# Point Cloud Resampling with Learnable Heat Diffusion

arXiv: https://arxiv.org/abs/2411.14120 · HTML: https://mlsanity.com/paper/2411.14120/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 32 references that are in the map.
- First posted on arXiv 21 Nov 2024.

## Builds on (most cited first, 20 of 20)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Point-E: A System for Generating 3D Point Clouds from Complex Prompts](https://mlsanity.com/paper/2212.08751/) (2022)
- [Cold Diffusion: Inverting Arbitrary Image Transforms Without Noise](https://mlsanity.com/paper/2208.09392/) (2022)
- [PU-Net: Point Cloud Upsampling Network](https://mlsanity.com/paper/1801.06761/) (2018)
- [Generative Modelling With Inverse Heat Dissipation](https://mlsanity.com/paper/2206.13397/) (2022)
- [PU-GAN: a Point Cloud Upsampling Adversarial Network](https://mlsanity.com/paper/1907.10844/) (2019)
- [Deep Learning for Image and Point Cloud Fusion in Autonomous Driving: A Review](https://mlsanity.com/paper/2004.05224/) (2020)
- [PU-GCN: Point Cloud Upsampling using Graph Convolutional Networks](https://mlsanity.com/paper/1912.03264/) (2019)
- [EC-Net: an Edge-aware Point set Consolidation Network](https://mlsanity.com/paper/1807.06010/) (2018)
- [Score-Based Point Cloud Denoising](https://mlsanity.com/paper/2107.10981/) (2021)
- [PUGeo-Net: A Geometry-centric Network for 3D Point Cloud Upsampling](https://mlsanity.com/paper/2002.10277/) (2020)
- [Differentiable Manifold Reconstruction for Point Cloud Denoising](https://mlsanity.com/paper/2007.13551/) (2020)
- [Neural Points: Point Cloud Representation with Neural Fields for Arbitrary Upsampling](https://mlsanity.com/paper/2112.04148/) (2021)
- [Grad-PU: Arbitrary-Scale Point Cloud Upsampling via Gradient Descent with Learned Distance Functions](https://mlsanity.com/paper/2304.11846/) (2023)
- [Meta-PU: An Arbitrary-Scale Upsampling Network for Point Cloud](https://mlsanity.com/paper/2102.04317/) (2021)
- [Deep Point Set Resampling via Gradient Fields](https://mlsanity.com/paper/2111.02045/) (2021)
- [Conditional Variational Diffusion Models](https://mlsanity.com/paper/2312.02246/) (2023)

## Built on by (most cited first, 2 of 2)

- [Graph-Aware Diffusion for Signal Generation](https://mlsanity.com/paper/2510.05036/) (2025)
- [Deep Learning For Point Cloud Denoising: A Survey](https://mlsanity.com/paper/2508.11932/) (2025)

## Abstract (arXiv)

Generative diffusion models have shown empirical successes in point cloud resampling, generating a denser and more uniform distribution of points from sparse or noisy 3D point clouds by progressively refining noise into structure. However, existing diffusion models employ manually predefined schemes, which often fail to recover the underlying point cloud structure due to the rigid and disruptive nature of the geometric degradation. To address this issue, we propose a novel learnable heat diffusion framework for point cloud resampling, which directly parameterizes the marginal distribution for the forward process by learning the adaptive heat diffusion schedules and local filtering scales of the time-varying heat kernel, and consequently, generates an adaptive conditional prior for the reverse process. Unlike previous diffusion models with a fixed prior, the adaptive conditional prior selectively preserves geometric features of the point cloud by minimizing a refined variational lower bound, guiding the points to evolve towards the underlying surface during the reverse process. Extensive experimental results demonstrate that the proposed point cloud resampling achieves state-of-the-art performance in representative reconstruction tasks including point cloud denoising and upsampling.