DefFusionNet: Diffusion-Based Shape Servoing

• DefFusionNet is a neural architecture that uses a diffusion-based probabilistic model to capture multimodal distributions of goal shapes for deformable object manipulation.
• It leverages a conditional diffusion process and VAE encoding to overcome deterministic averaging, ensuring distinct and realistic outcomes.
• Empirical applications in surgical robotics and manufacturing demonstrate improved collision avoidance, data efficiency, and robust recovery of valid goal configurations.

DefFusionNet is a neural architecture for deformable object manipulation that advances shape servoing by generating diverse, multimodal distributions over valid goal shapes using a diffusion-based probabilistic model. Unlike prior solutions reliant on deterministic prediction—which collapse multiple viable end states into a single, often invalid, average—DefFusionNet captures the full spectrum of possible goals, producing distinct and realistic shape outcomes in complex, real-world settings such as surgical robotics and manufacturing automation (2506.18779).

1. Motivation and Context

Shape servoing for deformable objects requires specifying a “goal shape” that a robot manipulates an object toward. Conventional strategies for goal acquisition, such as manual demonstration or domain-specific engineering, are often unscalable and impractical. DefGoalNet introduced data-driven goal learning from demonstrations but imposed a strong unimodal constraint: if demonstrations are diverse, the output converges to their mean, producing ambiguous or physically invalid goals. DefFusionNet remedies this by learning the full distribution $p_\theta(g \mid c, P)$ over goals $g$ given current object state $c$ and contextual input $P$, allowing for robust operation in tasks where solutions are inherently multimodal (e.g., surgical retraction with multiple safe trajectories).

2. Diffusion-Based Goal Shape Generation

DefFusionNet models the distribution over goal shapes using a conditional diffusion process, inspired by advances in image generation. The methodology is as follows:

• Forward Process: The ground-truth goal point cloud $g^{(0)}$ is gradually noised over $T$ steps to produce $g^{(T)}$ via:

$$x_i^{(t)} = \sqrt{\bar{\alpha}_t} x_i^{(0)} + \sqrt{1 - \bar{\alpha}_t} \varepsilon,\quad \bar{\alpha}_t = \prod_{s=1}^t \alpha_s$$

where $x_i$ is a point in the point cloud and $\varepsilon$ is Gaussian noise.

• Reverse Process: A neural noise predictor $\mu_\theta$ conditions on the noisy goal shape, contextual input, and a point-wise VAE encoding of the target goal:

$$p_\theta(x_i^{(t-1)} | x_i^{(t)}, c, z) = \mathcal{N}(x_i^{(t-1)} ; \mu_\theta(x_i^{(t)}, t, c, z), \beta_t I)$$

with $z$ a latent goal encoding obtained by encoding $g$ into $\mu + \sigma \odot \xi$ with $\xi \sim \mathcal{N}(0, I)$. The context encoding is typically extracted from both the current and goal point clouds using PointNet-based architectures.

• Conditional Sampling: At test time, sampling from the learned model yields distinct, valid goal shapes reflective of the underlying multimodal distribution demonstrated in the training data, with no averaging artifact.
• Gating Mechanism: Integration of context into each denoising step uses a feature gating operation:

$\varepsilon' = h(g^{(t)}) \odot \phi_g + \phi_b$

where $\phi_g$ and $\phi_b$ are context-dependent terms learned from $c$ and $P$.

3. Architectural Components

The network is comprised of two principal components:

• Latent Encoder: A variational autoencoder (VAE) encodes goal point clouds into compact latent vectors, capturing diverse modes of the goal distribution.
• Noise Predictor Network: This network leverages context and goal encodings to predict reverse diffusion steps, ultimately generating concrete goal point clouds from noise.

The architecture decouples goal generation (DefFusionNet) from shape control (DeformerNet), allowing for modular, independent optimization.

4. Empirical Applications

DefFusionNet is validated on two domains representing distinct manipulation challenges:

• Surgical Tissue Retraction: The objective is to generate goal shapes that enable safe, collision-free retraction in the presence of obstacles (e.g., surgical tools). When demonstrations include multiple safe retraction directions, the model learns a bimodal distribution, recovering both plausible options. Performance is assessed via collision rate and success percentage (fraction of tissue points placed beyond a surgical reference plane).
• Manufacturing-Oriented Object Packaging: Here, an object must be deformed to fit into a container, with potentially infinite valid configurations (e.g., variable fold angles). DefFusionNet captures this continuous, high-variance distribution and is evaluated by coverage metrics and Chamfer distance relative to the set of successful packing demonstrations.

In both cases, DefFusionNet outperforms deterministic baselines—even when provided with an order of magnitude fewer demonstration samples—producing individually valid, non-averaged goal geometries.

5. Overcoming Deterministic Model Limitations

Traditional models such as DefGoalNet lose fidelity in multimodal tasks, as their outputs converge to an average of all valid solutions, which is often impractical or physically unattainable for the robot. DefFusionNet’s diffusion model inherently supports sampling diverse, distinct solutions due to its probabilistic formulation, side-stepping mode collapse and preserving the integrity of all demonstrated behaviors.

The result is a dramatic improvement in both the quality and diversity of generated goal shapes, with empirical tasks demonstrating that DefFusionNet can recover all valid options present in the demonstrations, rather than an ambiguous weighted average.

6. Evaluation Metrics and Data Efficiency

DefFusionNet is quantitatively assessed using:

• Collision avoidance and success rate for surgical retraction (the ability to reach a target without colliding with anatomical obstacles).
• Coverage and Chamfer distance for packaging tasks (how closely the generated goal matches the ground-truth feasible set).
• Data Efficiency: Experiments show strong performance with minimal demonstrations (as few as 10), indicating high sample efficiency relative to deterministic models.

7. Future Directions

Future research directions include refining the architecture and training procedures to further enhance sample quality, extending applicability to broader classes of deformable object tasks, and developing even more data-efficient learning paradigms. Additional context encoding mechanisms are also proposed, enabling richer scene understanding and increasing deployment flexibility in real-world robotics (2506.18779).

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DefFusionNet thus represents a major advance in deformable object goal generation, enabling robots to flexibly, efficiently, and realistically handle the uncertainty and diversity intrinsic to physical manipulation tasks. Its generative, diffusion-based approach sets a new foundation for shape servoing in domains such as surgical robotics and soft material automation.