Source-linked AI summary
HyperDiffusion: Generating Implicit Neural Fields with Weight-Space Diffusion
Ziya Erkoç, Fangchang Ma, Qi Shan, Matthias Nießner, Angela Dai
TL;DR
Implicit neural fields are compact and high-fidelity but lack regular grids for direct generative modeling. HyperDiffusion fits MLPs to individual samples and learns diffusion directly in their weight space, generating new fields for 3D shapes and 4D animations. The paper reports high-fidelity synthesis across both settings, while noting limitations in surface awareness and large-scale multi-MLP scenes.
Problem
Implicit neural fields provide compact, high-fidelity representations, but their lack of explicit grid structure makes direct generative modeling challenging.
Method
HyperDiffusion first optimizes one MLP per data sample, then trains a diffusion model directly on the flattened optimized MLP weights.
Results
HyperDiffusion generates high-fidelity neural-field representations for 3D shapes and 4D deforming-shape animations within one unified framework.
Takeaways & Limitations
Direct diffusion over optimized neural-field weights supports unconditional, dimension-agnostic generation of novel high-fidelity implicit surfaces.
Takeaways & Limitations
The diffusion process currently operates only on optimized MLP parameters without surface-reconstruction knowledge, and the method uses individual MLPs rather than grids of MLPs for large-scale scenes.
Abstract
from arXiv · showhide
Implicit neural fields, typically encoded by a multilayer perceptron (MLP) that maps from coordinates (e.g., xyz) to signals (e.g., signed distances), have shown remarkable promise as a high-fidelity and compact representation. However, the lack of a regular and explicit grid structure also makes it challenging to apply generative modeling directly on implicit neural fields in order to synthesize new data. To this end, we propose HyperDiffusion, a novel approach for unconditional generative modeling of implicit neural fields. HyperDiffusion operates directly on MLP weights and generates new neural implicit fields encoded by synthesized MLP parameters. Specifically, a collection of MLPs is first optimized to faithfully represent individual data samples. Subsequently, a diffusion process is trained in this MLP weight space to model the underlying distribution of neural implicit fields. HyperDiffusion enables diffusion modeling over a implicit, compact, and yet high-fidelity representation of complex signals across 3D shapes and 4D mesh animations within one single unified framework.
1. Introduction
Implicit neural fields provide compact, high-fidelity, arbitrary-resolution representations, but their lack of explicit grids complicates generative modeling. HyperDiffusion addresses this by applying diffusion directly to optimized MLP weights for unconditional 3D and 4D surface generation.
- Representations: Implicit neural fields map coordinates to signals through MLPs, efficiently representing sparse high-dimensional data in compact weight spaces.Their continuous mappings support arbitrary-resolution sampling and mesh reconstruction without explicit point, mesh, or voxel grids.
- Motivation: HyperDiffusion models optimized neural-field MLP weights directly instead of raw surfaces, explicit representations, or learned latent manifolds.The approach exploits the compactness of optimized MLPs for high-dimensional 3D and 4D surfaces.
- Approach: HyperDiffusion applies diffusion to optimized MLP weights and uses the same dimension-agnostic method for unconditional 3D and 4D surface generation.A transformer-based network models the diffusion process in the low-dimensional weight space.
- Contribution: The paper presents diffusion modeling over neural-field MLP weights as a new paradigm for high-dimensional generative modeling.The contribution targets high-fidelity generation across both 3D shapes and 4D surfaces.
2. Related Work
Related work spans neural-field representations, GANs, diffusion models, and cross-dimensional generative modeling. HyperDiffusion differs by modeling optimized neural-field weights directly rather than relying on a separately learned latent manifold.
- Neural Implicit Fields: Neural-field methods represent geometry, appearance, and higher-order signals with coordinate-based MLPs, including DeepSDF and NeRF.These representations support high-fidelity 3D geometry and view synthesis.
- Generative Models: GANs have been applied to 3D generation using representations such as radiance-field MLPs, tri-planes, and multiplane images.The cited approaches adapt adversarial generation to different underlying 3D representations.
- Latent Diffusion: Latent neural-field diffusion methods require a high-quality learned latent manifold, whereas HyperDiffusion operates on per-instance optimized neural-field representations.The paper frames optimized weights as inherently high-quality representations that can be fit closely to each instance.
- Cross-Modality Diffusion: Cross-modality work seeks unified diffusion across dimensions and modalities, while HyperDiffusion offers an alternative based on direct MLP-weight generation.The related approaches include Functa, GEM, GASP, and explicit-field diffusion.
3. Method Overview
HyperDiffusion uses a two-phase pipeline: fit one MLP per training instance, then diffuse over the resulting flattened weights. Reverse diffusion synthesizes new MLPs that encode neural implicit fields across signal dimensionalities.
- Overview: HyperDiffusion is an unconditional generative model that operates directly on MLP weights to synthesize new implicit neural fields.Its training paradigm consists of per-instance MLP optimization followed by diffusion modeling in weight space.
- MLP Overfitting: The first phase optimizes each MLP to faithfully represent a training sample, producing accurate neural occupancy fields.The optimized weights are flattened into one-dimensional vectors and used as ground-truth signals for diffusion.
- Weight-Space Diffusion: The second phase trains a diffusion network on flattened optimized MLP weights without assumptions about the underlying signal dimensionality.Reverse diffusion starts from random noise and synthesizes valid MLP weights corresponding to new neural implicit fields.
- Decoding: For 3D and 4D generation, synthesized neural fields can be converted into meshes with Marching Cubes.This provides a route from generated MLP parameters to visualizable surfaces.
4. Per-Sample MLP Overfitting
HyperDiffusion first optimizes one MLP per training sample to obtain faithful neural-field representations, then uses these optimized weights as diffusion targets. Per-sample optimization avoids parameter sharing and preserves high-fidelity representations across 3D shapes and 4D animations.
- The MLP maps spatial locations to occupancy values, with parameters θ_i comprising its weights and biases.
- Binary cross entropy trains each MLP to fit the sample’s ground-truth occupancy field.
- Because optimized MLPs provide ground truth for diffusion, their ability to model high-fidelity shapes is crucial.
- Per-sample optimization removes the need for autoencoding or auto-decoding networks and avoids parameter sharing across dataset instances.
- The same occupancy-field MLP design supports both 3D shapes and 4D animations, with positional encoding adapted to input dimensionality.
- Consistent initialization starts later MLP optimizations from the weights optimized for the first training sample, encouraging a smooth weight-space diffusion process.
5. MLP Weight-Space Diffusion
HyperDiffusion models flattened optimized MLP weights with a transformer-based diffusion process, using the same formulation for neural fields representing 3D and 4D shapes. DDIM sampling iteratively denoises random weights into MLPs representing valid shapes.
- Optimized MLP weights and biases are flattened into vectors and modeled by a transformer denoising network.
- The weight-vector formulation is dimension-agnostic, enabling generative modeling of neural fields for both 3D and 4D shapes.
- The denoising visualization spans 0 steps of random MLP weights to 500 steps corresponding to a fully denoised shape.
- During training, Gaussian noise is applied to weight vectors, and the transformer predicts denoised weights using an MSE objective.
- DDIM sampling progressively transforms random MLP weights into denoised weights that represent valid 3D surfaces.
- The implementation flattens approximately 36k parameters from each 3-layer, 128-dimensional MLP for diffusion.
6. Results
HyperDiffusion is evaluated for unconditional 3D shape and 4D animation generation against voxel and point-cloud baselines, with ablations examining initialization and positional encoding. Results show improved 3D metrics, detailed and temporally consistent 4D outputs, novel shapes, and benefits from consistent initialization and positional encoding.
- Evaluation setup: HyperDiffusion is evaluated on ShapeNet airplanes, cars, and chairs, plus 16-frame animal animations from DeformingThings4D, using non-overlapping train, validation, and test partitions.The 3D categories contain 3533, 6778, and 4045 shapes; the 4D dataset contains 1772 sequences.
- Evaluation metrics: The evaluation uses MMD, Coverage, 1-NNA, and perceptual FPD, with lower MMD and FPD preferred, higher COV preferred, and 50% optimal for 1-NNA.Point-based measures use 2048 sampled points, including points sampled from extracted mesh surfaces for HyperDiffusion.
- 3D generation: HyperDiffusion improves over voxel, PVD, and DPC baselines across shape categories and evaluation metrics except MMD, while particularly improving perceptual FPD and preserving high-resolution detail.The comparison attributes MMD’s exception to its reported insensitivity to low-quality results.
- Ablations: Consistent initialization from one optimized MLP moderately improves 3D generation, especially FPD, while removing positional encoding noticeably degrades performance.The authors attribute the initialization benefit to keeping MLP weights relatively close to one another.
- Novel shape synthesis: HyperDiffusion generates novel 3D shapes that are not training-set copies, supporting generalization within the underlying distribution of 3D meshes.Novelty is assessed by comparing generated shapes with their top-three Chamfer-distance nearest neighbors from the training set.
- 4D generation: For 4D generation, HyperDiffusion produces more detailed, higher-quality, and temporally consistent animation sequences than voxel diffusion while preserving shape integrity during meaningful actions.The representation models deforming 3D shapes over time and avoids the voxel baseline’s rapid quartic dimensionality growth.
7. Limitations
HyperDiffusion has limitations related to surface awareness and scalability. Its diffusion process operates on individual optimized MLPs rather than reconstructed surfaces or collections of MLPs.
- The diffusion process operates only on optimized MLP parameters and lacks knowledge of the represented surface.A naive secondary reconstruction loss did not improve performance, while a more sophisticated surface-aware formulation may help.
- The method models datasets of individual MLPs, whereas large-scale neural implicit environments typically use MLPs arranged on a grid for greater spatial capacity.Modeling multiple MLPs could extend the approach to larger-scale scene surfaces.
8. Conclusion
HyperDiffusion models optimized neural-field MLP weights with diffusion to generate high-fidelity 3D shapes and 4D deforming-shape animations. The authors present this as a first step toward generative modeling with alternative representations for complex data.
- HyperDiffusion optimizes neural-field MLPs on individual training samples, then trains diffusion on their weights to synthesize new neural fields.The synthesized weights decode into high-fidelity shape surfaces.
- The framework generates high-fidelity surfaces for both 3D shapes and 4D animation sequences of deforming shapes.
- The authors characterize HyperDiffusion as a first step toward generative modeling of high-dimensional, complex data through alternative representations.
9. Appendix
Additional results show unconditional generation across 3D shapes and 4D animations, while the appendix describes implementation details and reports clean, smooth generated meshes usable in design software and game engines.
- Additional qualitative results: Additional unconditional results demonstrate diverse generated shape sets in both 3D and 4D settings.
- Additional qualitative results: Generated meshes are described as clean and smooth, with direct usability in 3D design software and game engines.
- Implementation: The MLP uses three hidden layers with 256 neurons each, and its weights are flattened into a 1D vector for transformer processing.
- Implementation: The transformer uses 12 layers, 16 self-attention heads, and 500 diffusion timesteps with a linear noise scheduler.
- Implementation: Generated 3D results are deduplicated by sampling twice the required amount and removing shapes that are very close to one another.