# TFDM: Time-Variant Frequency-Based Point Cloud Diffusion with Mamba

arXiv: https://arxiv.org/abs/2503.13004 · HTML: https://mlsanity.com/paper/2503.13004/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in 3D, point cloud and scene generation, one of 14 directions in Diffusion models.
- Builds on 34 of its 40 references that are in the map.
- First posted on arXiv 17 Mar 2025.

## Placed in

- Diffusion models / [3D, point cloud and scene generation](https://mlsanity.com/diffusion/3d-point-cloud-and-scene-generation/)
- State-space sequence models (S4, Mamba) / [Point clouds, detection and remote sensing](https://mlsanity.com/ssm/point-clouds-detection-and-remote-sensing/)

## Builds on (most cited first, 30 of 34)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [Point Transformer](https://mlsanity.com/paper/2011.00931/) (2020)
- [Diffusion Probabilistic Models for 3D Point Cloud Generation](https://mlsanity.com/paper/2103.01458/) (2021)
- [LION: Latent Point Diffusion Models for 3D Shape Generation](https://mlsanity.com/paper/2210.06978/) (2022)
- [3D Shape Generation and Completion through Point-Voxel Diffusion](https://mlsanity.com/paper/2104.03670/) (2021)
- [PointFlow: 3D Point Cloud Generation with Continuous Normalizing Flows](https://mlsanity.com/paper/1906.12320/) (2019)
- [Point-Voxel CNN for Efficient 3D Deep Learning](https://mlsanity.com/paper/1907.03739/) (2019)
- [PointNetLK: Robust & Efficient Point Cloud Registration using PointNet](https://mlsanity.com/paper/1903.05711/) (2019)
- [3DGen: Triplane Latent Diffusion for Textured Mesh Generation](https://mlsanity.com/paper/2303.05371/) (2023)
- [PointMamba: A Simple State Space Model for Point Cloud Analysis](https://mlsanity.com/paper/2402.10739/) (2024)
- [RenderDiffusion: Image Diffusion for 3D Reconstruction, Inpainting and Generation](https://mlsanity.com/paper/2211.09869/) (2022)
- [Diffusion Probabilistic Model Made Slim](https://mlsanity.com/paper/2211.17106/) (2022)
- [Wavelet Diffusion Models are fast and scalable Image Generators](https://mlsanity.com/paper/2211.16152/) (2022)
- [DiT-3D: Exploring Plain Diffusion Transformers for 3D Shape Generation](https://mlsanity.com/paper/2307.01831/) (2023)
- [DALL-E-Bot: Introducing Web-Scale Diffusion Models to Robotics](https://mlsanity.com/paper/2210.02438/) (2022)
- [SoftFlow: Probabilistic Framework for Normalizing Flow on Manifolds](https://mlsanity.com/paper/2006.04604/) (2020)
- [Discrete Point Flow Networks for Efficient Point Cloud Generation](https://mlsanity.com/paper/2007.10170/) (2020)
- [ZigMa: A DiT-style Zigzag Mamba Diffusion Model](https://mlsanity.com/paper/2403.13802/) (2024)
- [SetVAE: Learning Hierarchical Composition for Generative Modeling of Set-Structured Data](https://mlsanity.com/paper/2103.15619/) (2021)
- [DiM: Diffusion Mamba for Efficient High-Resolution Image Synthesis](https://mlsanity.com/paper/2405.14224/) (2024)
- [Learning Geometry-Disentangled Representation for Complementary Understanding of 3D Object Point Cloud](https://mlsanity.com/paper/2012.10921/) (2020)

## Abstract (arXiv)

Diffusion models currently demonstrate impressive performance over various generative tasks. Recent work on image diffusion highlights the strong capabilities of Mamba (state space models) due to its efficient handling of long-range dependencies and sequential data modeling. Unfortunately, joint consideration of state space models with 3D point cloud generation remains limited. To harness the powerful capabilities of the Mamba model for 3D point cloud generation, we propose a novel diffusion framework containing dual latent Mamba block (DM-Block) and a time-variant frequency encoder (TF-Encoder). The DM-Block apply a space-filling curve to reorder points into sequences suitable for Mamba state-space modeling, while operating in a latent space to mitigate the computational overhead that arises from direct 3D data processing. Meanwhile, the TF-Encoder takes advantage of the ability of the diffusion model to refine fine details in later recovery stages by prioritizing key points within the U-Net architecture. This frequency-based mechanism ensures enhanced detail quality in the final stages of generation. Experimental results on the ShapeNet-v2 dataset demonstrate that our method achieves state-of-the-art performance (ShapeNet-v2: 0.14% on 1-NNA-Abs50 EMD and 57.90% on COV EMD) on certain metrics for specific categories while reducing computational parameters and inference time by up to 10× and 9×, respectively. Source code is available in Supplementary Materials and will be released upon accpetance.