# MDNF: Multi-Diffusion-Nets for Neural Fields on Meshes

arXiv: https://arxiv.org/abs/2409.03034 · HTML: https://mlsanity.com/paper/2409.03034/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 41 references that are in the map.
- First posted on arXiv 4 Sep 2024.

## Builds on (most cited first, 25 of 25)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [TensoRF: Tensorial Radiance Fields](https://mlsanity.com/paper/2203.09517/) (2022)
- [Alias-Free Generative Adversarial Networks](https://mlsanity.com/paper/2106.12423/) (2021)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [Neural Geometric Level of Detail: Real-time Rendering with Implicit 3D Shapes](https://mlsanity.com/paper/2101.10994/) (2021)
- [Text2Mesh: Text-Driven Neural Stylization for Meshes](https://mlsanity.com/paper/2112.03221/) (2021)
- [Texture Fields: Learning Texture Representations in Function Space](https://mlsanity.com/paper/1905.07259/) (2019)
- [ARCH++: Animation-Ready Clothed Human Reconstruction Revisited](https://mlsanity.com/paper/2108.07845/) (2021)
- [DiffusionNet: Discretization Agnostic Learning on Surfaces](https://mlsanity.com/paper/2012.00888/) (2020)
- [NASA: Neural Articulated Shape Approximation](https://mlsanity.com/paper/1912.03207/) (2019)
- [NeuMesh: Learning Disentangled Neural Mesh-based Implicit Field for Geometry and Texture Editing](https://mlsanity.com/paper/2207.11911/) (2022)
- [NeuTex: Neural Texture Mapping for Volumetric Neural Rendering](https://mlsanity.com/paper/2103.00762/) (2021)
- [MeshCNN: A Network with an Edge](https://mlsanity.com/paper/1809.05910/) (2018)
- [Primal-Dual Mesh Convolutional Neural Networks](https://mlsanity.com/paper/2010.12455/) (2020)
- [CNNs on Surfaces using Rotation-Equivariant Features](https://mlsanity.com/paper/2006.01570/) (2020)
- [Generalised Implicit Neural Representations](https://mlsanity.com/paper/2205.15674/) (2022)
- [Neural Fourier Filter Bank](https://mlsanity.com/paper/2212.01735/) (2022)
- [NSF: Neural Surface Fields for Human Modeling from Monocular Depth](https://mlsanity.com/paper/2308.14847/) (2023)
- [Intrinsic Neural Fields: Learning Functions on Manifolds](https://mlsanity.com/paper/2203.07967/) (2022)
- [BANF: Band-limited Neural Fields for Levels of Detail Reconstruction](https://mlsanity.com/paper/2404.13024/) (2024)

## Abstract (arXiv)

We propose a novel framework for representing neural fields on triangle meshes that is multi-resolution across both spatial and frequency domains. Inspired by the Neural Fourier Filter Bank (NFFB), our architecture decomposes the spatial and frequency domains by associating finer spatial resolution levels with higher frequency bands, while coarser resolutions are mapped to lower frequencies. To achieve geometry-aware spatial decomposition we leverage multiple DiffusionNet components, each associated with a different spatial resolution level. Subsequently, we apply a Fourier feature mapping to encourage finer resolution levels to be associated with higher frequencies. The final signal is composed in a wavelet-inspired manner using a sine-activated MLP, aggregating higher-frequency signals on top of lower-frequency ones. Our architecture attains high accuracy in learning complex neural fields and is robust to discontinuities, exponential scale variations of the target field, and mesh modification. We demonstrate the effectiveness of our approach through its application to diverse neural fields, such as synthetic RGB functions, UV texture coordinates, and vertex normals, illustrating different challenges. To validate our method, we compare its performance against two alternatives, showcasing the advantages of our multi-resolution architecture.