# FrePolad: Frequency-Rectified Point Latent Diffusion for Point Cloud Generation

arXiv: https://arxiv.org/abs/2311.12090 · HTML: https://mlsanity.com/paper/2311.12090/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Placed in 3D, point cloud and scene generation, one of 14 directions in Diffusion models.
- Builds on 82 of its 103 references that are in the map.
- First posted on arXiv 20 Nov 2023.

## Placed in

- Diffusion models / [3D, point cloud and scene generation](https://mlsanity.com/diffusion/3d-point-cloud-and-scene-generation/)

## Builds on (most cited first, 30 of 82)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Taming Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2012.09841/) (2020)
- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Perceptual Losses for Real-Time Style Transfer and Super-Resolution](https://mlsanity.com/paper/1603.08155/) (2016)
- [InstructPix2Pix: Learning to Follow Image Editing Instructions](https://mlsanity.com/paper/2211.09800/) (2022)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Align your Latents: High-Resolution Video Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2304.08818/) (2023)
- [Generating Diverse High-Fidelity Images with VQ-VAE-2](https://mlsanity.com/paper/1906.00446/) (2019)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Cascaded Diffusion Models for High Fidelity Image Generation](https://mlsanity.com/paper/2106.15282/) (2021)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [Diffusion Probabilistic Models for 3D Point Cloud Generation](https://mlsanity.com/paper/2103.01458/) (2021)
- [Autoregressive Image Generation using Residual Quantization](https://mlsanity.com/paper/2203.01941/) (2022)
- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)
- [WaveGrad: Estimating Gradients for Waveform Generation](https://mlsanity.com/paper/2009.00713/) (2020)

## Built on by (most cited first, 9 of 9)

- [Efficient and Scalable Point Cloud Generation with Sparse Point-Voxel Diffusion Models](https://mlsanity.com/paper/2408.06145/) (2024)
- [Terra: Explorable Native 3D World Model with Point Latents](https://mlsanity.com/paper/2510.14977/) (2025)
- [MFM-point: Multi-scale Flow Matching for Point Cloud Generation](https://mlsanity.com/paper/2511.20041/) (2025)
- [Trajectory Consistency for One-Step Generation on Euler Mean Flows](https://mlsanity.com/paper/2602.02571/) (2026)
- [BrickAnything: Geometry-Conditioned Buildable Brick Generation with Structure-Aware Tokenization](https://mlsanity.com/paper/2605.26182/) (2026)
- [Quartet of Diffusions: Structure-Aware Point Cloud Generation through Part and Symmetry Guidance](https://mlsanity.com/paper/2601.20425/) (2026)
- [TFDM: Time-Variant Frequency-Based Point Cloud Diffusion with Mamba](https://mlsanity.com/paper/2503.13004/) (2025)
- [FreNBRDF: A Frequency-Rectified Neural Material Representation](https://mlsanity.com/paper/2507.00476/) (2025)
- [PrintAnything: Learning an Intermediate Representation for 3D printing G-code Generation](https://mlsanity.com/paper/2607.27729/) (2026)

## Abstract (arXiv)

We propose FrePolad: frequency-rectified point latent diffusion, a point cloud generation pipeline integrating a variational autoencoder (VAE) with a denoising diffusion probabilistic model (DDPM) for the latent distribution. FrePolad simultaneously achieves high quality, diversity, and flexibility in point cloud cardinality for generation tasks while maintaining high computational efficiency. The improvement in generation quality and diversity is achieved through (1) a novel frequency rectification via spherical harmonics designed to retain high-frequency content while learning the point cloud distribution; and (2) a latent DDPM to learn the regularized yet complex latent distribution. In addition, FrePolad supports variable point cloud cardinality by formulating the sampling of points as conditional distributions over a latent shape distribution. Finally, the low-dimensional latent space encoded by the VAE contributes to FrePolad's fast and scalable sampling. Our quantitative and qualitative results demonstrate FrePolad's state-of-the-art performance in terms of quality, diversity, and computational efficiency. Project page: https://chenliang-zhou.github.io/FrePolad/.