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3DShape2VecSet: A 3D Shape Representation for Neural Fields and Generative Diffusion Models
Biao Zhang, Jiapeng Tang, Matthias Niessner, Peter Wonka
TL;DR
Existing 3D diffusion systems need a suitable representation for continuous neural fields and varied shape inputs. 3DShape2VecSet encodes shapes as neural fields over a learned set of latent vectors and trains diffusion models in that latent space. The authors report improved shape encoding and generative modeling across unconditional, conditioned, completion, and image-conditioned tasks.
Problem
Adapting diffusion models to 3D requires a suitable shape representation, especially because neural fields are continuous functions and diffusion models often operate on fixed-size data.
Method
3DShape2VecSet uses a learned fixed-size set of latent vectors, transformer-compatible cross-attention, and a two-stage autoencoder-plus-latent-diffusion training strategy.
Results
The method improves 3D shape encoding and generative modeling, including unconditional, category-conditioned, text-conditioned, point-cloud completion, and image-conditioned generation.
Takeaways & Limitations
The representation supports neural-field generation from surface models or point clouds across a broad set of 3D generation and reconstruction applications.
Takeaways & Limitations
The two-stage pipeline increases training time, and the first stage may require retraining when the shape data changes.
Abstract
from arXiv · showhide
We introduce 3DShape2VecSet, a novel shape representation for neural fields designed for generative diffusion models. Our shape representation can encode 3D shapes given as surface models or point clouds, and represents them as neural fields. The concept of neural fields has previously been combined with a global latent vector, a regular grid of latent vectors, or an irregular grid of latent vectors. Our new representation encodes neural fields on top of a set of vectors. We draw from multiple concepts, such as the radial basis function representation and the cross attention and self-attention function, to design a learnable representation that is especially suitable for processing with transformers. Our results show improved performance in 3D shape encoding and 3D shape generative modeling tasks. We demonstrate a wide variety of generative applications: unconditioned generation, category-conditioned generation, text-conditioned generation, point-cloud completion, and image-conditioned generation.
1 INTRODUCTION
3DShape2VecSet addresses the challenge of adapting diffusion models to 3D by learning a compact neural-field representation based on a fixed-size set of latent vectors. The method combines transformer-compatible processing with latent diffusion and improves shape encoding and generation across several applications.
- Adapting diffusion models to 3D requires a suitable shape representation, which is the central focus of this work.
- The method uses learned latent representations and trains in two stages: a variational autoencoder followed by diffusion in latent space.Latent-space encoding is especially useful because diffusion models often require fixed-size data, whereas neural fields are continuous functions.
- 3DShape2VecSet represents shapes with a fixed-size set of latent vectors processed through linear layers and cross-attention to produce neural fields.Unlike representations tied to regular or irregular spatial grids, its latent vectors do not have associated 3D positions.
- The proposed architecture aggregates information from large point clouds using cross-attention and is designed for transformer-based processing.
- The approach improves 3D shape autoencoding, producing high-fidelity reconstructions that include local details.
- Latent-set diffusion improves 3D generation according to FID, KID, FPD, and KPD, supporting unconditional, category-conditioned, text-conditioned, completion, and image-conditioned applications.
2 RELATED WORK
Prior 3D shape work spans voxels, point clouds, neural fields, and several generative-model families. The paper positions diffusion with neural fields as comparatively underexplored, while contrasting coordinate-based representations with its latent-set direction.
- 3D shape representations: Voxel decoders incur cubic computational and memory costs as grid resolution increases, limiting many methods to low-resolution outputs.
- Neural fields: Neural fields represent shapes implicitly through networks that map 3D coordinates to scalar or vector outputs and support arbitrary topologies and infinite resolution.
- Neural fields: Existing neural-field methods use global latents or spatially arranged latents on regular or irregular grids, but coordinate-dependent approaches retain explicit spatial organization.
- Generative models: 3D generative modeling has used GANs, autoregressive models, and other families, whereas diffusion models for 3D shapes remain relatively unexplored.
- Generative models: Point-cloud diffusion can struggle to produce clean manifold surfaces, and combining diffusion models with neural fields remains underexplored.
3 PRELIMINARIES
The preliminaries describe attention as comparing queries with keys and using the resulting coefficients to combine values. Cross-attention operates between two sets, while self-attention uses the same set for both inputs.
- Attention: An attention layer takes queries, keys, and values as inputs, compares queries with keys, and linearly combines the values using the resulting coefficients.
- Cross-attention: In cross-attention, queries are constructed from one input set while keys and values are constructed from another input set.
- Self-attention: Self-attention is obtained by letting the two attention input sets be identical.
4 LATENT REPRESENTATION FOR NEURAL FIELDS
The paper develops a neural-field representation that replaces many spatially anchored points with a compact learned latent set. Its interpolation combines RBF-inspired weighting with cross attention, while transformer operations process and decode the latent information.
- RBF foundation: Radial basis functions represent a continuous function using weighted points whose contributions depend on similarity between a query and each anchor.
- Autoencoding pipeline: The autoencoding pipeline samples a point cloud, encodes it into latent codes, optionally compresses and regularizes them, then uses self-attention and cross-attention for occupancy prediction.
- Motivation: RBF representations may require very many points to retain 3D shape details, motivating a more compact learned neural-field representation.
- Neural-field representation: The proposed representation uses a shared encoder-decoder approach, encoding each shape into a learned latent space before decoding it as a neural field.
- Latent sets: The latent-set design preserves interpolation while eliminating explicit point coordinates and integrating cross attention so the network encodes spatial information.
- Point-cloud encoding: The point-cloud encoder can use either a learnable query set or a downsampled set of input point embeddings.
5 NETWORK ARCHITECTURE FOR SHAPE REPRESENTATION LEARNING
The representation learns neural-field shapes through a set-to-set encoder, optional KL compression, and attention-based decoding. Point-cloud queries aggregate input information into a fixed-size latent set that can be compressed for diffusion.
- Architecture: The variational autoencoder comprises a 3D shape encoder, KL regularization block, and 3D shape decoder.
- Shape encoding: The encoder aggregates potentially large point clouds with a set-to-set network rather than assigning one latent vector per patch.
- Shape encoding: Point queries are obtained by furthest-point subsampling and cross-attending to the full point cloud; the final model uses M=512 and C=512.
- KL regularization: KL regularization projects latent vectors to lower-dimensional means and variances, producing compressed latents with total size M·C0 ≪ M·C.
- Shape decoding: The compressed latents are decoded after FCup restores higher dimensionality, while query interpolation and a fully connected layer produce occupancy values.
6 SHAPE GENERATION
Shape generation diffuses compressed latent sets and denoises them with attention-based set transformers. Conditional information enters through cross-attention, while unconditional generation uses self-attention alone.
- Latent diffusion: The diffusion model operates in the compressed latent bottleneck rather than directly on continuous neural fields.
- Denoising: Its denoising objective uses noise-level conditioning and optional categories, images, partial point clouds, or text.
- Denoising network: The denoising network is a set-to-set function implemented with self-attention and condition-injecting cross-attention blocks.
- Denoising network: For unconditional generation, cross-attention reduces to self-attention; conditional generation uses cross-attention to inject context information.
7 EXPERIMENTAL SETUP
Experiments benchmark ShapeNet-v2 shape reconstruction and generation against representative reconstruction and generative baselines. Evaluation combines reconstruction metrics with image-rendering and 3D feature distances.
- Dataset: ShapeNet-v2 provides 55 categories of man-made objects, with watertight, normalized meshes and dense surface point clouds used for neural-field learning.
- Baselines: Shape autoencoding is compared with OccNet, ConvOccNet, IF-Net, and 3DILG, spanning global, regular-grid, multiscale-grid, and irregular-grid latents.
- Baselines: Generation is compared with PVD, 3DILG, and NeuralWavelet, representing point-cloud diffusion, autoregressive, and frequency-domain diffusion models.
- Evaluation metrics: Reconstruction uses Chamfer distance, volumetric IoU, and F-score; higher is better for IoU and F-score, while lower is better for Chamfer.
- Evaluation metrics: Generation quality is measured with Rendering-FID and Rendering-KID from ten viewpoints, plus FPD and KPD from PointNet++ features of sampled surface points.
8 RESULTS
The experiments report improved reconstruction and generation quality across several applications. Ablations show that point queries and KL-based channel compression provide favorable design choices, while larger latent sets improve reconstruction but increase computation.
- Applications: The study covers autoencoding, unconditional and category-conditioned generation, text conditioning, shape completion, image conditioning, and novelty analysis.
- Shape autoencoding: Point-query shape encoding outperforms learnable queries across all evaluated categories and is used in later experiments.
- Comparison: The representation differs from 3DILG by using learned cross-attention, unpositioned latent sets, and feature-space interpolation.
- Shape autoencoding: The reconstruction metrics improve toward their maximum value of 1 for IoU and F-score, alongside highlighted visual improvements.
- Ablations: Larger M improves reconstruction but increases transformer training time; experiments therefore set M=512 and cannot explore larger values computationally.
- Ablations: Reducing C0 increases compression without greatly reducing reconstruction, while larger C0 can make second-stage diffusion training more difficult.
8.2 Unconditional Shape Generation
The method is evaluated across unconditional, category-conditioned, and point-cloud generation settings, with comparisons spanning surface and point-cloud diffusion baselines. Results indicate strong generation quality, including higher recall in category-conditioned generation and a large margin over PVD.
- The method is compared with Grid-83, PVD, and NeuralWavelet across unconditional, point-cloud, and category-conditioned generation settings.Grid-83 matches AutoSDF's latent grid size, PVD generates point clouds without normals, and NeuralWavelet trains separate models per category.
- For unconditional generation, results are best with C0 = 32 across all reported metrics, while C0 = 64 performs worse.This supports the authors' conjecture that a larger latent size makes training more difficult.
- The method beats PVD by a large margin on point-cloud generation metrics.Surface-FPD and Surface-KPD use a pretrained PointNet++ extractor without normals for the PVD comparison.
- The method achieves significantly better recall than other category-conditioned methods while maintaining high precision.Precision measures similarity to training samples, whereas recall measures the percentage of training data that can be generated.
8.4 Text-conditioned generation
The model demonstrates text-conditioned 3D shape generation and extends latent set diffusion to point-cloud completion and single-view reconstruction. These applications support probabilistic or multi-modal predictions alongside improved reconstruction details.
- Text-conditioned generation: Text-conditioned diffusion generates shapes from text prompts and supports sampling because the model is probabilistic.The authors describe this as the first demonstrated use of diffusion models for text-conditioned 3D shape generation, to their knowledge.
- Point-cloud completion: Latent set diffusion produces more accurate and diverse point-cloud completions than ShapeFormer.The comparison uses a partial point cloud as the conditioning input.
- Single-view reconstruction: Compared with OccNet and IM-Net, latent set diffusion reconstructs more accurate surface details, including long rods and tiny holes.The cited examples concern details that are difficult to recover under single-view occlusion.
- Single-view reconstruction: Latent set diffusion supports multi-modal single-view reconstruction, a property suited to severe occlusions.The method is contrasted with deterministic reconstruction methods.
8.7 Shape novelty analysis
Shape retrieval is used to test whether generated shapes merely overfit the training set. Retrieved-shape visualizations indicate that the model synthesizes new shapes with realistic structures, while training remains costly and requires two stages.
- Novelty analysis: Shape retrieval compares each generated shape with training shapes using Chamfer distance to assess whether generation overfits the training set.The top-1 similar training shape is visualized alongside the generated shape.
- Novelty analysis: Retrieved-shape visualizations show that the model can synthesize new shapes with realistic structures.The generated examples come from category-conditioned generation results.
- Limitations: The method requires two-stage training, and first-stage training is more time-consuming than using manually designed wavelet features.The authors state that the two-stage design improves generation quality but increases training demands.
- Limitations: The first stage may require retraining when the shape data changes, while second-stage diffusion training is also relatively time-consuming.The authors identify speeding up training, especially for diffusion models, as future work.
9 CONCLUSION
The conclusion presents 3DShape2VecSet as a learnable latent-set neural-field representation for diffusion-based 3D shape generation. It accepts meshes and point clouds and supports a broad set of generative applications, with future work targeting scanned-point-cloud reconstruction and content creation.
- Conclusion: 3DShape2VecSet combines radial basis functions, neural-field architectures, variational autoencoding, cross attention, and self-attention.These components are used to design the learnable representation.
- Conclusion: The representation encodes triangle meshes and point clouds as neural fields built on a set of latent vectors.This is the central representation described in the conclusion.
- Conclusion: The model addresses unconditioned, category-conditioned, text-conditioned, point-cloud-completion, and image-conditioned shape generation.The conclusion lists these applications as generative modeling tasks.
- Future work: The authors identify surface reconstruction from scanned point clouds as a future application of the 3DShape2VecSet architecture.They also propose textured 3D model generation for content-creation tasks.