# Learning Gradient Fields for Scalable and Generalizable Irregular Packing

arXiv: https://arxiv.org/abs/2310.19814 · HTML: https://mlsanity.com/paper/2310.19814/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 53 references that are in the map.
- First posted on arXiv 18 Oct 2023.

## Builds on (most cited first, 15 of 15)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Feature Pyramid Networks for Object Detection](https://mlsanity.com/paper/1612.03144/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [Score-Based Point Cloud Denoising](https://mlsanity.com/paper/2107.10981/) (2021)
- [GFPose: Learning 3D Human Pose Prior with Gradient Fields](https://mlsanity.com/paper/2212.08641/) (2022)
- [Stable bin packing of non-convex 3D objects with a robot manipulator](https://mlsanity.com/paper/1812.04093/) (2018)
- [Learning Practically Feasible Policies for Online 3D Bin Packing](https://mlsanity.com/paper/2108.13680/) (2021)
- [TarGF: Learning Target Gradient Field to Rearrange Objects without Explicit Goal Specification](https://mlsanity.com/paper/2209.00853/) (2022)
- [TAP-Net: Transport-and-Pack using Reinforcement Learning](https://mlsanity.com/paper/2009.01469/) (2020)
- [A Generalized Reinforcement Learning Algorithm for Online 3D Bin-Packing](https://mlsanity.com/paper/2007.00463/) (2020)
- [Shapes In A Box -- Disassembling 3D objects for efficient packing and fabrication](https://mlsanity.com/paper/2104.05281/) (2021)
- [Towards Zero-Waste Furniture Design](https://mlsanity.com/paper/1604.00047/) (2016)

## Built on by (most cited first, 3 of 3)

- [Omni6DPose: A Benchmark and Model for Universal 6D Object Pose Estimation and Tracking](https://mlsanity.com/paper/2406.04316/) (2024)
- [GFPack++: Improving 2D Irregular Packing by Learning Gradient Field with Attention](https://mlsanity.com/paper/2406.07579/) (2024)
- [By-Example Synthesis of Vector Textures](https://mlsanity.com/paper/2501.13812/) (2025)

## Abstract (arXiv)

The packing problem, also known as cutting or nesting, has diverse applications in logistics, manufacturing, layout design, and atlas generation. It involves arranging irregularly shaped pieces to minimize waste while avoiding overlap. Recent advances in machine learning, particularly reinforcement learning, have shown promise in addressing the packing problem. In this work, we delve deeper into a novel machine learning-based approach that formulates the packing problem as conditional generative modeling. To tackle the challenges of irregular packing, including object validity constraints and collision avoidance, our method employs the score-based diffusion model to learn a series of gradient fields. These gradient fields encode the correlations between constraint satisfaction and the spatial relationships of polygons, learned from teacher examples. During the testing phase, packing solutions are generated using a coarse-to-fine refinement mechanism guided by the learned gradient fields. To enhance packing feasibility and optimality, we introduce two key architectural designs: multi-scale feature extraction and coarse-to-fine relation extraction. We conduct experiments on two typical industrial packing domains, considering translations only. Empirically, our approach demonstrates spatial utilization rates comparable to, or even surpassing, those achieved by the teacher algorithm responsible for training data generation. Additionally, it exhibits some level of generalization to shape variations. We are hopeful that this method could pave the way for new possibilities in solving the packing problem.