DAGDiff: Dual-Arm Diffusion for Grasp Generation

• DAGDiff is an end-to-end diffusion framework that generates dual-arm grasp pairs directly in the combined SE(3)×SE(3) space.
• It employs an energy-based score formulation with classifier-guided force-closure and collision heads to ensure both stability and physical validity.
• Evaluations show improved grasp success and reduced collisions compared to baselines, making it significant for complex dual-arm manipulations.

DAGDiff is an end-to-end diffusion framework for dual-arm grasp generation that maps an object point cloud $P \in \mathbb{R}^{n \times 3}$ to a pair of parallel-jaw grasps $H=(H_1,H_2)\in SE(3)\times SE(3)$. Its central design choice is to generate grasp pairs directly in the joint pose space, rather than composing two independently proposed single-arm grasps, and to steer denoising with geometry-, stability-, and collision-aware guidance so that the resulting pair is physically valid and force-closure compliant (Karim et al., 25 Sep 2025).

1. Problem formulation and conceptual scope

DAGDiff addresses dual-arm manipulation of large or geometrically complex objects such as monitors, buckets, trays, chairs, or cookware. In this setting, the goal is not merely to find two individually plausible grasps. The pair must jointly satisfy dual-arm force closure, proper contact geometry, and collision avoidance, while also generalizing to previously unseen objects from point-cloud input alone (Karim et al., 25 Sep 2025).

The method is motivated by two limitations in earlier dual-arm pipelines. First, many prior systems effectively decompose the task into two single-arm grasp proposals and then combine them, often by selecting two “farthest” object regions or two semantic parts. Second, several methods rely on region priors, heuristics, or semantic part reasoning, including VLM-based part identification and affordance pipelines. DAGDiff argues that these strategies do not model the coupled nature of dual-arm stability: two individually good grasps may still form an unstable or colliding pair (Karim et al., 25 Sep 2025).

A common misconception is to interpret DAGDiff as a post hoc scoring or reranking method layered on top of conventional single-arm proposals. In the paper’s formulation, it is instead a paired-space generative model: the object-conditioned diffusion process directly denoises in $SE(3)\times SE(3)$, so opposite-side placement, compatible relative orientation, and force-balancing configurations are represented inside the generative state itself (Karim et al., 25 Sep 2025).

2. Paired-pose representation and diffusion process

DAGDiff represents a dual-arm grasp pair by mapping the two rigid poses into a 12-dimensional Lie-algebra coordinate system. The dual-arm logarithmic map is defined as

$$v=\operatorname{Logmap}_2(H):=\operatorname{Logmap}(H_1)\oplus \operatorname{Logmap}(H_2)\in\mathbb{R}^{12},$$

with inverse

$$H=\operatorname{Expmap}_2(v):=\left(\operatorname{Expmap}(v_{[:6]}),\operatorname{Expmap}(v_{[6:]})\right).$$

This converts diffusion over paired poses into diffusion over a Euclidean tangent-space representation (Karim et al., 25 Sep 2025).

The forward corruption process perturbs a ground-truth grasp pair by Gaussian noise in this 12D space: $$\tilde{H}_t=\operatorname{Expmap}_2\!\left(\operatorname{Logmap}_2(H)+\epsilon_t\right),\qquad \epsilon_t\sim\mathcal N(0,\sigma_t^2 I_{12}).$$ The model uses an energy-based score formulation rather than a DDPM-style direct noise-prediction parameterization. The score is

$s(H,P,t)=\nabla_H \log p_t(H\mid P),$

and a learned energy head defines

$s_\alpha(H,P,t)=-\nabla_H E_\alpha(H,P,t).$

This gives a denoising vector field and a scalar energy that can also rank grasps (Karim et al., 25 Sep 2025).

Inference follows a Langevin-style reverse update: $$H_{t-1}=\operatorname{Expmap}_2\!\left(\frac{\eta_t^2}{2}\,s_\alpha(H_t,P,t)+\eta_t\epsilon\right)H_t, \qquad \epsilon\sim\mathcal N(0,I_{12}).$$ Training uses an $L_1$ score-matching objective,

$H=(H_1,H_2)\in SE(3)\times SE(3)$0

This formulation places correlation structure between the two grippers inside the learned score field itself, rather than deferring dual-arm compatibility to a later combinatorial stage (Karim et al., 25 Sep 2025).

3. Guidance by geometry, force closure, and collision

The distinctive mechanism in DAGDiff is classifier-guided physical steering during reverse diffusion. The base energy model provides geometry-aware denoising, but two additional heads inject explicit preferences for stable and collision-free grasps (Karim et al., 25 Sep 2025).

The force-closure head is defined as

$H=(H_1,H_2)\in SE(3)\times SE(3)$1

where $H=(H_1,H_2)\in SE(3)\times SE(3)$2 indicates that the dual-arm grasp pair satisfies force closure. It is trained with binary cross entropy,

$H=(H_1,H_2)\in SE(3)\times SE(3)$3

At inference time, its gradient

$H=(H_1,H_2)\in SE(3)\times SE(3)$4

is added to the reverse-time score so that denoising moves toward regions of paired-grasp space with higher predicted stability (Karim et al., 25 Sep 2025).

The collision head predicts grasp-object collision probability: $H=(H_1,H_2)\in SE(3)\times SE(3)$5 with training loss

$H=(H_1,H_2)\in SE(3)\times SE(3)$6

Its inference-time contribution is

$H=(H_1,H_2)\in SE(3)\times SE(3)$7

which pushes the sample away from predicted interpenetration (Karim et al., 25 Sep 2025).

The complete guided score is

$H=(H_1,H_2)\in SE(3)\times SE(3)$8

Collision guidance is activated only late in denoising; in the reported setup the total denoising length is $H=(H_1,H_2)\in SE(3)\times SE(3)$9, and the last 50 steps are reserved for collision refinement (Karim et al., 25 Sep 2025).

The paper also emphasizes that collision handling is not performed by directly optimizing predicted SDF values. Although the network predicts SDFs of query points for geometric supervision, those SDF predictions are not used directly for collision refinement. This suggests that DAGDiff treats collision avoidance as a learned classification-and-guidance problem rather than a direct differentiable geometry-penalty problem (Karim et al., 25 Sep 2025).

4. Network architecture and training pipeline

The object encoder begins from a point cloud $SE(3)\times SE(3)$0. DAGDiff uses VN-PointNet to extract $SE(3)\times SE(3)$1-equivariant per-point features, then applies multi-plane projections and a U-Net backbone to produce dense planar feature maps. A fixed query point cloud

$SE(3)\times SE(3)$2

is transformed by the current dual-arm grasp pose to define local grasp-conditioned query regions. Features at the projected query locations are sampled by bilinear interpolation, aggregated, and passed through a feature encoder $SE(3)\times SE(3)$3 conditioned on timestep $SE(3)\times SE(3)$4 (Karim et al., 25 Sep 2025).

The encoder predicts both a latent representation and the SDF of the query points for geometric supervision. The latent representation is then processed by three heads: an energy head $SE(3)\times SE(3)$5, a force-closure head $SE(3)\times SE(3)$6, and a collision head $SE(3)\times SE(3)$7. The total training objective is

$SE(3)\times SE(3)$8

The paper states that the vision encoder, energy head, and FC head are trained jointly, while the collision head is trained afterward, once those components have converged (Karim et al., 25 Sep 2025).

Training data come from DG16M, which contains 4,143 objects and roughly 2,000 positive and negative dual-arm grasps per object, labeled under improved force-closure evaluation. A separate synthetic dataset of colliding and non-colliding grasp pairs is constructed for collision-head training (Karim et al., 25 Sep 2025).

At inference, each object mesh is represented by 1000 sampled points, a batch of dual-arm grasp pairs is randomly initialized, and the reverse process is run for $SE(3)\times SE(3)$9 steps. The paper does not report optimizer, learning rate, batch size, or wall-clock inference time in the visible text, so those details remain unspecified in the published description (Karim et al., 25 Sep 2025).

5. Evaluation methodology and empirical results

DAGDiff is evaluated on three complementary metrics. Force Closure Evaluation (FCE) analytically checks whether a grasp pair can resist arbitrary external wrenches under friction and force constraints. Grasp Success Rate (GSR) measures execution success in Isaac Gym, where the grippers close, gravity is enabled, and success requires lifting the object to a target height while maintaining a stable grasp. Grasp Collision Rate (GCR) measures the fraction of generated grasps whose final pose intersects the object geometry (Karim et al., 25 Sep 2025).

On the held-out DG16M test split of 400 unseen objects, DAGDiff reports 60.1% FCE, 72.5% GSR, and 15.1% GCR. The paper characterizes this as roughly twice the stability and success of prior methods, with collisions reduced by more than half relative to baselines, although the extracted text does not reproduce the full baseline table numerically (Karim et al., 25 Sep 2025).

The comparison set spans three baseline families. The farthest-region family includes CGDF and a VCGS adaptation constrained to two selected regions. The VLM-region family includes UniDiffGrasp and RoboBrainGrasp variants using bounding boxes or keypoints. The affordance family includes DualAfford. DAGDiff’s reported advantage is that it does not require heuristic object partitioning or semantic region naming, but instead discovers stable paired placements directly in grasp space (Karim et al., 25 Sep 2025).

The ablations isolate the guidance heads. Removing the force-closure head significantly reduces FCE and GSR. Removing the collision head increases collision rate from

$$v=\operatorname{Logmap}_2(H):=\operatorname{Logmap}(H_1)\oplus \operatorname{Logmap}(H_2)\in\mathbb{R}^{12},$$0

while also harming FCE and GSR. Training the FC head only post hoc, with the backbone frozen, also degrades FCE and GSR, implying that stability information must shape the learned representation rather than being appended only at inference time (Karim et al., 25 Sep 2025).

The real-world evaluation uses a heterogeneous dual-arm system with xArm7 and xArm6 Lite, perceived by two Intel RealSense D455 cameras whose views are fused by ICP. Over 10 trials per object, the reported grasp-and-lift successes are: Tray 6/10, Bucket 8/10, Saucepan 7/10, Frypan 6/10, and Drone 5/10. The main reported failure mode is loss of geometric detail in reconstructed point clouds, leading to incorrect grasp placement (Karim et al., 25 Sep 2025).

6. Interpretation, limitations, and position within diffusion research

DAGDiff’s main technical significance lies in treating dual-arm grasping as direct generation in paired pose space and in injecting physical constraints through gradient guidance rather than heuristic preselection. A plausible implication is that it reframes dual-arm stability as a property of the reverse-time trajectory itself, not merely of a final accept-reject stage (Karim et al., 25 Sep 2025).

The method also clarifies the scope of its physical modeling. The collision formulation primarily concerns gripper-object collision; the paper does not present an explicit treatment of arm-arm collision, arm-environment collision, or closed-chain feasibility. The authors explicitly state that the framework does not account for closed-chain kinematics, assumes complete segmented point clouds, and remains limited by the iterative cost of diffusion inference (Karim et al., 25 Sep 2025).

Within the broader diffusion literature, DAGDiff belongs to the family of methods that steer denoising with auxiliary gradients. A plausible comparison is to classifier-guided unrestricted adversarial sampling, where reverse diffusion is nudged by gradients of a target model at each step (Dai et al., 2023). DAGDiff applies the same general principle to robotic grasp synthesis, but its guidance signals are physical—force closure and collision—rather than semantic or adversarial (Karim et al., 25 Sep 2025).

Despite its name, DAGDiff in this usage is unrelated to directed acyclic graph methods such as "LayerDAG" (Li et al., 2024) or "DAGGER" (Ramdas et al., 2017). Here, “DAG” denotes Dual-Arm Grasp, and the method’s subject is robotic manipulation rather than graph generation or DAG-structured inference.