# GFPack++: Improving 2D Irregular Packing by Learning Gradient Field with Attention

arXiv: https://arxiv.org/abs/2406.07579 · HTML: https://mlsanity.com/paper/2406.07579/

## Key facts

- Cited by 2 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 21 of its 44 references that are in the map.
- First posted on arXiv 9 Jun 2024.

## 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, 21 of 21)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [PointNeXt: Revisiting PointNet++ with Improved Training and Scaling Strategies](https://mlsanity.com/paper/2206.04670/) (2022)
- [Self-Attention Graph Pooling](https://mlsanity.com/paper/1904.08082/) (2019)
- [LEGO-Net: Learning Regular Rearrangements of Objects in Rooms](https://mlsanity.com/paper/2301.09629/) (2023)
- [StructDiffusion: Language-Guided Creation of Physically-Valid Structures using Unseen Objects](https://mlsanity.com/paper/2211.04604/) (2022)
- [Online 3D Bin Packing with Constrained Deep Reinforcement Learning](https://mlsanity.com/paper/2006.14978/) (2020)
- [Breaking Bad: A Dataset for Geometric Fracture and Reassembly](https://mlsanity.com/paper/2210.11463/) (2022)
- [PuzzleFusion: Unleashing the Power of Diffusion Models for Spatial Puzzle Solving](https://mlsanity.com/paper/2211.13785/) (2022)
- [Attend2Pack: Bin Packing through Deep Reinforcement Learning with Attention](https://mlsanity.com/paper/2107.04333/) (2021)
- [TarGF: Learning Target Gradient Field to Rearrange Objects without Explicit Goal Specification](https://mlsanity.com/paper/2209.00853/) (2022)
- [Learning Physically Realizable Skills for Online Packing of General 3D Shapes](https://mlsanity.com/paper/2212.02094/) (2022)
- [Planning Irregular Object Packing via Hierarchical Reinforcement Learning](https://mlsanity.com/paper/2211.09382/) (2022)
- [SDF-Pack: Towards Compact Bin Packing with Signed-Distance-Field Minimization](https://mlsanity.com/paper/2307.07356/) (2023)
- [Learning based 2D Irregular Shape Packing](https://mlsanity.com/paper/2309.10329/) (2023)
- [Learning Gradient Fields for Scalable and Generalizable Irregular Packing](https://mlsanity.com/paper/2310.19814/) (2023)
- [Neural Packing: from Visual Sensing to Reinforcement Learning](https://mlsanity.com/paper/2311.09233/) (2023)

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

- [Geometry-Aware Reinforcement Learning for 2D Irregular Nesting](https://mlsanity.com/paper/2606.10611/) (2026)
- [GeoNest: Learning to Select Failure-Aware Neighborhoods for the Irregular Knapsack Problem in a Circular Container](https://mlsanity.com/paper/2609.38863/) (2026)

## Abstract (arXiv)

2D irregular packing is a classic combinatorial optimization problem with various applications, such as material utilization and texture atlas generation. Due to its NP-hard nature, conventional numerical approaches typically encounter slow convergence and high computational costs. Previous research (GFPack) introduced a generative method for gradient-based packing, providing early evidence of its feasibility but faced limitations such as insufficient rotation support, poor boundary adaptability, and high overlap ratios. In this paper, we propose GFPack++, a deeply investigated framework that adopts attention-based geometry and relation encoding, enabling more comprehensive modeling of complex packing relationships. We further design a constrained gradient and a weighting function to enhance both the feasibility of the produced solutions and the learning effectiveness. Experimental results on multiple datasets demonstrate that GFPack++ achieves higher space utilization, supports continuous rotation, generalizes well to arbitrary boundaries, and infers orders of magnitude faster than previous approaches. Codes for this paper are at https://github.com/TimHsue/GFPack-pp.