# Point-MF: Stabilizing One-Step Mean Flows for Single-Image Point Cloud Reconstruction

arXiv: https://arxiv.org/abs/2604.24586 · HTML: https://mlsanity.com/paper/2604.24586/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 69 of its 74 references that are in the map.
- First posted on arXiv 27 Apr 2026.

## Builds on (most cited first, 30 of 69)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [DINOv3](https://mlsanity.com/paper/2508.10104/) (2025)
- [LRM: Large Reconstruction Model for Single Image to 3D](https://mlsanity.com/paper/2311.04400/) (2023)
- [Structured 3D Latents for Scalable and Versatile 3D Generation](https://mlsanity.com/paper/2412.01506/) (2024)
- [Diffusion Probabilistic Models for 3D Point Cloud Generation](https://mlsanity.com/paper/2103.01458/) (2021)
- [Point-E: A System for Generating 3D Point Clouds from Complex Prompts](https://mlsanity.com/paper/2212.08751/) (2022)
- [Pixel2Mesh: Generating 3D Mesh Models from Single RGB Images](https://mlsanity.com/paper/1804.01654/) (2018)
- [3D-R2N2: A Unified Approach for Single and Multi-view 3D Object Reconstruction](https://mlsanity.com/paper/1604.00449/) (2016)
- [Mean Flows for One-step Generative Modeling](https://mlsanity.com/paper/2505.13447/) (2025)
- [LION: Latent Point Diffusion Models for 3D Shape Generation](https://mlsanity.com/paper/2210.06978/) (2022)
- [AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generation](https://mlsanity.com/paper/1802.05384/) (2018)
- [Point-NeRF: Point-based Neural Radiance Fields](https://mlsanity.com/paper/2201.08845/) (2022)
- [Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusion](https://mlsanity.com/paper/2310.02279/) (2023)
- [Improved Techniques for Training Consistency Models](https://mlsanity.com/paper/2310.14189/) (2023)
- [One Step Diffusion via Shortcut Models](https://mlsanity.com/paper/2410.12557/) (2024)
- [Shap-E: Generating Conditional 3D Implicit Functions](https://mlsanity.com/paper/2305.02463/) (2023)

## Abstract (arXiv)

Single-image point cloud reconstruction requires recovering complete object-level geometry, including occluded regions, from a single RGB image. Diffusion- and flow-based reconstructors can model this ambiguity, but their iterative sampling requires many network function evaluations, while naive one-step point-space updates often produce outliers and density imbalance. We propose Point-MF, a one-step conditional Mean-Flow framework for geometry-only point cloud reconstruction. Point-MF predicts an interval-averaged velocity field directly in point-cloud space and reconstructs the output with a single network function evaluation, without training a point-cloud autoencoder. To stabilize large Mean-Flow jumps, we introduce Denoised Space Anchor (DSA), a set-distance auxiliary loss that anchors the denoised point set implied by the predicted velocity to the ground-truth geometry. On all 13 ShapeNet-R2N2 categories and Pix3D, Point-MF achieves strong reconstruction quality under the aligned point-set protocol, improving average CD and EMD over the evaluated point-cloud reconstruction baselines. It runs in 40.72 ms per sample on an RTX A4000, within the same latency order as the feedforward RGB2point baseline and substantially faster than iterative diffusion baselines such as PC2 and BDM. These results show that denoised-space geometric anchoring enables stable one-step Mean Flow directly in point-cloud space.