true, "final_justification": "Thanks for the new baselines and the profiling results. Since real experiments and the pose metric are still missing, the reviewer will keep the original score.", "rebuttal": "We sincerely thank the reviewer for their time and insightful feedback. We are encouraged that the reviewer found our formulation \"novel and interesting\" and our presentation \"of high quality.\" We address the identified weaknesses below.\n\n> *W1-3*: Regarding pose alignment metric, efficiency report, and comparison with Dex-Retargeting and CrossDex.\n\nWe appreciate the reviewer's suggestions regarding evaluation metrics, efficiency, and comparisons to other relevant work. We group these points as they all relate to the application context of our method.\n\n**Clarification: Grasp Translation vs. Teleoperation**\n\nWhile our work is technically related to teleoperation, we wish to clarify that our formulation of *grasp translation* has a fundamentally different goal.\n- *Teleoperation* is typically manipulator-oriented, often relying on a human-in-the-loop for perception and feedback, and aims to mimic the source agent's actions as closely as possible.\n- Our formulation of *grasp translation* is object-centric and aims to transfer the functional intent of a grasp, which does not necessarily require a human source and allows for morphologically and posturally different but functionally equivalent outcomes.\n\nFor example, to turn on a TV remote, a source grasp might be from below, palm up, with the thumb on the power button. A teleoperation system would try to replicate this exact pose. Our method, however, recognizes the functional goal (applying force to the power button while supporting the remote) and could generate a target grasp from above, palm down, with the index finger on the button and other fingers providing support. We consider both grasps *functionally equivalent*.\n\nBack to your question about metrics, in our problem setting, we can imagine that two functionally equivalent grasps are likely to induce similar contact patterns (like in the remote example, contact at the bottom to fight gravity and at the on/off button for functionality) and/or wrench profiles (force and torque the grasp can exert). Similar contact patterns often lead to similar wrenches, as one can only exert force during contact, but similar wrenches do not necessarily indicate a similar contact pattern. You can imagine that flipping a water bottle requires torques about any axis on the horizontal plane, where any pinches on the side of the object are likely to induce these types of torques. \n\nThis distinction motivates our choice of the 6D Grasp Wrench Hull (GWH) IoU as a primary alignment metric. Functionally equivalent grasps should be able to exert similar forces and torques on the object, which is precisely what GWH measures.\n\n**Additional Experiments: Baselines and Metrics**\n\nAs per the reviewer's suggestion, we have conducted new experiments to include the positional retargeting module from Dex-Retargeting [1] as baselines. We also tweak the retargeting neural network from CrossDex [2] to be trained with generated data from positional retargeting to output both wrist pose and finger joint configuration as an additional baseline. Further, we introduce a new Contact Alignment metric as a proxy to pose alignment metric, inspired by Dex-Retargeting's positional optimization objective, which measures the squared Chamfer distance between source and target grasp contact maps.\n\n*A note on baselines*: Both Dex-Retargeting and CrossDex require pre-defined link-to-link correspondences between the source and target hands. This information is not typically available in large-scale grasp datasets, and we had to manually annotate it for these comparisons. This requirement limits their generality. For instance, they cannot retarget to a hand with more fingers than the source. Our method has no such constraints.\n\nThe results, shown in the tables below, demonstrate that our method significantly outperforms these new baselines across all key metrics.\n\n***Table 1: Comparison on Success Rate (%)↑***\n|                      | H→A   | H→S   | S→A   | Mean  |\n|----------------------|-------|-------|-------|-------|\n| Dex-Retargeting      | 56.93 | 16.21 | 56.44 | 43.19 |\n| CrossDex Retargeting | 36.51 | 8.97  | 35.12 | 26.87 |\n| RobotFingerPrint     | 66.80 | 33.89 | 70.31 | 57.00 |\n| Ours (Contact OT)    | ***74.78*** | ***37.10*** | ***76.37*** | ***62.75*** |\n| Ours (GWH OT)        | **77.73** | **42.59** | **78.74** | **66.34** |\n\n***Table 2: Comparison on Diversity (rad)↑***\n|                      | H→A   | H→S   | S→A   | Mean  |\n|----------------------|-------|-------|-------|-------|\n| Dex-Retargeting      | 0.221 | 0.186 | 0.196 | 0.201 |\n| CrossDex Retargeting | 0.195 | 0.201 | 0.223 | 0.206 |\n| RobotFingerPrint     | 0.225 | 0.186 | 0.199 | 0.203 |\n| Ours (Contact OT)    | **0.294** | **0.211** | **0.311** | **0.272** |\n| Ours (GWH OT)        | ***0.293*** | ***0.197*** | ***0.309*** | ***0.266*** |\n\n***Table 3: Comparison on 6D GWH IoU (%)↑***\n|                      | H→A   | H→S   | S→A   | Mean  |\n|----------------------|-------|-------|-------|-------|\n| Dex-Retargeting      | 5.67  | 4.41  | 6.97  | 5.68  |\n| CrossDex Retargeting | 5.69  | 4.24  | 5.86  | 5.26  |\n| RobotFingerPrint     | 7.51  | 6.62  | 8.99  | 7.77  |\n| Ours (Contact OT)    | **15.89** | **15.18** | ***12.54*** | ***14.54*** |\n| Ours (GWH OT)        | ***15.09*** | ***14.14*** | **14.67** | **14.63** |\n\n***Table 4: Comparison on Contact Alignment (cm^2)↓***\n|                      | H→A   | H→S   | S→A   | Mean  |\n|----------------------|-------|-------|-------|-------|\n| Dex-Retargeting      | ***9.53***  | 12.92 | ***6.68***  | 9.71  |\n| CrossDex Retargeting | 9.85  | 14.52 | 7.06  | 10.48 |\n| RobotFingerPrint     | 19.21 | 16.66 | 11.27 | 15.71 |\n| Ours (Contact OT)    | **5.05**  | **3.37**  | **6.54**  | **4.99**  |\n| Ours (GWH OT)        | 10.71 | ***7.26***  | 10.19 | ***9.39***  |\n\nOur analysis suggests the baselines struggle because their IK-style optimization focuses only on select distal links, ignoring potential collisions from other parts of the hand (e.g., the palm), which leads to physically invalid grasps. The CrossDex model, trained on this suboptimal data, inherits these limitations and fails to generalize due to its simple architecture and small size (4-layer MLP). We will integrate these results into the final paper and add this discussion to the related works.\n\n**Efficiency Report**\n\nWe provide a more detailed inference time report below. While our method is designed primarily as an offline planner, its amortized inference time is on the same order of magnitude as the baselines and significantly faster than the optimization-based RobotFingerPrint [3]. CrossDex Retargeting network is significantly faster due to its simple architecture, and it only needs to do the forward pass once.\n\n***Table 5: Average Inference Time per Grasp, Amortized (s)***\n|                       | H→A    | H→S    | S→A    |\n|-----------------------|--------|--------|--------|\n| Dex-Retargeting       | 0.13   | 0.16   | 7.98e-2 |\n| CrossDex Retargeting  | 1.1e-5 | 1.1e-5 | 1.1e-5 |\n| RobotFingerPrint      | 5.2    | 5.8    | 5.1    |\n| Diffusion (100 steps) | 0.5    | 0.5    | 0.5    |\n| Ours (100 steps)      | 0.8    | 0.8    | 0.8    |\n\n> *W4*: Regarding real-world experiments.\n\nWe agree that real-world validation is a crucial step to demonstrate the full impact of our work. Given the short rebuttal period, we were unable to conduct these experiments. However, our current work focuses on the core algorithmic contributions for grasp translation, which we believe are sound and well-supported by our extensive simulation results. We are fully committed to incorporating real-world experiments in future work.\n\n#### Reference:\n[1] Qin et al., \"Anyteleop: A general vision-based dexterous robot arm-hand teleoperation system.\" RSS 2023.\n\n[2] Yuan et al., \"Cross-embodiment dexterous grasping with reinforcement learning.\" ICLR 2025.\n\n[3] Khargonkar et al., \"RobotFingerPrint: Unified Gripper Coordinate Space for Multi-Gripper Grasp Synthesis and Transfer.\" arXiv 2024."}, {"review_id": "zQoTCUm4gg", "reviewer": "Reviewer_DVx1", "summary": "The paper introduces a vision-based dexterous grasp translation method framed as a Schrödinger Bridge problem. This method aims to translate grasp intentions from a source robotic hand to a target hand with different morphologies without relying on paired demonstrations. By employing physics-informed cost functions and learning distributional grasp translations, the method attempts to bridge morphological gaps between diverse robotic manipulators.", "questions": "- Regarding the human hand scenario, the input to the VAE consists of rendered images of a skeletal hand model, making practical application to actual human hands infeasible. This effectively treats the human hand as merely another robotic hand model. Could the authors clarify how their approach can be realistically extended to accommodate real human hand data?\n- It is unclear whether the input to the VAE is RGB image or point cloud. Figure 2 indicates point cloud, while the text description indicates RGB. If it’s RGB, how to do the segmentation in real-world? What if the input image is a highly occluded one, which is quite common in dex mainpulation? If it’s point cloud, how to obtain it during inference?\n- Do we need contact anchor during inference? My current understanding is “yes”. But how can we get it during inference?", "limitations": "See Weakness and Question", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**Strengths:**\n\n- The proposed method leverages an innovative Schrödinger Bridge formulation, enabling a principled probabilistic approach to grasp translation.\n- Introducing physics-informed cost functions is a valuable contribution, effectively guiding the grasp translation process to maintain functional grasp similarity despite morphological differences.\n- The method demonstrates promising performance in simulation environments across multiple hand-object pairs, indicating strong potential for generalization.\n\n**Weaknesses:**\n\n- The paper appears to be slightly over-claiming, which needs further clarification:\n    - A central claim made by the authors is that *“While recent works in data-driven grasp generation have shown success in generating feasible grasps for specific hand object pairs, they often rely on large-scale datasets curated through computationally expensive simulation or real-world trials.”.* However, the proposed method itself is trained on MultiGripperGrasp, a substantial dataset containing approximately 30.4 million grasps across 11 robotic manipulators and 345 objects. Thus, the claim is misleading.\n    - More critically, another prominent claim is about overcoming the hand-specific limitations of existing models *“Moreover, such models typically operate in a hand-specific setting, which requires retraining or significant fine-tuning to adapt to new robotic hands.”*. The authors argue their approach generalizes to unseen dexterous hands without requiring retraining or significant fine-tuning. To validate this claim meaningfully, the authors need explicit evidence demonstrating robust generalization to unseen robotic hands not included in the training dataset. Otherwise, the claimed advantage over existing hand-specific methods becomes questionable.\n- Tables and figures are not self-contained or sufficiently explained. For instance, in Figure 3, terms like \"pose\" and \"contact\" lack clear definitions within the figure caption, causing confusion and reducing readability.\n- The paper lacks real-world experiments entirely. Without empirical validation in real-world scenarios, the practicality and applicability of the proposed method remain questionable.", "was_revised": true, "final_justification": "Most of my questions have been answered in the rebuttal, and I have accordingly raised my rating. However, there are still several reasons why I am unable to give a higher score:\n\n1. The responses highlight a key limitation: the current pipeline is difficult to deploy in real-world scenarios. It relies on oracle contact anchors and clean, segmented point clouds as input — both of which are extremely challenging to obtain in real-world inference, especially in dexterous grasping tasks where occlusions are common.\n\n2. The writing of the paper remains quite rough. While the authors have proposed some revisions in the rebuttal and promised to improve the clarity, the extent of revision required — including adjustments to some core claims — is substantial. Given this, I am not confident that all necessary changes can be adequately addressed in the camera-ready version. It would be best to undergo another round of revision to fully address these issues.", "rebuttal": "We sincerely thank the reviewer for their time and insightful feedback. We are encouraged that the reviewer found our formulation \"innovative\" and our contribution \"valuable.\" We address each point below.\n\n> *W1 & W2*: On Claims, Datasets, and Generalization\n\nWe thank the reviewer for highlighting a potential ambiguity in our paper's motivation versus its direct claims. We agree that the introduction could be framed more precisely, and we will revise it accordingly.\n\n**Our Core Contribution: Translation without *Paired* Data**\n\nThe central motivation of our work is to overcome the need for paired demonstration data for grasp translation. While single-hand grasp datasets can be generated efficiently with modern simulators (e.g., GraspIt! [1], GenDexGrasp [2]), creating a large-scale dataset of corresponding *functionally equivalent* grasps across two different hands is extremely expensive and often intractable.\n\nOur method addresses this bottleneck. We use the MultiGripperGrasp dataset [3] for its rich collection of single-hand grasps, but our framework **does not use or require any pre-existing pairings** between them. Instead, the Schrödinger Bridge formulation, guided by our physics-informed OT designs, learns to discover these functional correspondences automatically from unpaired sets of grasps. This is analogous to machine translation: while monolingual text data is abundant, high-quality parallel corpora (paired sentences) are scarce and expensive. Our work provides a new perspective on how to scale up grasp translation by leveraging readily available, unpaired grasp examples.\n\n**Clarification on Unseen Hand Generalization**\n\nWe also wish to clarify that generalizing to unseen hands is a long-term **motivation** for this research area, not a **claimed contribution** of our current model. We believe our approach is a meaningful step towards this motivation. The current implementation does not generalize to unseen hands at inference time because our VAE decoder learns the hand's kinematic structure implicitly from the training data. To generate a grasp for a new hand, the decoder would need to be retrained or fine-tuned on data from that hand. We acknowledge this limitation and view the development of learning-based methods that can generalize to new hand kinematics on-the-fly as an important and open research direction.\n\nTo address these points and prevent misunderstanding, we will revise the introductory section (Lines 16-22) as follows:\n\n\"A key challenge in data-driven grasp synthesis is the heavy reliance on large-scale datasets, which are often curated for a specific hand through computationally expensive simulation or real-world trials. Transferring grasp knowledge to a new robotic hand is non-trivial, as models trained for one hand often require complete retraining or significant fine-tuning for another, which poses a practical bottleneck. A particularly challenging aspect is the acquisition of **paired demonstration data**, where a grasp for a source hand is mapped to a corresponding functional grasp for a target hand. Manually creating or algorithmically discovering such pairings at scale is extremely difficult. This motivates the need for a framework that can learn to translate the *intent* of a grasp from a source hand to a target hand using only unpaired, hand-specific grasp datasets while leveraging the underlying object geometry and physics to bridge the morphological gap.\"\n\n> *W3*: Tables and figures are not self-contained.\n\nThank you for this feedback. We will improve the clarity of our figures. For Figure 3, the labels \"Pose,\" \"Contact,\" \"GWH,\" and \"Jacobian\" refer to variants of our model trained with the different OT cost functions described in Section 4.2. We will add the following sentence to the caption to make it self-contained:\n\n\"The 'Pose', 'Contact', 'GWH', and 'Jacobian' columns show results from our method when trained using the respective OT cost functions from Sec. 4.2.\"\n\nWe will perform another round of proofreading on all figures and tables to ensure they are self-contained and easy to understand.\n\n> *W4*: Lack real-world experiments\n\nWe agree that real-world validation is a crucial step. Given the rebuttal timeframe, we were unable to conduct and document physical experiments. Our current research has focused on the core algorithmic contributions and their validation in a high-fidelity simulator. We fully recognize the importance of this aspect and are committed to including real-world experiments in future work.\n\nHowever, to further strengthen the paper's evaluation based on the reviewers' feedback, we have conducted extensive new simulation experiments, including comparisons to two additional strong baselines (Dex-Retargeting [4], CrossDex [5]), evaluation with a new pose alignment metric, a detailed efficiency report, and evaluation on the remaining three transfer settings (A→H, S→H, and A→S). Please refer to Table 1-5 of our response to reviewer AEMy and Table 2-4 of our response to reviewer 4u79 if interested. We believe these additions strengthen our empirical results and address key questions about performance and applicability.\n\n> *Q1*: Human hand as source and extension to real human data.\n\nThis is an excellent question. The human hand in our experiments is a fully articulated 3D model derived from MANO [6]. Specifically, we use distinct part meshes for each link, which are kinematically chained. While this means the complete mesh surface can appear discontinuous at the joints, this has little negative impact on our method. The input to our VAE is a **point cloud** sampled from the surfaces of these parts, which is an inherently discrete representation. Thus, the visual difference between a point cloud sampled from our articulated model versus one from a continuous, skinned MANO model is not significant.\n\nTherefore, our method can be directly applied to real human hand data, assuming that a system can provide a full, segmented point cloud of the hand grasping the object. We will provide some thoughts on how to obtain that in our response to your next question.\n\n> *Q2*: Input modality to VAE\n\nWe apologize for the confusion. The input to the VAE is a **full hand point cloud**, as shown in the architecture diagram (Figure 2). We will clarify this in the text.\n\nWe acknowledge that obtaining a complete, segmented point cloud in the real world is challenging due to occlusion. This is indeed a common problem in robotic perception. Standard solutions include:\n1. **Multi-camera systems** to fuse views and reconstruct a more complete point cloud, which is often seen in real-world experimental setups.\n2. **Pose estimation**: If 3D models of the object and hand are known, the problem can be reduced to a 3D hand-object pose estimation (HOPE) task, which is generally well studied with 3D inputs [7]. Once the poses are estimated, complete point clouds can be generated from the models and used as input to our system.\n\n> *Q3*: Regarding contact anchor\n\nYes, your understanding is correct. Contact anchors are required at inference. They are derived directly from the assumed input: the segmented source hand and object point clouds. The procedure is deterministic and computationally inexpensive:\n1. For each point on the object, we calculate its minimum distance to the source hand point cloud.\n2. Points with a distance below a small threshold (e.g., 0.005m in our experiments) are identified as the contact map on the object.\n3. We then apply Farthest Point Sampling (FPS) to this contact map to select the 5 contact anchors.\n\nThis process requires no additional information beyond the input point clouds that are already conditioned upon. We will clarify this procedure in the implementation details.\n\n#### Reference:\n[1] Miller and Allen. \"Graspit! a versatile simulator for robotic grasping.\" RA-M 2004.\n\n[2] Li et al., \"Gendexgrasp: Generalizable dexterous grasping.\" ICRA 2023.\n\n[3] Casas et al., \"Multigrippergrasp: A dataset for robotic grasping from parallel jaw grippers to dexterous hands.\" IROS 2024.\n\n[4] Qin et al., \"Anyteleop: A general vision-based dexterous robot arm-hand teleoperation system.\" RSS 2023.\n\n[5] Yuan et al., \"Cross-embodiment dexterous grasping with reinforcement learning.\" ICLR 2025.\n\n[6] Romero et al., \"Embodied hands: Modeling and capturing hands and bodies together.\" SIGGRAPH ASIA 2017.\n\n[7] Hampali et al., \"Honnotate: A method for 3d annotation of hand and object poses.\" CVPR 2020."}, {"review_id": "Vf9LnvaPof", "reviewer": "Reviewer_Xi3Y", "summary": "The paper introduces Grasp2Grasp, a method for grasp pose translation that aims to transfer grasping poses from one embodiment to another. Grasp2Grasp adopts a novel strategy by modeling valid grasps as an object-conditioned distribution and learning a distributional transformation between different embodiments. The translation process involves sampling from the latent space of the source embodiment, transforming the latent representation to align with the target embodiment's distribution, and decoding it into a corresponding grasp pose. To ensure the plausibility of the translated grasps, the method incorporates several cost terms that measure differences between grasp poses not only in appearance but also in terms of task effectiveness. Experimental results demonstrate the method’s ability to generate plausible and task-relevant grasping poses across embodiments.", "questions": "- Does the encoding process take the grasping pose into account? According to the formulation $z_0\\sim q_0(z_{source}\\vert o_{obj})$, only the object observation is used. However, Figure 2 suggests that the observation also includes the hand pose. \n- The roles of the source hand pose gsg_sgs in Algorithms 2 and 3 are unclear. It appears that $g_s$ is not involved in either the encoding or the sampling process. \n- What metric is used to compute the distance between the two 6D rotation representations in Equation 9? \n- Are the generated grasping poses validated in a physics simulator?", "limitations": "- Quality. The quality of the results is not satisfactory. Moreover, the paper lacks a thorough discussion and analysis of the experimental outcomes, which weakens the overall impact and clarity of the contributions.\n- Method and the presentation. The methodological description and overall presentation are unclear. It is difficult to grasp the detailed process proposed in the paper, which raises doubts about whether the method can effectively address the grasping pose *translation* problem.", "rating": 3, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths\n\n- The paper presents a well-formulated problem and an interesting approach. Framing grasp pose translation as a stochastic process that transforms the source distribution into the target distribution is both a strong and reasonable formulation. The use of SB to model the relationship between the two distributions, combined with OT to complete the pose transformation, is well-designed and conceptually sound.\n- The inclusion of algorithms in the method section enhances clarity and facilitates quick understanding of the approach.\n\nWeaknesses\n\n- **Experiments**: The experimental results raise several concerns regarding quality. As shown in Figure 3 and the supplementary figures, although the generated grasp poses do not exhibit significant penetrations into the object, they appear physically unstable. Furthermore, the qualitative results are limited and insufficient to convincingly demonstrate the method’s effectiveness, as only results on two objects—*sofa* and *cup*—are included. In particular, the generated poses for the *cup* differ significantly from the source poses, suggesting that the method sacrifices too much visual similarity in favor of physical validity.\n\n  Additionally, no real-world experiments are presented. This absence raises further doubts about whether the generated poses are truly physically plausible in practical settings.\n\n- **Presentation**: The paper's presentation requires substantial improvement. In Section 4, it is unclear why equations from Section 3 are reused without further clarification. In Section 4.2, the integration of the proposed cost terms into the OT process is not adequately explained. Simply stating \"following XXX\" is insufficient; the authors should not assume that readers are fully familiar with the referenced works. Clear and self-contained explanations are essential for understanding the methodology.", "was_revised": true, "final_justification": "Thank you to the authors for their efforts during the rebuttal period. Unfortunately, my main concerns about the qualitative results remain unresolved. Based on the original results—particularly Figure 1 and Figure 4 in the supplementary material—I am not convinced that the transferred grasps preserve functional similarity to the original grasps or that they are physically plausible. In addition, the diversity of object geometries is limited.\n\nThe rebuttal presents additional quantitative results and comparisons. However, I would regard the contribution as a substantial improvement only if both the quantitative metrics and the qualitative evidence clearly distinguish the method from prior work. The current qualitative results do not give me confidence that the method achieves reasonable performance or that it generally outperforms existing approaches. Dexonomy demonstrates what is physically plausible functional grasp synthesis -- The presented results should at least match this level.\n\nThe paper also lacks real-world experiments. \n\nFor detailed reasoning regarding why the qualitative results are worrying, please see my comment “Clarification on main concerns.”\n\nThe rebuttal commits to include results on a broader set of objects and also argues that the current focus is on the simulation while the real-world exps are to be explored in future work. However:\n\n- Given the current results on cup, sofa, and shoe objects, I am not confident that performance on other objects will be satisfactory.\n- Real-world results may differ a lot from those in the simulation. I cannot believe that the method can achieve good performance in the real world. \n\nFor these reasons, I do not believe the paper meets the bar for acceptance at this time.", "rebuttal": "We sincerely thank the reviewer for their time and insightful feedback. We are encouraged that the reviewer found our approach \"well-formulated\" and \"interesting.\" We address each point below.\n\n> *W1*: On Experimental Quality, Plausibility, and Analysis\n\n**Physical Plausibility and Validation**\n\nWe acknowledge that static images can sometimes appear unstable due to challenging viewpoints or occlusion. However, we want to emphasize that all generated grasps are quantitatively validated for physical stability in the high-fidelity IsaacGym simulator. We followed the rigorous protocol from GenDexGrasp [1], which we detail on Lines 292 - 299 in our manuscript:\n\n\"We report the grasp success rate using IsaacGym, following the GenDexGrasp [1] evaluation protocol. A grasp is considered successful if it maintains a stable hold on the object under six perturbation trials, where external forces are applied along $\\pm x$, $\\pm y$, and $\\pm z$ axes. We apply each force as a uniform acceleration of 0.5 m/s$^2$ for 60 simulation steps and measure whether the object translates more than 2 cm. A grasp passes if it withstands all six trials. Simulation parameters include a friction coefficient of 10 and an object density of 10,000. We use IsaacGym’s built-in positional controller to achieve the desired joint configurations.\"\n\nOur experimental results show that our method generates grasps that are not only stable but are **more stable** than all baselines. In response to other reviewers' feedback, we have also compared against two additional baselines, Dex-Retargeting [2] and CrossDex [3]. Our method continues to achieve the highest success rate, as shown below.\n\n***Table 1: Comparison on Success Rate (%)↑***\n|                      | H→A   | H→S   | S→A   | Mean  |\n|----------------------|-------|-------|-------|-------|\n| Dex-Retargeting      | 56.93 | 16.21 | 56.44 | 43.19 |\n| CrossDex Retargeting | 36.51 | 8.97  | 35.12 | 26.87 |\n| RobotFingerPrint     | 66.80 | 33.89 | 70.31 | 57.00 |\n| Ours (Contact OT)    | ***74.78*** | ***37.10*** | ***76.37*** | ***62.75*** |\n| Ours (GWH OT)        | **77.73** | **42.59** | **78.74** | **66.34** |\n\n**Qualitative Results and Visual Similarity**\n\nWe accept the criticism that the qualitative results in the initial submission were limited to two objects. Unfortunately, we are not allowed to present any multimedia results via external links as per the rebuttal guideline. We promise to include a more diverse set of qualitative examples from our 34 unseen test objects in the final version.\n\nRegarding the \"generated poses for the cup differ significantly from the source poses,\" we wish to reiterate the core goal of our work. Our formulation of **grasp translation** is object-centric and aims to transfer the **functional intent** of a grasp, which allows for morphologically and posturally different but functionally equivalent outcomes.\n\nFor example, to turn on a TV remote, a source grasp might be from below, palm up, with the thumb on the power button. A teleoperation system would try to replicate this exact pose. Our method, however, recognizes the functional goal (applying force to the power button while supporting the remote) and could generate a target grasp from above, palm down, with the index finger on the button and other fingers providing support. We consider both grasps **functionally equivalent** though they might appear very different visually.\n\nWe believe the qualitative examples for the cup in Figure 3 all share a similar functional intent: the hand approaches from the bottom, with fingers touching the bottom of the cup, and the thumb positioned near the handle for stability. Our method successfully transfers this intent, while the baseline method RobotFingerPrint [4] fails to generate a stable grasp for this specific example.\n\n> *W2*: Regarding real-world experiments.\n\nWe agree that real-world validation is crucial. Given the short rebuttal period, we were unable to conduct these experiments. Our work currently focuses on the core algorithmic contributions, validated in simulation. We are committed to including real-world experiments in future work.\n\nHowever, to strengthen the paper now, we have conducted extensive new simulation experiments, including comparisons to two additional strong baselines (Dex-Retargeting [2], CrossDex [3]), evaluation with a new pose alignment metric, a detailed efficiency report, and evaluation on the remaining three transfer settings (A→H, S→H, and A→S). Please refer to Table 1-5 of our response to reviewer AEMy and Table 2-4 of our response to reviewer 4u79 if interested. We believe these additions strengthen our empirical results and address key questions about performance and applicability.\n\n> *W3 & L2*: On Methodological Clarity\n\nThank you for pointing out areas where the presentation can be improved. We will revise the manuscript to be more self-contained. To clarify the link between Sections 3 and 4, we will add the following at the beginning of Section 4.1:\n\n\"We now apply the general Schrödinger Bridge framework from Section 3 to our specific problem of grasp translation. The abstract distributions $q_0$ and $q_1$  become the latent distributions of source and target grasps, respectively. The transport process between them is learned by optimizing the SF$^2$M objective from Eq. 7 in a latent space.\"\n\nTo clarify the integration of OT costs, we will add the following at the beginning of Section 4.2:\n\n\"To guide the Schrödinger Bridge, we must first compute an entropic OT plan $\\pi_{\\varepsilon}^* $ (Eq. 2), which is defined by a ground cost $d(\\cdot, \\cdot)$. We design several physics-informed costs for this purpose. For a given cost, we compute the OT plan between minibatches of source and target latent samples. We then draw pairs $(z_0, z_1) \\sim \\pi_{\\varepsilon}^*$ and use these pairs to construct the conditional training targets for the SB model as described in Section 3.2 and used in the loss function of Eq. 7.\"\n\nWe will also move some of the general formulation details from Section 3 to the appendix to improve the main manuscript's flow. To provide the intuition the reviewer requested, we will add a new figure to Sec 4.1 showing the learned transport process on a 2D toy example (e.g., translating from a two-moons distribution to an 8-Gaussians distribution). This will visually illustrate the latent evolution concept that underpins our method.\n\n> *Q1 & Q2*: Role of Grasp Pose $g_s$ and Encoding Input\n\nThis is a great catch. The $o_\\mathrm{hand}$ in Figure 2 represents the visual observation of the hand, which is used as the input to the VAE encoder. The grasp configuration $g$ is used during VAE training as part of the reconstruction loss in Eq. 8, but it is not an input to the SB model. In Algorithms 2 and 3 (SB training and inference), $g_s$ is not used. The process is conditioned only on the encoded visual observation $o_s$. We will correct the algorithms to remove $g_s$ from the requirements for Latent SB training and inference to avoid confusion.\n\n> *Q3*: Metric on SO(3).\n\nWe apologize for the lack of clarity. We use the squared Frobenius norm between the two rotation matrices in SO(3). The 6D continuous representation is first converted to a $3\\times 3$ matrix representation via Gram-Schmidt orthogonalization. The term is actually $\\left\\lVert R_{\\mathrm{source}} - R_{\\mathrm{target}} \\right\\rVert^2_F$ in Eq. 9. We will add this explicit definition to the paper.\n\n> *Q4*: Are the generated grasping poses validated in a physics simulator?\n\nYes. As detailed in our response to W1, all grasps are rigorously tested for stability in the IsaacGym physics simulator using a 6-axis perturbation protocol.\n\n> *L1*: Thorough discussion and analysis of the experimental outcomes.\n\nWe agree that a more thorough analysis would strengthen the paper. We will add the following discussion to Section 5 to better interpret the results from Table 1:\n\n\"Our results in Table 1 reveal a key trade-off between the different physics-informed objectives. The Jacobian-based cost yields the highest mean success rate (67.45%), suggesting it is most effective at capturing the kinematic relationship for producing stable grasps. However, the GWH and Contact costs achieve superior functional alignment, measured by 6D GWH IoU (14.63% and 14.54%, respectively). This indicates that directly optimizing for force-exertion capabilities (GWH) or contact patterns (Contact) is more effective for transferring the grasp's underlying mechanical intent, even if this sometimes results in a slightly lower stability score compared to a pure manipulability-based objective (Jacobian).\"\n\n#### Reference:\n[1] Li et al., \"Gendexgrasp: Generalizable dexterous grasping.\" ICRA 2023.\n\n[2] Qin et al., \"Anyteleop: A general vision-based dexterous robot arm-hand teleoperation system.\" RSS 2023.\n\n[3] Yuan et al., \"Cross-embodiment dexterous grasping with reinforcement learning.\" ICLR 2025.\n\n[4] Khargonkar et al., \"RobotFingerPrint: Unified Gripper Coordinate Space for Multi-Gripper Grasp Synthesis and Transfer.\" arXiv 2024."}, {"review_id": "xq4g5y2Oys", "reviewer": "Reviewer_4u79", "summary": "This paper addresses the problem of transferring successful grasps from one robot hand to another based on the well-known Simulation-Free Schrödinger Bridges. The method first encodes grasps from each hand into a shared latent space, then uses the Schrödinger Bridge to model the optimal transport between the two latent distributions. Extensive experiments show that the proposed approach significantly outperforms existing grasp transfer methods.", "questions": "- Would it be possible to include the remaining three transfer settings (A→H, S→H, and A→S)? Including these would make the evaluation more completed and reduce potential bias.", "limitations": "Yes.", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 3, "significance": 4, "originality": 3, "strengths_and_weaknesses": "**Strengths:**\n- Overall, this is a well-written and insightful paper that addresses the long-standing challenge of transferring dexterous grasp.\n\n- The use of Simulation-Free Schrödinger Bridges for transferring grasp is both novel and well-motivated.\n\n- Experiments on the MultiGripperGrasp dataset demonstrate substantial improvements over state-of-the-art methods.\n\n- The ablation studies (Tables 1–3) further validate the effectiveness of the proposed optimal transport cost design.\n\n**Weaknesses:**\n\nI have no major concerns about the paper. However, here are some suggestions to improve clarity and completeness:\n-  *Lack of evaluation of the VAE*. Although the VAE is used primarily as a means to encode grasps across different robot hands, its performance should still be evaluated, for instance, reconstruction quality. Additionally, some visualization of the latent space trajectories during the Simulation-Free Schrödinger Bridge process would help further understand the proposed solution.\n- *Concerns over presentation.* While the paper is generally well-written, I find Sections 3.1 and 3.2 to be somewhat redundant, as they closely follow the original Simulation-Free Schrödinger Bridges paper [78]. These sections could be reduced or moved to the appendix. In contrast, the core technical contribution—modeling the Schrödinger Bridge between latent grasp spaces via $v_\\theta(t, z)$ and $s_\\theta(t, z)$—is essential to the paper but is currently under-explained. I recommend moving this part to the main text to better clarity.", "was_revised": true, "final_justification": "My concerns have been addressed. I encourage the authors to consider and address all reviewers' feedback in the final version. I maintain my positive rating.", "rebuttal": "We sincerely thank the reviewer for their time and insightful feedback. We are encouraged that the reviewer found our manuscript \"insightful\" and our method \"novel and well-motivated.\" We address each point below.\n\n> *W1*: On VAE Evaluation and Latent Space Visualization.\n\nThank you for these concrete suggestions to improve the paper's completeness.\n\n**VAE Evaluation**\n\nWe agree that an evaluation of the VAE is important. We have conducted an additional ablation study to validate our design choices. We compare our full VAE against three alternatives:\n- A **PointNet VAE** baseline based on [1] that reconstructs the hand point cloud via Chamfer distance and decodes hand parameters in a separate branch.\n- **Ours w/o Mesh Loss**: Our VAE trained only on the hand parameter reconstruction loss, without the FK layer and mesh vertex loss.\n- **Ours w/o Param Loss**: Our VAE trained only on the mesh vertex loss, without the direct parameter loss.\n\nWe evaluate performance using the Hand Parameters L2 Error on a held-out set of objects. We choose this metric for evaluating reconstruction quality because our VAE ultimately decodes the hand parameters. As shown in the table below, our proposed VAE architecture significantly outperforms all alternatives.\n\n**Table 1: Evaluation for VAE: Hand Parameters L2 Error**\n|                     | Allegro | Shadow | Human  |\n|---------------------|---------|--------|--------|\n| PointNet VAE        | 0.1965  | 0.2001 | 0.2468 |\n| Ours w/o Mesh Loss  | 0.0967  | 0.0933 | 0.1270 |\n| Ours w/o Param Loss | 0.0439  | 0.0441 | 0.0534 |\n| Ours                | **0.0335**  | **0.0286** | **0.0523** |\n\nOur analysis indicates that the PointNet VAE struggles because the Chamfer distance loss is often indiscriminative, as evidenced by many works [1]. It can achieve a low value even when the reconstructed grasp pose is incorrect but has large overlapping regions. Ablating the mesh loss harms performance on fine-grained details, while ablating the parameter loss can lead to memorization issues given the high capacity of the latent space, as the size of the hand configuration space (typically ~20) is relatively small compared to the size of the latent space (e.g., 768 in our case). We will include this table and analysis in the appendix of the revised manuscript.\n\n**Latent Trajectory Visualization**\n\nThis is an excellent idea. Direct visualization of the latent trajectory by decoding intermediate points (i.e., for $t$ between 0 and 1) is unfortunately not straightforward. While the latent space is shared, the VAE decoder is hand-specific due to the use of the forward kinematics (FK) layer. Decoding an intermediate latent $z_t$ would be ill-defined, as it is unclear which hand's FK layer should be used for visualization.\n\nHowever, to provide the intuition the reviewer requested, we will add a new figure to Section 4 showing the learned transport process on a 2D toy example (e.g., translating from a two-moons distribution to an 8-Gaussians distribution). This will visually illustrate the latent evolution concept that underpins our method.\n\n> *W2*: Presentation of core technical contribution.\n\nWe appreciate this valuable feedback on improving the paper's structure and clarity. We will implement the following changes:\n1. We will streamline Sections 3.1 and 3.2, moving the general background on Schrödinger Bridges (SB) and the derivation of the SF$^2$M to the appendix. We will retain only the key equations and concepts in the main text that are directly referenced in our methodology (e.g., the entropic OT plan and the final conditional loss function).\n2. We will use the freed-up space to expand Section 4.1, providing a more detailed explanation of our core technical contribution: modeling the SB between latent grasp spaces. This new text will elaborate on how the neural networks $v_{\\theta}(t,z)$ and $s_{\\theta}(t,z)$ approximate the conditional flow and score, how they are trained using paired samples drawn from the OT plan, and how they are used at inference time to evolve a source latent code to a target one.\n3. The new 2D visualization figure mentioned above will be included in this revised section to make the explanation more intuitive.\n\n> *Q1*: Remaining three transfer settings (A→H, S→H, and A→S)\n\nYes, this is a great suggestion to make our evaluation more comprehensive. We have run experiments on the remaining three transfer settings: Allegro→Human (A→H), Shadow→Human (S→H), and Allegro→Shadow (A→S).\n\nWe must note a technical limitation: we were unable to report the *IsaacGym success rate* for settings where the target is the human hand (A→H and S→H). This is because our human hand model is an articulated version of the MANO model [2] with non-watertight link meshes, which causes instability in the IsaacGym simulator. Porting our evaluation to a simulator capable of handling such assets (e.g., IsaacSim) is beyond the current scope of this work and is planned for future development.\n\nHowever, we are able to report the success rate for A→S and the other metrics (Diversity, 6D GWH IoU) for all three new settings. The results are presented below.\n\n***Table 2: Comparison on Success Rate (%)↑***\n|     | RobotFingerPrint | Diffusion | Ours (Contact OT) | Ours (GWH OT) |\n|-----|------------------|-----------|-------------------|---------------|\n| A→S | 30.27            | 33.96     | ***38.00***             | **41.49**         |\n\n***Table 3: Comparison on Diversity (rad)↑***\n|                   | A→H   | S→H   | A→S   | Mean  |\n|-------------------|-------|-------|-------|-------|\n| RobotFingerPrint  | 0.196 | 0.180 | 0.182 | 0.186 |\n| Diffusion         | 0.283 | 0.298 | ***0.207*** | 0.263 |\n| Ours (Contact OT) | **0.317** | **0.332** | **0.212** | **0.287** |\n| Ours (GWH OT)     | ***0.310*** | ***0.327*** | 0.178 | ***0.272*** |\n\n***Table 4: Comparison on 6D GWH IoU (%)↑***\n|                   | A→H  | S→H  | A→S  | Mean |\n|-------------------|------|------|------|------|\n| RobotFingerPrint  | 3.46 | 4.11 | 3.51 | 3.69 |\n| Diffusion         | 10.41 | 11.82 | 8.78 | 10.34 |\n| Ours (Contact OT) | **13.59** | **15.37** | ***8.87*** | **12.61** |\n| Ours (GWH OT)     | ***11.76*** | ***13.30*** | **9.16** | ***11.41*** |\n\nOur method consistently outperforms both baselines in preserving functional intent, achieving significantly higher 6D GWH IoU (Table 4), particularly when transferring to the more complex human hand. We also generate a more diverse set of plausible grasps (Table 3), highlighting the flexibility of our learned transport plan. Finally, in the A→S setting where a direct stability comparison was possible, our method achieved the highest success rate (Table 2), demonstrating superior physical plausibility. These findings show that the advantages of our approach are robust, even in these challenging transfer settings.\n\nWe will add these tables, along with the analysis and corresponding qualitative results, to the appendix to provide a more complete picture of our method's performance.\n\n#### Reference:\n[1] Achlioptas et al., \"Learning representations and generative models for 3d point clouds.\" ICML 2018.\n\n[2] Romero et al., \"Embodied hands: Modeling and capturing hands and bodies together.\" SIGGRAPH ASIA 2017."}]

Author rebuttal:

Meta-review: The paper presents a novel cross-morphology grasp transfer method based on Schrödinger Bridges. Reviewers found the approach both novel and probabilistically principled, though initial concerns were raised about evaluation, clarity, and qualitative results.

Post-rebuttal, these concerns were largely addressed with stronger evaluations, baselines, and metrics. The main remaining issue was the lack of real-world experiments. The AC agrees with the authors that NeurIPS primarily rewards algorithmic contributions, and given the paper does not claim system-level robotics contributions, thorough simulation studies are sufficient. Reviewer Xi3Y also noted contact stability issues and requested a comparison with Dextonomy, but since that work is concurrent (later acknowledged by Reviewer), the AC excluded it from consideration. In comparison to prior baselines, the proposed method already demonstrates superior performance, while some improvement space does remain, as pointed out by Xi3Y.

Overall, the AC finds the method and evaluation sufficient to justify acceptance, and encourages the authors to include the promised revisions and 3D interactive visualizations to better highlight grasping quality.
Decision: Accept (poster)