# PUFM++: Point Cloud Upsampling via Enhanced Flow Matching

arXiv: https://arxiv.org/abs/2512.20988 · HTML: https://mlsanity.com/paper/2512.20988/

## 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 44 of its 55 references that are in the map.
- First posted on arXiv 24 Dec 2025.

## 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 44)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (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)
- [ScanNet: Richly-annotated 3D Reconstructions of Indoor Scenes](https://mlsanity.com/paper/1702.04405/) (2017)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Point Transformer](https://mlsanity.com/paper/2011.00931/) (2020)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [KPConv: Flexible and Deformable Convolution for Point Clouds](https://mlsanity.com/paper/1904.08889/) (2019)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Diffusion Probabilistic Models for 3D Point Cloud Generation](https://mlsanity.com/paper/2103.01458/) (2021)
- [Point Transformer V3: Simpler, Faster, Stronger](https://mlsanity.com/paper/2312.10035/) (2023)
- [3D Shape Generation and Completion through Point-Voxel Diffusion](https://mlsanity.com/paper/2104.03670/) (2021)
- [Point Transformer V2: Grouped Vector Attention and Partition-based Pooling](https://mlsanity.com/paper/2210.05666/) (2022)
- [ABC: A Big CAD Model Dataset For Geometric Deep Learning](https://mlsanity.com/paper/1812.06216/) (2018)
- [PU-Net: Point Cloud Upsampling Network](https://mlsanity.com/paper/1801.06761/) (2018)
- [Scalable Adaptive Computation for Iterative Generation](https://mlsanity.com/paper/2212.11972/) (2022)
- [PU-GAN: a Point Cloud Upsampling Adversarial Network](https://mlsanity.com/paper/1907.10844/) (2019)
- [PointMixup: Augmentation for Point Clouds](https://mlsanity.com/paper/2008.06374/) (2020)
- [Patch-based Progressive 3D Point Set Upsampling](https://mlsanity.com/paper/1811.11286/) (2018)
- [PU-GCN: Point Cloud Upsampling using Graph Convolutional Networks](https://mlsanity.com/paper/1912.03264/) (2019)
- [Visual Point Cloud Forecasting enables Scalable Autonomous Driving](https://mlsanity.com/paper/2312.17655/) (2023)
- [EC-Net: an Edge-aware Point set Consolidation Network](https://mlsanity.com/paper/1807.06010/) (2018)
- [Point Cloud Upsampling via Disentangled Refinement](https://mlsanity.com/paper/2106.04779/) (2021)
- [PUGeo-Net: A Geometry-centric Network for 3D Point Cloud Upsampling](https://mlsanity.com/paper/2002.10277/) (2020)
- [Fast Point Cloud Generation with Straight Flows](https://mlsanity.com/paper/2212.01747/) (2022)
- [Neural Points: Point Cloud Representation with Neural Fields for Arbitrary Upsampling](https://mlsanity.com/paper/2112.04148/) (2021)

## Abstract (arXiv)

Recent advances in generative modeling have demonstrated strong promise for high-quality point cloud upsampling. In this work, we present PUFM++, an enhanced flow-matching framework for reconstructing dense and accurate point clouds from sparse, noisy, and partial observations. PUFM++ improves flow matching along three key axes: (i) geometric fidelity, (ii) robustness to imperfect input, and (iii) consistency with downstream surface-based tasks. We introduce a two-stage flow-matching strategy that first learns a direct, straight-path flow from sparse inputs to dense targets, and then refines it using noise-perturbed samples to approximate the terminal marginal distribution better. To accelerate and stabilize inference, we propose a data-driven adaptive time scheduler that improves sampling efficiency based on interpolation behavior. We further impose on-manifold constraints during sampling to ensure that generated points remain aligned with the underlying surface. Finally, we incorporate a recurrent interface network~(RIN) to strengthen hierarchical feature interactions and boost reconstruction quality. Extensive experiments on synthetic benchmarks and real-world scans show that PUFM++ sets a new state of the art in point cloud upsampling, delivering superior visual fidelity and quantitative accuracy across a wide range of tasks. Code and pretrained models are publicly available at https://github.com/Holmes-Alan/Enhanced_PUFM.