Model Architecture
Overview of the proposed method: (a) Given an object point cloud \(P\), our
network
encodes
geometric features into dense feature maps. Next,
randomly initialized dual-arm grasps \(H\) are used to transform a fixed query cloud into query
points, followed by feature sampling through bilinear interpolation. Conditioned on the noise
step \(t\)
these features are passed through \(F_{\theta}\), which predicts the SDF of the query points and
a feature vector.
This vector is then used by three output heads that predict energy \((E_\alpha)\), force-closure
probability \((C_{\beta}^{\text{fc}})\) and
collision probability \((C_{\gamma}^{\text{col}})\), jointly guiding the diffusion process.
(b) At
inference, denoising proceeds from random
intialization \((t=250\)) to refine grasps \((t=0\)). The energy head drives the generative
dynamics, while the force-closure and collision heads bias the generation until stable,
collision-free dual-arm grasps emerge.
\(SE(3) \times SE(3) \longleftrightarrow \mathbb{R}^{12}\)
Denoising in the dual-arm grasp space: Additionally, dual-arm grasp poses are represented as
pairs of rigid-body transformations
in \(SE(3) \times SE(3)\), which are mapped into a \(12\text{D}\) Euclidean space for diffusion and
back.
Each \(SE(3)\) element is
first projected into its \(6\text{D}\) Lie algebra representation via the logarithmic map
\((\operatorname{Logmap_{2}})\), and
concatenated to form a vector in \(\mathbb{R}^{12}\).
The diffusion process is then carried out in this Euclidean space. To obtain valid grasp poses, the exponential map \((\operatorname{Expmap_{2}})\) maps vectors in \(\mathbb{R}^{12}\) back to \(SE(3) \times SE(3)\). This bidirectional mapping enables diffusion while ensuring grasps remain consistent with rigid-body motion.
The diffusion process is then carried out in this Euclidean space. To obtain valid grasp poses, the exponential map \((\operatorname{Expmap_{2}})\) maps vectors in \(\mathbb{R}^{12}\) back to \(SE(3) \times SE(3)\). This bidirectional mapping enables diffusion while ensuring grasps remain consistent with rigid-body motion.
Denoising using Classifier Guidance
Noisy Grasp Pairs
Stable Grasp Pairs
Overview of the denoising process: The above clip shows the joint denoising process step by step.
As the
time progresses, the Energy \((E_\alpha)\) gradually
decreases, which means grasps are moving towards the object and
not just floating in free space. At the same time, the Force-Closure Probability \((C_{\beta}^{\text{fc}})\) steadily
increases,
highlighting how the grasp becomes more stable and reliable over time. Finally, in the later stages of
denoising, colliding grasps are
refined for a small number of iterations using Collision Classifier
\((C_{\gamma}^{\text{col}})\), resulting in dual-arm grasps that are force-closure stable as
well as collision-free.