# Learn2Fold: Structured Origami Generation with World Model Planning arXiv: https://arxiv.org/abs/2603.29585 ยท HTML: https://mlsanity.com/paper/2603.29585/ ## Key facts - Cited by 5 papers in the map (data through 14 Oct 2026). - Placed in Embodied and robot world models, one of 11 directions in World models. - Builds on 30 of its 46 references that are in the map. - First posted on arXiv 2 Feb 2026. ## Placed in - World models / [Embodied and robot world models](https://mlsanity.com/wm/embodied-and-robot-world-models/) ## Builds on (most cited first, 30 of 30) - [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021) - [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022) - [RT-2: Vision-Language-Action Models Transfer Web Knowledge to Robotic Control](https://mlsanity.com/paper/2307.15818/) (2023) - [Dream to Control: Learning Behaviors by Latent Imagination](https://mlsanity.com/paper/1912.01603/) (2019) - [Learning Latent Dynamics for Planning from Pixels](https://mlsanity.com/paper/1811.04551/) (2018) - [ProlificDreamer: High-Fidelity and Diverse Text-to-3D Generation with Variational Score Distillation](https://mlsanity.com/paper/2305.16213/) (2023) - [OpenAI GPT-5 System Card](https://mlsanity.com/paper/2601.03267/) (2025) - [Vision-Language Models for Vision Tasks: A Survey](https://mlsanity.com/paper/2304.00685/) (2023) - [Genie: Generative Interactive Environments](https://mlsanity.com/paper/2402.15391/) (2024) - [Scene Graph Generation by Iterative Message Passing](https://mlsanity.com/paper/1701.02426/) (2017) - [GET3D: A Generative Model of High Quality 3D Textured Shapes Learned from Images](https://mlsanity.com/paper/2209.11163/) (2022) - [SV3D: Novel Multi-view Synthesis and 3D Generation from a Single Image using Latent Video Diffusion](https://mlsanity.com/paper/2403.12008/) (2024) - [Image Generation from Scene Graphs](https://mlsanity.com/paper/1804.01622/) (2018) - [TripoSG: High-Fidelity 3D Shape Synthesis using Large-Scale Rectified Flow Models](https://mlsanity.com/paper/2502.06608/) (2025) - [Guided Open Vocabulary Image Captioning with Constrained Beam Search](https://mlsanity.com/paper/1612.00576/) (2016) - [Offline Reinforcement Learning from Images with Latent Space Models](https://mlsanity.com/paper/2012.11547/) (2020) - [LN3DIFF++: Scalable Latent Neural Fields Diffusion for Speedy 3D Generation](https://mlsanity.com/paper/2403.12019/) (2024) - [Step1X-3D: Towards High-Fidelity and Controllable Generation of Textured 3D Assets](https://mlsanity.com/paper/2505.07747/) (2025) - [SceneDreamer: Unbounded 3D Scene Generation from 2D Image Collections](https://mlsanity.com/paper/2302.01330/) (2023) - [3D-LDM: Neural Implicit 3D Shape Generation with Latent Diffusion Models](https://mlsanity.com/paper/2212.00842/) (2022) - [Direct2.5: Diverse Text-to-3D Generation via Multi-view 2.5D Diffusion](https://mlsanity.com/paper/2311.15980/) (2023) - [AVID: Adapting Video Diffusion Models to World Models](https://mlsanity.com/paper/2410.12822/) (2024) - [Generating Physically Stable and Buildable Brick Structures from Text](https://mlsanity.com/paper/2505.05469/) (2025) - [Folding Deformable Objects using Predictive Simulation and Trajectory Optimization](https://mlsanity.com/paper/1512.06922/) (2015) - [Diffusion Dynamics Models with Generative State Estimation for Cloth Manipulation](https://mlsanity.com/paper/2503.11999/) (2025) - [Learning Fabric Manipulation in the Real World with Human Videos](https://mlsanity.com/paper/2211.02832/) (2022) - [VISTAv2: World Imagination for Indoor Vision-and-Language Navigation](https://mlsanity.com/paper/2512.00041/) (2025) - [FabricFolding: Learning Efficient Fabric Folding without Expert Demonstrations](https://mlsanity.com/paper/2303.06587/) (2023) - [Learning a General Model: Folding Clothing with Topological Dynamics](https://mlsanity.com/paper/2504.20720/) (2025) - [From Pixels to Predicates Structuring urban perception with scene graphs](https://mlsanity.com/paper/2512.19221/) (2025) ## Built on by (most cited first, 5 of 5) - [Can AI Understand the Language of Origami?](https://mlsanity.com/paper/2603.13856/) (2026) - [PhyDrawGen: Physically Grounded Diagram Generation from Natural Language](https://mlsanity.com/paper/2605.30512/) (2026) - [FoldingAgent: Inferring Parametric Origami Procedures from Demonstration Videos](https://mlsanity.com/paper/2609.00377/) (2026) - [Beyond Static Graph World Models: Learning Stochastic Latent Dynamics over Evolving Topologies](https://mlsanity.com/paper/2609.28670/) (2026) - [Text2Sim: Agentic Physics-Based Simulation Generation with Distilled Expertise](https://mlsanity.com/paper/2609.36593/) (2026) ## Abstract (arXiv) The ability to transform a flat sheet into a complex three-dimensional structure is a fundamental test of physical intelligence. Unlike cloth manipulation, origami is governed by strict geometric axioms and hard kinematic constraints, where a single invalid crease or collision can invalidate the entire folding sequence. As a result, origami demands long-horizon constructive reasoning that jointly satisfies precise physical laws and high-level semantic intent. Existing approaches fall into two disjoint paradigms: optimization-based methods enforce physical validity but require dense, precisely specified inputs, making them unsuitable for sparse natural language descriptions, while generative foundation models excel at semantic and perceptual synthesis yet fail to produce long-horizon, physics-consistent folding processes. Consequently, generating valid origami folding sequences directly from text remains an open challenge. To address this gap, we introduce Learn2Fold, a neuro-symbolic framework that formulates origami folding as conditional program induction over a crease-pattern graph. Our key insight is to decouple semantic proposal from physical verification. A large language model generates candidate folding programs from abstract text prompts, while a learned graph-structured world model serves as a differentiable surrogate simulator that predicts physical feasibility and failure modes before execution. Integrated within a lookahead planning loop, Learn2Fold enables robust generation of physically valid folding sequences for complex and out-of-distribution patterns, demonstrating that effective spatial intelligence arises from the synergy between symbolic reasoning and grounded physical simulation.